LMFDB - Embedded newform 546.2.bx.a.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(97,546)]

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, 6, 5]))

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

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

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bx (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			97.1
Character	$\chi$	$=$	546.97
Dual form			546.2.bx.a.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-3.04339 - 3.04339i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-1.02848 - 2.43767i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-3.04339 - 3.04339i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-1.02848 - 2.43767i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.15200 + 3.72738i) q^{10} +(-2.01177 + 0.539051i) q^{11} +1.00000 q^{12} +(0.973091 + 3.47176i) q^{13} +(-2.08842 + 1.62435i) q^{14} +(1.11396 + 4.15735i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.994265 - 1.72212i) q^{17} +(0.707107 - 0.707107i) q^{18} +(1.11396 - 4.15735i) q^{19} +(4.15735 + 1.11396i) q^{20} +(-0.328149 + 2.62532i) q^{21} +(1.04137 + 1.80370i) q^{22} +(0.911529 + 0.526272i) q^{23} +(-0.258819 - 0.965926i) q^{24} +13.5244i q^{25} +(3.10160 - 1.83849i) q^{26} -1.00000i q^{27} +(2.10952 + 1.59685i) q^{28} +(2.33721 - 4.04816i) q^{29} +(3.72738 - 2.15200i) q^{30} +(5.73502 + 5.73502i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(2.01177 + 0.539051i) q^{33} +(-1.40610 + 1.40610i) q^{34} +(-4.28873 + 10.5488i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(2.17565 - 0.582965i) q^{37} -4.30401 q^{38} +(0.893156 - 3.49318i) q^{39} -4.30400i q^{40} +(-9.88660 + 2.64911i) q^{41} +(2.62080 - 0.362516i) q^{42} +(-7.68448 + 4.43663i) q^{43} +(1.47272 - 1.47272i) q^{44} +(1.11396 - 4.15735i) q^{45} +(0.272418 - 1.01668i) q^{46} +(-0.833826 + 0.833826i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-4.88447 + 5.01417i) q^{49} +(13.0636 - 3.50038i) q^{50} +1.98853i q^{51} +(-2.57860 - 2.52008i) q^{52} -6.61122 q^{53} +(-0.965926 + 0.258819i) q^{54} +(7.76314 + 4.48205i) q^{55} +(0.996451 - 2.45094i) q^{56} +(-3.04339 + 3.04339i) q^{57} +(-4.51513 - 1.20983i) q^{58} +(7.58185 + 2.03155i) q^{59} +(-3.04339 - 3.04339i) q^{60} +(-9.14314 + 5.27879i) q^{61} +(4.05527 - 7.02394i) q^{62} +(1.59685 - 2.10952i) q^{63} +1.00000i q^{64} +(7.60441 - 13.5274i) q^{65} -2.08273i q^{66} +(-3.51620 - 13.1227i) q^{67} +(1.72212 + 0.994265i) q^{68} +(-0.526272 - 0.911529i) q^{69} +(11.2994 + 1.41235i) q^{70} +(3.38987 + 0.908313i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(4.18769 - 4.18769i) q^{73} +(-1.12620 - 1.95064i) q^{74} +(6.76222 - 11.7125i) q^{75} +(1.11396 + 4.15735i) q^{76} +(3.38308 + 4.34962i) q^{77} +(-3.60531 + 0.0413775i) q^{78} -2.85526 q^{79} +(-4.15735 + 1.11396i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.11768 + 8.86408i) q^{82} +(-9.59920 - 9.59920i) q^{83} +(-1.02848 - 2.43767i) q^{84} +(-2.21514 + 8.26701i) q^{85} +(6.27435 + 6.27435i) q^{86} +(-4.04816 + 2.33721i) q^{87} +(-1.80370 - 1.04137i) q^{88} +(-1.02170 - 3.81303i) q^{89} -4.30400 q^{90} +(7.46220 - 5.94269i) q^{91} -1.05254 q^{92} +(-2.09916 - 7.83418i) q^{93} +(1.02122 + 0.589604i) q^{94} +(-16.0427 + 9.26224i) q^{95} +(0.707107 + 0.707107i) q^{96} +(1.29605 - 4.83691i) q^{97} +(6.10751 + 3.42028i) q^{98} +(-1.47272 - 1.47272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 + 20 * q^9	$ 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39} - 4 q^{41} + 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} + 32 q^{53} - 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} + 84 q^{59} - 48 q^{61} - 4 q^{62} - 4 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 36 q^{70} - 40 q^{71} - 48 q^{73} + 8 q^{74} + 36 q^{75} + 16 q^{76} - 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} + 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{89} - 48 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} + 8 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{12}\right)$

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
$3$	−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
$5$	−3.04339	−	3.04339i	−1.36105	−	1.36105i	−0.872588	−	0.488458i	$-0.837560\pi$
$5$	−3.04339	−	3.04339i	−1.36105	−	1.36105i	−0.488458	−	0.872588i	$-0.662440\pi$
$6$	−0.258819	+	0.965926i	−0.105662	+	0.394338i
$7$	−1.02848	−	2.43767i	−0.388727	−	0.921353i
$7$	−1.02848	−	2.43767i	−0.388727	−	0.921353i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.15200	+	3.72738i	−0.680523	+	1.17870i
$11$	−2.01177	+	0.539051i	−0.606571	+	0.162530i	−0.549015	−	0.835812i	$-0.684997\pi$
$11$	−2.01177	+	0.539051i	−0.606571	+	0.162530i	−0.0575552	+	0.998342i	$0.518331\pi$
$12$	1.00000			0.288675
$13$	0.973091	+	3.47176i	0.269887	+	0.962892i
$13$	0.973091	+	3.47176i	0.269887	+	0.962892i
$14$	−2.08842	+	1.62435i	−0.558154	+	0.434125i
$15$	1.11396	+	4.15735i	0.287623	+	1.07342i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.994265	−	1.72212i	−0.241145	−	0.417675i	0.719896	−	0.694082i	$-0.244189\pi$
$17$	−0.994265	−	1.72212i	−0.241145	−	0.417675i	−0.961041	+	0.276407i	$0.910856\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	1.11396	−	4.15735i	0.255560	−	0.953762i	−0.712218	−	0.701958i	$-0.752309\pi$
$19$	1.11396	−	4.15735i	0.255560	−	0.953762i	0.967778	−	0.251804i	$-0.0810240\pi$
$20$	4.15735	+	1.11396i	0.929611	+	0.249089i
$21$	−0.328149	+	2.62532i	−0.0716080	+	0.572892i
$22$	1.04137	+	1.80370i	0.222020	+	0.384550i
$23$	0.911529	+	0.526272i	0.190067	+	0.109735i	0.592014	−	0.805928i	$-0.298333\pi$
$23$	0.911529	+	0.526272i	0.190067	+	0.109735i	−0.401947	+	0.915663i	$0.631666\pi$
$24$	−0.258819	−	0.965926i	−0.0528312	−	0.197169i
$25$			13.5244i			2.70489i
$26$	3.10160	−	1.83849i	0.608275	−	0.360558i
$27$		−	1.00000i		−	0.192450i
$28$	2.10952	+	1.59685i	0.398662	+	0.301776i
$29$	2.33721	−	4.04816i	0.434008	−	0.751724i	−0.563206	−	0.826317i	$-0.690432\pi$
$29$	2.33721	−	4.04816i	0.434008	−	0.751724i	0.997214	+	0.0745925i	$0.0237656\pi$
$30$	3.72738	−	2.15200i	0.680523	−	0.392900i
$31$	5.73502	+	5.73502i	1.03004	+	1.03004i	0.999535	+	0.0305053i	$0.00971165\pi$
$31$	5.73502	+	5.73502i	1.03004	+	1.03004i	0.0305053	+	0.999535i	$0.490288\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	2.01177	+	0.539051i	0.350204	+	0.0938368i
$34$	−1.40610	+	1.40610i	−0.241145	+	0.241145i
$35$	−4.28873	+	10.5488i	−0.724927	+	1.78308i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	2.17565	−	0.582965i	0.357675	−	0.0958388i	−0.0755066	−	0.997145i	$-0.524057\pi$
$37$	2.17565	−	0.582965i	0.357675	−	0.0958388i	0.433182	+	0.901306i	$0.357391\pi$
$38$	−4.30401			−0.698203
$39$	0.893156	−	3.49318i	0.143019	−	0.559356i
$40$		−	4.30400i		−	0.680523i
$41$	−9.88660	+	2.64911i	−1.54403	+	0.413721i	−0.927564	−	0.373664i	$-0.878101\pi$
$41$	−9.88660	+	2.64911i	−1.54403	+	0.413721i	−0.616463	+	0.787384i	$0.711435\pi$
$42$	2.62080	−	0.362516i	0.404398	−	0.0559374i
$43$	−7.68448	+	4.43663i	−1.17187	+	0.676580i	−0.954120	−	0.299424i	$-0.903206\pi$
$43$	−7.68448	+	4.43663i	−1.17187	+	0.676580i	−0.217751	+	0.976004i	$0.569872\pi$
$44$	1.47272	−	1.47272i	0.222020	−	0.222020i
$45$	1.11396	−	4.15735i	0.166059	−	0.619741i
$46$	0.272418	−	1.01668i	0.0401659	−	0.149901i
$47$	−0.833826	+	0.833826i	−0.121626	+	0.121626i	−0.765300	−	0.643674i	$-0.777409\pi$
$47$	−0.833826	+	0.833826i	−0.121626	+	0.121626i	0.643674	+	0.765300i	$0.277409\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−4.88447	+	5.01417i	−0.697782	+	0.716310i
$50$	13.0636	−	3.50038i	1.84747	−	0.495029i
$51$			1.98853i			0.278450i
$52$	−2.57860	−	2.52008i	−0.357588	−	0.349473i
$53$	−6.61122			−0.908121			−0.454060	−	0.890971i	$-0.650025\pi$
$53$	−6.61122			−0.908121			−0.454060	+	0.890971i	$0.650025\pi$
$54$	−0.965926	+	0.258819i	−0.131446	+	0.0352208i
$55$	7.76314	+	4.48205i	1.04678	+	0.604359i
$56$	0.996451	−	2.45094i	0.133156	−	0.327520i
$57$	−3.04339	+	3.04339i	−0.403107	+	0.403107i
$58$	−4.51513	−	1.20983i	−0.592866	−	0.158858i
$59$	7.58185	+	2.03155i	0.987072	+	0.264485i	0.716020	−	0.698080i	$-0.245962\pi$
$59$	7.58185	+	2.03155i	0.987072	+	0.264485i	0.271052	+	0.962565i	$0.412628\pi$
$60$	−3.04339	−	3.04339i	−0.392900	−	0.392900i
$61$	−9.14314	+	5.27879i	−1.17066	+	0.675880i	−0.953835	−	0.300331i	$-0.902903\pi$
$61$	−9.14314	+	5.27879i	−1.17066	+	0.675880i	−0.216824	+	0.976211i	$0.569570\pi$
$62$	4.05527	−	7.02394i	0.515020	−	0.892041i
$63$	1.59685	−	2.10952i	0.201184	−	0.265775i
$64$			1.00000i			0.125000i
$65$	7.60441	−	13.5274i	0.943211	−	1.67787i
$66$		−	2.08273i		−	0.256367i
$67$	−3.51620	−	13.1227i	−0.429573	−	1.60319i	−0.753730	−	0.657184i	$-0.771747\pi$
$67$	−3.51620	−	13.1227i	−0.429573	−	1.60319i	0.324157	−	0.946003i	$-0.394919\pi$
$68$	1.72212	+	0.994265i	0.208837	+	0.120572i
$69$	−0.526272	−	0.911529i	−0.0633556	−	0.109735i
$70$	11.2994	+	1.41235i	1.35054	+	0.168809i
$71$	3.38987	+	0.908313i	0.402304	+	0.107797i	0.454297	−	0.890851i	$-0.349891\pi$
$71$	3.38987	+	0.908313i	0.402304	+	0.107797i	−0.0519929	+	0.998647i	$0.516557\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	4.18769	−	4.18769i	0.490132	−	0.490132i	−0.418216	−	0.908348i	$-0.637344\pi$
$73$	4.18769	−	4.18769i	0.490132	−	0.490132i	0.908348	+	0.418216i	$0.137344\pi$
$74$	−1.12620	−	1.95064i	−0.130918	−	0.226757i
$75$	6.76222	−	11.7125i	0.780834	−	1.35244i
$76$	1.11396	+	4.15735i	0.127780	+	0.476881i
$77$	3.38308	+	4.34962i	0.385538	+	0.495686i
$78$	−3.60531	+	0.0413775i	−0.408221	+	0.00468508i
$79$	−2.85526			−0.321242			−0.160621	−	0.987016i	$-0.551350\pi$
$79$	−2.85526			−0.321242			−0.160621	+	0.987016i	$0.551350\pi$
$80$	−4.15735	+	1.11396i	−0.464806	+	0.124544i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.11768	+	8.86408i	0.565153	+	0.978874i
$83$	−9.59920	−	9.59920i	−1.05365	−	1.05365i	−0.998477	−	0.0551717i	$-0.982429\pi$
$83$	−9.59920	−	9.59920i	−1.05365	−	1.05365i	−0.0551717	−	0.998477i	$-0.517571\pi$
$84$	−1.02848	−	2.43767i	−0.112216	−	0.265972i
$85$	−2.21514	+	8.26701i	−0.240265	+	0.896683i
$86$	6.27435	+	6.27435i	0.676580	+	0.676580i
$87$	−4.04816	+	2.33721i	−0.434008	+	0.250575i
$88$	−1.80370	−	1.04137i	−0.192275	−	0.111010i
$89$	−1.02170	−	3.81303i	−0.108300	−	0.404180i	0.890399	−	0.455181i	$-0.150425\pi$
$89$	−1.02170	−	3.81303i	−0.108300	−	0.404180i	−0.998699	+	0.0510011i	$0.983759\pi$
$90$	−4.30400			−0.453682
$91$	7.46220	−	5.94269i	0.782251	−	0.622964i
$92$	−1.05254			−0.109735
$93$	−2.09916	−	7.83418i	−0.217673	−	0.812367i
$94$	1.02122	+	0.589604i	0.105331	+	0.0608130i
$95$	−16.0427	+	9.26224i	−1.64594	+	0.950285i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	1.29605	−	4.83691i	0.131594	−	0.491114i	−0.868395	−	0.495873i	$-0.834848\pi$
$97$	1.29605	−	4.83691i	0.131594	−	0.491114i	0.999989	+	0.00475884i	$0.00151479\pi$
$98$	6.10751	+	3.42028i	0.616952	+	0.345500i
$99$	−1.47272	−	1.47272i	−0.148014	−	0.148014i
$100$	−6.76222	−	11.7125i	−0.676222	−	1.17125i
$101$	−6.00643	+	10.4034i	−0.597662	+	1.03518i	0.395503	+	0.918465i	$0.370570\pi$
$101$	−6.00643	+	10.4034i	−0.597662	+	1.03518i	−0.993165	+	0.116717i	$0.962763\pi$
$102$	1.92077	−	0.514669i	0.190185	−	0.0509599i
$103$	6.76216			0.666295			0.333148	−	0.942875i	$-0.391889\pi$
$103$	6.76216			0.666295			0.333148	+	0.942875i	$0.391889\pi$
$104$	−1.76682	+	3.14298i	−0.173251	+	0.308195i
$105$	8.98856	−	6.99119i	0.877194	−	0.682271i
$106$	1.71111	+	6.38595i	0.166198	+	0.620258i
$107$	8.67208	−	15.0205i	0.838361	−	1.45208i	−0.0529026	−	0.998600i	$-0.516847\pi$
$107$	8.67208	−	15.0205i	0.838361	−	1.45208i	0.891264	−	0.453485i	$-0.149819\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−4.31030	+	4.31030i	−0.412852	+	0.412852i	−0.882731	−	0.469879i	$-0.844297\pi$
$109$	−4.31030	+	4.31030i	−0.412852	+	0.412852i	0.469879	+	0.882731i	$0.344297\pi$
$110$	2.32008	−	8.65865i	0.221211	−	0.825570i
$111$	−2.17565	−	0.582965i	−0.206504	−	0.0553326i
$112$	−2.62532	−	0.328149i	−0.248070	−	0.0310072i
$113$	1.72442	+	2.98679i	0.162220	+	0.280974i	0.935665	−	0.352890i	$-0.114801\pi$
$113$	1.72442	+	2.98679i	0.162220	+	0.280974i	−0.773444	+	0.633864i	$0.781468\pi$
$114$	3.72738	+	2.15200i	0.349101	+	0.201554i
$115$	−1.17249	−	4.37579i	−0.109335	−	0.408044i
$116$			4.67441i			0.434008i
$117$	−2.52008	+	2.57860i	−0.232982	+	0.238392i
$118$		−	7.84930i		−	0.722587i
$119$	−3.17538	+	4.19485i	−0.291086	+	0.384541i
$120$	−2.15200	+	3.72738i	−0.196450	+	0.340261i
$121$	−5.76965	+	3.33111i	−0.524513	+	0.302828i
$122$	7.46534	+	7.46534i	0.675880	+	0.675880i
$123$	9.88660	+	2.64911i	0.891444	+	0.238862i
$124$	−7.83418	−	2.09916i	−0.703530	−	0.188510i
$125$	25.9432	−	25.9432i	2.32043	−	2.32043i
$126$	−2.45094	−	0.996451i	−0.218347	−	0.0887709i
$127$	−15.2015	−	8.77657i	−1.34891	−	0.778794i	−0.360816	−	0.932637i	$-0.617502\pi$
$127$	−15.2015	−	8.77657i	−1.34891	−	0.778794i	−0.988095	+	0.153843i	$0.950835\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	8.87327			0.781248
$130$	−15.0346	−	3.84415i	−1.31862	−	0.337154i
$131$			8.48449i			0.741294i	0.928774	+	0.370647i	$0.120864\pi$
$131$			8.48449i			0.741294i	−0.928774	+	0.370647i	$0.879136\pi$
$132$	−2.01177	+	0.539051i	−0.175102	+	0.0469184i
$133$	−11.2799	+	1.56027i	−0.978095	+	0.135293i
$134$	−11.7654	+	6.79279i	−1.01638	+	0.586807i
$135$	−3.04339	+	3.04339i	−0.261933	+	0.261933i
$136$	0.514669	−	1.92077i	0.0441325	−	0.164705i
$137$	−4.21490	+	15.7302i	−0.360103	+	1.34392i	0.513836	+	0.857888i	$0.328224\pi$
$137$	−4.21490	+	15.7302i	−0.360103	+	1.34392i	−0.873939	+	0.486035i	$0.838443\pi$
$138$	−0.744260	+	0.744260i	−0.0633556	+	0.0633556i
$139$	−3.43066	+	1.98069i	−0.290985	+	0.168000i	−0.638386	−	0.769717i	$-0.720398\pi$
$139$	−3.43066	+	1.98069i	−0.290985	+	0.168000i	0.347401	+	0.937717i	$0.387064\pi$
$140$	−1.56027	−	11.2799i	−0.131867	−	0.953327i
$141$	1.13903	−	0.305202i	0.0959234	−	0.0257026i
$142$		−	3.50945i		−	0.294507i
$143$	−3.82909	−	6.45982i	−0.320205	−	0.540197i
$144$	1.00000			0.0833333
$145$	−19.4331	+	5.20710i	−1.61384	+	0.432426i
$146$	−5.12885	−	2.96115i	−0.424467	−	0.245066i
$147$	6.73716	−	1.90016i	0.555672	−	0.156723i
$148$	−1.59269	+	1.59269i	−0.130918	+	0.130918i
$149$	−16.6309	−	4.45624i	−1.36246	−	0.365070i	−0.497740	−	0.867327i	$-0.665836\pi$
$149$	−16.6309	−	4.45624i	−1.36246	−	0.365070i	−0.864718	+	0.502257i	$0.832503\pi$
$150$	−13.0636	−	3.50038i	−1.06664	−	0.285805i
$151$	9.21747	+	9.21747i	0.750107	+	0.750107i	0.974499	−	0.224392i	$-0.0720395\pi$
$151$	9.21747	+	9.21747i	0.750107	+	0.750107i	−0.224392	+	0.974499i	$0.572040\pi$
$152$	3.72738	−	2.15200i	0.302331	−	0.174551i
$153$	0.994265	−	1.72212i	0.0803815	−	0.139225i
$154$	3.32581	−	4.39357i	0.268001	−	0.354044i
$155$		−	34.9078i		−	2.80386i
$156$	0.973091	+	3.47176i	0.0779097	+	0.277963i
$157$			5.12086i			0.408689i	0.978899	+	0.204345i	$0.0655063\pi$
$157$			5.12086i			0.408689i	−0.978899	+	0.204345i	$0.934494\pi$
$158$	0.738996	+	2.75797i	0.0587913	+	0.219412i
$159$	5.72548	+	3.30561i	0.454060	+	0.262152i
$160$	2.15200	+	3.72738i	0.170131	+	0.294675i
$161$	0.345391	−	2.76327i	0.0272206	−	0.217776i
$162$	0.965926	+	0.258819i	0.0758903	+	0.0203347i
$163$	5.59853	−	20.8940i	0.438510	−	1.63654i	−0.294013	−	0.955801i	$-0.594991\pi$
$163$	5.59853	−	20.8940i	0.438510	−	1.63654i	0.732524	−	0.680742i	$-0.238342\pi$
$164$	7.23749	−	7.23749i	0.565153	−	0.565153i
$165$	−4.48205	−	7.76314i	−0.348927	−	0.604359i
$166$	−6.78766	+	11.7566i	−0.526824	+	0.912486i
$167$	0.493450	+	1.84158i	0.0381843	+	0.142506i	0.982386	−	0.186861i	$-0.0598314\pi$
$167$	0.493450	+	1.84158i	0.0381843	+	0.142506i	−0.944202	+	0.329367i	$0.893165\pi$
$168$	−2.08842	+	1.62435i	−0.161125	+	0.125321i
$169$	−11.1062	+	6.75667i	−0.854322	+	0.519744i
$170$	8.55864			0.656417
$171$	4.15735	−	1.11396i	0.317921	−	0.0851866i
$172$	4.43663	−	7.68448i	0.338290	−	0.585936i
$173$	7.54265	+	13.0642i	0.573457	+	0.993256i	0.996207	+	0.0870103i	$0.0277313\pi$
$173$	7.54265	+	13.0642i	0.573457	+	0.993256i	−0.422751	+	0.906246i	$0.638935\pi$
$174$	3.30531	+	3.30531i	0.250575	+	0.250575i
$175$	32.9681	−	13.9096i	2.49216	−	1.05146i
$176$	−0.539051	+	2.01177i	−0.0406325	+	0.151643i
$177$	−5.55030	−	5.55030i	−0.417186	−	0.417186i
$178$	−3.41866	+	1.97377i	−0.256240	+	0.147940i
$179$	−9.55501	−	5.51659i	−0.714175	−	0.412329i	0.0984300	−	0.995144i	$-0.468618\pi$
$179$	−9.55501	−	5.51659i	−0.714175	−	0.412329i	−0.812605	+	0.582815i	$0.801951\pi$
$180$	1.11396	+	4.15735i	0.0830295	+	0.309870i
$181$	10.6621			0.792507			0.396254	−	0.918141i	$-0.370310\pi$
$181$	10.6621			0.792507			0.396254	+	0.918141i	$0.370310\pi$
$182$	−7.67156	−	5.66985i	−0.568654	−	0.420277i
$183$	10.5576			0.780439
$184$	0.272418	+	1.01668i	0.0200829	+	0.0749505i
$185$	−8.39555	−	4.84718i	−0.617253	−	0.356371i
$186$	−7.02394	+	4.05527i	−0.515020	+	0.297347i
$187$	2.92854	+	2.92854i	0.214156	+	0.214156i
$188$	0.305202	−	1.13903i	0.0222591	−	0.0830721i
$189$	−2.43767	+	1.02848i	−0.177314	+	0.0748106i
$190$	13.0988	+	13.0988i	0.950285	+	0.950285i
$191$	−0.298154	−	0.516418i	−0.0215737	−	0.0373667i	0.855037	−	0.518567i	$-0.173534\pi$
$191$	−0.298154	−	0.516418i	−0.0215737	−	0.0373667i	−0.876611	+	0.481200i	$0.840201\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−17.6852	+	4.73873i	−1.27301	+	0.341101i	−0.831182	−	0.556001i	$-0.812335\pi$
$193$	−17.6852	+	4.73873i	−1.27301	+	0.341101i	−0.441824	+	0.897102i	$0.645669\pi$
$194$	−5.00754			−0.359521
$195$	−13.3493	+	7.91287i	−0.955964	+	0.566652i
$196$	1.72299	−	6.78464i	0.123071	−	0.484617i
$197$	1.02956	+	3.84238i	0.0733534	+	0.273758i	0.992855	−	0.119328i	$-0.0380740\pi$
$197$	1.02956	+	3.84238i	0.0733534	+	0.273758i	−0.919502	+	0.393086i	$0.871407\pi$
$198$	−1.04137	+	1.80370i	−0.0740068	+	0.128183i
$199$	5.66011	+	9.80361i	0.401235	+	0.694959i	0.993875	−	0.110508i	$-0.0352478\pi$
$199$	5.66011	+	9.80361i	0.401235	+	0.694959i	−0.592640	+	0.805467i	$0.701914\pi$
$200$	−9.56322	+	9.56322i	−0.676222	+	0.676222i
$201$	−3.51620	+	13.1227i	−0.248014	+	0.925601i
$202$	11.6035	+	3.10916i	0.816422	+	0.218760i
$203$	−12.2718	−	1.53390i	−0.861314	−	0.107659i
$204$	−0.994265	−	1.72212i	−0.0696125	−	0.120572i
$205$	38.1510	+	22.0265i	2.66458	+	1.53840i
$206$	−1.75017	−	6.53174i	−0.121940	−	0.455088i
$207$			1.05254i			0.0731568i
$208$	3.49318	+	0.893156i	0.242208	+	0.0619292i
$209$			8.96411i			0.620061i
$210$	−9.07939	−	6.87283i	−0.626537	−	0.474270i
$211$	−1.00012	+	1.73226i	−0.0688510	+	0.119253i	−0.898396	−	0.439187i	$-0.855267\pi$
$211$	−1.00012	+	1.73226i	−0.0688510	+	0.119253i	0.829545	+	0.558440i	$0.188600\pi$
$212$	5.72548	−	3.30561i	0.393228	−	0.227030i
$213$	−2.48156	−	2.48156i	−0.170034	−	0.170034i
$214$	−16.7532	−	4.48900i	−1.14522	−	0.306862i
$215$	36.8893	+	9.88445i	2.51583	+	0.674114i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	8.08176	−	19.8784i	0.548625	−	1.34943i
$218$	5.27901	+	3.04784i	0.357540	+	0.206426i
$219$	−5.72049	+	1.53280i	−0.386555	+	0.103577i
$220$	−8.96410			−0.604359
$221$	5.01126	−	5.12762i	0.337094	−	0.344921i
$222$			2.25240i			0.151171i
$223$	−4.91474	+	1.31690i	−0.329116	+	0.0881863i	−0.419593	−	0.907712i	$-0.637827\pi$
$223$	−4.91474	+	1.31690i	−0.329116	+	0.0881863i	0.0904776	+	0.995898i	$0.471161\pi$
$224$	0.362516	+	2.62080i	0.0242216	+	0.175109i
$225$	−11.7125	+	6.76222i	−0.780834	+	0.450815i
$226$	2.43871	−	2.43871i	0.162220	−	0.162220i
$227$	0.827373	−	3.08780i	0.0549147	−	0.204944i	−0.933018	−	0.359831i	$-0.882834\pi$
$227$	0.827373	−	3.08780i	0.0549147	−	0.204944i	0.987932	+	0.154886i	$0.0495011\pi$
$228$	1.11396	−	4.15735i	0.0737738	−	0.275328i
$229$	−13.9782	+	13.9782i	−0.923706	+	0.923706i	−0.997289	−	0.0735832i	$-0.976557\pi$
$229$	−13.9782	+	13.9782i	−0.923706	+	0.923706i	0.0735832	+	0.997289i	$0.476557\pi$
$230$	−3.92322	+	2.26507i	−0.258690	+	0.149355i
$231$	−0.755025	−	5.45843i	−0.0496770	−	0.359138i
$232$	4.51513	−	1.20983i	0.296433	−	0.0794290i
$233$			17.9614i			1.17669i	0.808610	+	0.588345i	$0.200220\pi$
$233$			17.9614i			1.17669i	−0.808610	+	0.588345i	$0.799780\pi$
$234$	3.14298	+	1.76682i	0.205463	+	0.115501i
$235$	5.07532			0.331077
$236$	−7.58185	+	2.03155i	−0.493536	+	0.132243i
$237$	2.47273	+	1.42763i	0.160621	+	0.0927345i
$238$	4.87376	+	1.98147i	0.315919	+	0.128440i
$239$	−6.83320	+	6.83320i	−0.442003	+	0.442003i	−0.892685	−	0.450682i	$-0.851181\pi$
$239$	−6.83320	+	6.83320i	−0.442003	+	0.442003i	0.450682	+	0.892685i	$0.351181\pi$
$240$	4.15735	+	1.11396i	0.268356	+	0.0719057i
$241$	−3.65178	−	0.978490i	−0.235232	−	0.0630301i	0.139277	−	0.990253i	$-0.455522\pi$
$241$	−3.65178	−	0.978490i	−0.235232	−	0.0630301i	−0.374509	+	0.927223i	$0.622189\pi$
$242$	4.71090	+	4.71090i	0.302828	+	0.302828i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	5.27879	−	9.14314i	0.337940	−	0.585329i
$245$	30.1254	−	0.394718i	1.92464	−	0.0252176i
$246$		−	10.2354i		−	0.652583i
$247$	15.5173	−	0.178089i	0.987343	−	0.0113315i
$248$			8.11054i			0.515020i
$249$	3.51355	+	13.1127i	0.222662	+	0.830986i
$250$	−31.7738	−	18.3446i	−2.00955	−	1.16021i
$251$	−3.92610	−	6.80020i	−0.247813	−	0.429225i	0.715106	−	0.699016i	$-0.246379\pi$
$251$	−3.92610	−	6.80020i	−0.247813	−	0.429225i	−0.962919	+	0.269792i	$0.913045\pi$
$252$	−0.328149	+	2.62532i	−0.0206714	+	0.165380i
$253$	−2.11747	−	0.567375i	−0.133124	−	0.0356706i
$254$	−4.54309	+	16.9550i	−0.285059	+	1.06385i
$255$	6.05187	−	6.05187i	0.378983	−	0.378983i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.746507	−	1.29299i	0.0465658	−	0.0806543i	−0.841803	−	0.539785i	$-0.818506\pi$
$257$	0.746507	−	1.29299i	0.0465658	−	0.0806543i	0.888369	+	0.459130i	$0.151839\pi$
$258$	−2.29657	−	8.57092i	−0.142978	−	0.533602i
$259$	−3.65868	−	4.70396i	−0.227340	−	0.292290i
$260$	0.178089	+	15.5173i	0.0110446	+	0.962341i
$261$	4.67441			0.289339
$262$	8.19539	−	2.19595i	0.506313	−	0.135666i
$263$	−5.69163	+	9.85819i	−0.350961	+	0.607882i	−0.986418	−	0.164254i	$-0.947478\pi$
$263$	−5.69163	+	9.85819i	−0.350961	+	0.607882i	0.635457	+	0.772136i	$0.280812\pi$
$264$	1.04137	+	1.80370i	0.0640917	+	0.111010i
$265$	20.1205	+	20.1205i	1.23599	+	1.23599i
$266$	4.42657	+	10.4918i	0.271410	+	0.643291i
$267$	−1.02170	+	3.81303i	−0.0625268	+	0.233353i
$268$	9.60645	+	9.60645i	0.586807	+	0.586807i
$269$	−16.4336	+	9.48797i	−1.00198	+	0.578492i	−0.908833	−	0.417161i	$-0.863025\pi$
$269$	−16.4336	+	9.48797i	−1.00198	+	0.578492i	−0.0931442	+	0.995653i	$0.529692\pi$
$270$	3.72738	+	2.15200i	0.226841	+	0.130967i
$271$	−7.70538	−	28.7569i	−0.468069	−	1.74686i	−0.646510	−	0.762906i	$-0.723772\pi$
$271$	−7.70538	−	28.7569i	−0.468069	−	1.74686i	0.178441	−	0.983951i	$-0.442895\pi$
$272$	−1.98853			−0.120572
$273$	−9.43380	+	1.41543i	−0.570960	+	0.0856655i
$274$	16.2851			0.983820
$275$	−7.29037	−	27.2080i	−0.439626	−	1.64071i
$276$	0.911529	+	0.526272i	0.0548676	+	0.0316778i
$277$	28.7061	−	16.5735i	1.72478	−	0.995804i	0.816636	−	0.577153i	$-0.195837\pi$
$277$	28.7061	−	16.5735i	1.72478	−	0.995804i	0.908147	−	0.418651i	$-0.137497\pi$
$278$	2.80112	+	2.80112i	0.168000	+	0.168000i
$279$	−2.09916	+	7.83418i	−0.125674	+	0.469020i
$280$	−10.4917	+	4.42656i	−0.627001	+	0.264538i
$281$	7.06146	+	7.06146i	0.421251	+	0.421251i	0.885634	−	0.464383i	$-0.153724\pi$
$281$	7.06146	+	7.06146i	0.421251	+	0.421251i	−0.464383	+	0.885634i	$0.653724\pi$
$282$	−0.589604	−	1.02122i	−0.0351104	−	0.0608130i
$283$	11.8908	−	20.5954i	0.706832	−	1.22427i	−0.259194	−	0.965825i	$-0.583457\pi$
$283$	11.8908	−	20.5954i	0.706832	−	1.22427i	0.966026	−	0.258444i	$-0.0832097\pi$
$284$	−3.38987	+	0.908313i	−0.201152	+	0.0538985i
$285$	18.5245			1.09729
$286$	−5.24867	+	5.37054i	−0.310360	+	0.317567i
$287$	16.6258	+	21.3757i	0.981388	+	1.26177i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	6.52288	−	11.2980i	0.383699	−	0.664585i
$290$	10.0593	+	17.4233i	0.590705	+	1.02313i
$291$	−3.54087	+	3.54087i	−0.207569	+	0.207569i
$292$	−1.53280	+	5.72049i	−0.0897004	+	0.334767i
$293$	−25.1368	−	6.73537i	−1.46851	−	0.393485i	−0.566087	−	0.824346i	$-0.691543\pi$
$293$	−25.1368	−	6.73537i	−1.46851	−	0.393485i	−0.902418	+	0.430861i	$0.858210\pi$
$294$	−3.57912	−	6.01580i	−0.208739	−	0.350849i
$295$	−16.8917	−	29.2573i	−0.983474	−	1.70343i
$296$	1.95064	+	1.12620i	0.113379	+	0.0654591i
$297$	0.539051	+	2.01177i	0.0312789	+	0.116735i
$298$			17.2176i			0.997388i
$299$	−0.940085	+	3.67672i	−0.0543665	+	0.212630i
$300$			13.5244i			0.780834i
$301$	18.7184	+	14.1692i	1.07891	+	0.816702i
$302$	6.51774	−	11.2891i	0.375054	−	0.649612i
$303$	10.4034	−	6.00643i	0.597662	−	0.345060i
$304$	−3.04339	−	3.04339i	−0.174551	−	0.174551i
$305$	43.8915	+	11.7607i	2.51322	+	0.673416i
$306$	−1.92077	−	0.514669i	−0.109803	−	0.0294217i
$307$	−6.27350	+	6.27350i	−0.358048	+	0.358048i	−0.863093	−	0.505045i	$-0.831476\pi$
$307$	−6.27350	+	6.27350i	−0.358048	+	0.358048i	0.505045	+	0.863093i	$0.331476\pi$
$308$	−5.10465	−	2.07534i	−0.290864	−	0.118254i
$309$	−5.85620	−	3.38108i	−0.333148	−	0.192343i
$310$	−33.7183	+	9.03480i	−1.91507	+	0.513142i
$311$	−2.56836			−0.145638			−0.0728192	−	0.997345i	$-0.523200\pi$
$311$	−2.56836			−0.145638			−0.0728192	+	0.997345i	$0.523200\pi$
$312$	3.10160	−	1.83849i	0.175594	−	0.104084i
$313$		−	1.16919i		−	0.0660866i	−0.999454	−	0.0330433i	$-0.989480\pi$
$313$		−	1.16919i		−	0.0660866i	0.999454	−	0.0330433i	$-0.0105199\pi$
$314$	4.94637	−	1.32538i	0.279140	−	0.0747953i
$315$	−11.2799	+	1.56027i	−0.635552	+	0.0879112i
$316$	2.47273	−	1.42763i	0.139102	−	0.0803105i
$317$	−5.14263	+	5.14263i	−0.288839	+	0.288839i	−0.836621	−	0.547782i	$-0.815472\pi$
$317$	−5.14263	+	5.14263i	−0.288839	+	0.288839i	0.547782	+	0.836621i	$0.315472\pi$
$318$	1.71111	−	6.38595i	0.0959542	−	0.358106i
$319$	−2.51975	+	9.40383i	−0.141079	+	0.526513i
$320$	3.04339	−	3.04339i	0.170131	−	0.170131i
$321$	−15.0205	+	8.67208i	−0.838361	+	0.484028i
$322$	−2.75850	+	0.381564i	−0.153725	+	0.0212637i
$323$	−8.26702	+	2.21514i	−0.459989	+	0.123254i
$324$		−	1.00000i		−	0.0555556i
$325$	−46.9536	+	13.1605i	−2.60452	+	0.730014i
$326$	−21.6310			−1.19803
$327$	5.88798	−	1.57768i	0.325606	−	0.0872458i
$328$	−8.86408	−	5.11768i	−0.489437	−	0.282577i
$329$	2.89016	+	1.17502i	0.159340	+	0.0647811i
$330$	−6.33857	+	6.33857i	−0.348927	+	0.348927i
$331$	11.2708	+	3.02000i	0.619498	+	0.165994i	0.554900	−	0.831917i	$-0.312757\pi$
$331$	11.2708	+	3.02000i	0.619498	+	0.165994i	0.0645984	+	0.997911i	$0.479423\pi$
$332$	13.1127	+	3.51355i	0.719655	+	0.192831i
$333$	1.59269	+	1.59269i	0.0872789	+	0.0872789i
$334$	1.65111	−	0.953271i	0.0903450	−	0.0521607i
$335$	−29.2362	+	50.6385i	−1.59734	+	2.76668i
$336$	2.10952	+	1.59685i	0.115084	+	0.0871151i
$337$		−	21.0955i		−	1.14915i	−0.818453	−	0.574573i	$-0.805168\pi$
$337$		−	21.0955i		−	1.14915i	0.818453	−	0.574573i	$-0.194832\pi$
$338$	9.40094	+	8.97900i	0.511344	+	0.488393i
$339$		−	3.44885i		−	0.187316i
$340$	−2.21514	−	8.26701i	−0.120133	−	0.448341i
$341$	−14.6290	−	8.44605i	−0.792205	−	0.457379i
$342$	−2.15200	−	3.72738i	−0.116367	−	0.201554i
$343$	17.2465	+	6.74978i	0.931221	+	0.364454i
$344$	−8.57092	−	2.29657i	−0.462113	−	0.123823i
$345$	−1.17249	+	4.37579i	−0.0631247	+	0.235584i
$346$	10.6669	−	10.6669i	0.573457	−	0.573457i
$347$	−2.00774	−	3.47750i	−0.107781	−	0.186682i	0.807090	−	0.590428i	$-0.201041\pi$
$347$	−2.00774	−	3.47750i	−0.107781	−	0.186682i	−0.914871	+	0.403746i	$0.867708\pi$
$348$	2.33721	−	4.04816i	0.125287	−	0.217004i
$349$	−6.01907	−	22.4635i	−0.322194	−	1.20244i	−0.917103	−	0.398650i	$-0.869479\pi$
$349$	−6.01907	−	22.4635i	−0.322194	−	1.20244i	0.594909	−	0.803793i	$-0.297188\pi$
$350$	−21.9684	−	28.2447i	−1.17426	−	1.50974i
$351$	3.47176	−	0.973091i	0.185309	−	0.0519398i
$352$	2.08273			0.111010
$353$	0.898217	−	0.240677i	0.0478073	−	0.0128099i	−0.234836	−	0.972035i	$-0.575455\pi$
$353$	0.898217	−	0.240677i	0.0478073	−	0.0128099i	0.282643	+	0.959225i	$0.408789\pi$
$354$	−3.92465	+	6.79770i	−0.208593	+	0.361294i
$355$	−7.55235	−	13.0810i	−0.400837	−	0.694270i
$356$	2.79133	+	2.79133i	0.147940	+	0.147940i
$357$	4.84738	−	2.04515i	0.256551	−	0.108241i
$358$	−2.85560	+	10.6572i	−0.150923	+	0.563252i
$359$	25.3378	+	25.3378i	1.33728	+	1.33728i	0.898686	+	0.438592i	$0.144523\pi$
$359$	25.3378	+	25.3378i	1.33728	+	1.33728i	0.438592	+	0.898686i	$0.355477\pi$
$360$	3.72738	−	2.15200i	0.196450	−	0.113420i
$361$	0.411795	+	0.237750i	0.0216734	+	0.0125132i
$362$	−2.75955	−	10.2988i	−0.145039	−	0.541293i
$363$	6.66222			0.349676
$364$	−3.49110	+	8.87762i	−0.182984	+	0.465314i
$365$	−25.4896			−1.33418
$366$	−2.73250	−	10.1978i	−0.142830	−	0.533050i
$367$	15.4008	+	8.89167i	0.803916	+	0.464141i	0.844839	−	0.535021i	$-0.179696\pi$
$367$	15.4008	+	8.89167i	0.803916	+	0.464141i	−0.0409224	+	0.999162i	$0.513030\pi$
$368$	0.911529	−	0.526272i	0.0475167	−	0.0274338i
$369$	−7.23749	−	7.23749i	−0.376769	−	0.376769i
$370$	−2.50908	+	9.36402i	−0.130441	+	0.486812i
$371$	6.79948	+	16.1160i	0.353011	+	0.836699i
$372$	5.73502	+	5.73502i	0.297347	+	0.297347i
$373$	−11.8985	−	20.6087i	−0.616079	−	1.06708i	−0.990194	−	0.139698i	$-0.955387\pi$
$373$	−11.8985	−	20.6087i	−0.616079	−	1.06708i	0.374115	−	0.927382i	$-0.377946\pi$
$374$	2.07079	−	3.58671i	0.107078	−	0.185465i
$375$	−35.4391	+	9.49587i	−1.83007	+	0.490364i
$376$	−1.17921			−0.0608130
$377$	16.3285	+	4.17498i	0.840962	+	0.215022i
$378$	1.62435	+	2.08842i	0.0835474	+	0.107417i
$379$	−3.33767	−	12.4564i	−0.171445	−	0.639841i	−0.997130	−	0.0757095i	$-0.975878\pi$
$379$	−3.33767	−	12.4564i	−0.171445	−	0.639841i	0.825685	−	0.564131i	$-0.190789\pi$
$380$	9.26224	−	16.0427i	0.475143	−	0.822971i
$381$	8.77657	+	15.2015i	0.449637	+	0.778794i
$382$	−0.421653	+	0.421653i	−0.0215737	+	0.0215737i
$383$	4.41323	−	16.4704i	0.225506	−	0.841599i	−0.756696	−	0.653767i	$-0.773188\pi$
$383$	4.41323	−	16.4704i	0.225506	−	0.841599i	0.982201	−	0.187831i	$-0.0601458\pi$
$384$	−0.965926	−	0.258819i	−0.0492922	−	0.0132078i
$385$	2.94156	−	23.5336i	0.149916	−	1.19939i
$386$	9.15452	+	15.8561i	0.465953	+	0.807054i
$387$	−7.68448	−	4.43663i	−0.390624	−	0.225527i
$388$	1.29605	+	4.83691i	0.0657968	+	0.245557i
$389$			10.9561i			0.555495i	0.960654	+	0.277748i	$0.0895879\pi$
$389$			10.9561i			0.555495i	−0.960654	+	0.277748i	$0.910412\pi$
$390$	11.0983	+	10.8464i	0.561984	+	0.549231i
$391$		−	2.09301i		−	0.105848i
$392$	−6.99940	+	0.0917094i	−0.353523	+	0.00463202i
$393$	4.24225	−	7.34779i	0.213993	−	0.370647i
$394$	3.44499	−	1.98896i	0.173556	−	0.100203i
$395$	8.68967	+	8.68967i	0.437225	+	0.437225i
$396$	2.01177	+	0.539051i	0.101095	+	0.0270884i
$397$	−19.3289	−	5.17916i	−0.970089	−	0.259935i	−0.261224	−	0.965278i	$-0.584126\pi$
$397$	−19.3289	−	5.17916i	−0.970089	−	0.259935i	−0.708865	+	0.705344i	$0.750793\pi$
$398$	8.00461	−	8.00461i	0.401235	−	0.401235i
$399$	10.5489	+	4.28873i	0.528103	+	0.214705i
$400$	11.7125	+	6.76222i	0.585625	+	0.338111i
$401$	−24.7304	+	6.62649i	−1.23498	+	0.330911i	−0.816516	−	0.577323i	$-0.804097\pi$
$401$	−24.7304	+	6.62649i	−1.23498	+	0.330911i	−0.418462	+	0.908234i	$0.637431\pi$
$402$	13.5856			0.677587
$403$	−14.3299	+	25.4913i	−0.713823	+	1.26981i
$404$		−	12.0129i		−	0.597662i
$405$	4.15735	−	1.11396i	0.206580	−	0.0553530i
$406$	1.69455	+	12.2507i	0.0840990	+	0.607991i
$407$	−4.06266	+	2.34558i	−0.201379	+	0.116266i
$408$	−1.40610	+	1.40610i	−0.0696125	+	0.0696125i
$409$	8.37730	−	31.2645i	0.414231	−	1.54593i	−0.372141	−	0.928176i	$-0.621376\pi$
$409$	8.37730	−	31.2645i	0.414231	−	1.54593i	0.786372	−	0.617754i	$-0.211957\pi$
$410$	11.4018	−	42.5519i	0.563093	−	2.10149i
$411$	11.5153	−	11.5153i	0.568009	−	0.568009i
$412$	−5.85620	+	3.38108i	−0.288514	+	0.166574i
$413$	−2.84550	−	20.5714i	−0.140018	−	1.01225i
$414$	1.01668	−	0.272418i	0.0499670	−	0.0133886i
$415$			58.4282i			2.86813i
$416$	−0.0413775	−	3.60531i	−0.00202870	−	0.176765i
$417$	3.96138			0.193990
$418$	8.65867	−	2.32008i	0.423509	−	0.113479i
$419$	−22.6376	−	13.0698i	−1.10592	−	0.638502i	−0.168149	−	0.985762i	$-0.553779\pi$
$419$	−22.6376	−	13.0698i	−1.10592	−	0.638502i	−0.937769	+	0.347260i	$0.887112\pi$
$420$	−4.28873	+	10.5488i	−0.209268	+	0.514730i
$421$	14.3223	−	14.3223i	0.698026	−	0.698026i	−0.265958	−	0.963984i	$-0.585688\pi$
$421$	14.3223	−	14.3223i	0.698026	−	0.698026i	0.963984	+	0.265958i	$0.0856884\pi$
$422$	1.93208	+	0.517699i	0.0940522	+	0.0252012i
$423$	−1.13903	−	0.305202i	−0.0553814	−	0.0148394i
$424$	−4.67484	−	4.67484i	−0.227030	−	0.227030i
$425$	23.2907	−	13.4469i	1.12976	−	0.652269i
$426$	−1.75473	+	3.03927i	−0.0850168	+	0.147253i
$427$	22.2715	+	16.8588i	1.07779	+	0.815857i
$428$			17.3442i			0.838361i
$429$	0.0861784	+	7.50891i	0.00416073	+	0.362534i
$430$		−	38.1906i		−	1.84171i
$431$	−4.51481	−	16.8495i	−0.217471	−	0.811613i	−0.985282	−	0.170936i	$-0.945321\pi$
$431$	−4.51481	−	16.8495i	−0.217471	−	0.811613i	0.767811	−	0.640676i	$-0.221346\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−3.52085	−	6.09829i	−0.169201	−	0.293065i	0.768938	−	0.639323i	$-0.220785\pi$
$433$	−3.52085	−	6.09829i	−0.169201	−	0.293065i	−0.938139	+	0.346258i	$0.887452\pi$
$434$	−21.2928	−	2.66147i	−1.02209	−	0.127754i
$435$	19.4331	+	5.20710i	0.931748	+	0.249661i
$436$	1.57768	−	5.88798i	0.0755571	−	0.281983i
$437$	3.20330	−	3.20330i	0.153235	−	0.153235i
$438$	2.96115	+	5.12885i	0.141489	+	0.245066i
$439$	1.20823	−	2.09272i	0.0576657	−	0.0998800i	−0.835751	−	0.549108i	$-0.814968\pi$
$439$	1.20823	−	2.09272i	0.0576657	−	0.0998800i	0.893417	+	0.449228i	$0.148301\pi$
$440$	2.32008	+	8.65865i	0.110605	+	0.412785i
$441$	−6.78464	−	1.72299i	−0.323078	−	0.0820473i
$442$	−6.24991	−	3.51338i	−0.297278	−	0.167114i
$443$	−21.8204			−1.03672			−0.518359	−	0.855163i	$-0.673457\pi$
$443$	−21.8204			−1.03672			−0.518359	+	0.855163i	$0.673457\pi$
$444$	2.17565	−	0.582965i	0.103252	−	0.0276663i
$445$	−8.49510	+	14.7139i	−0.402706	+	0.697508i
$446$	2.54406	+	4.40644i	0.120465	+	0.208651i
$447$	12.1747	+	12.1747i	0.575842	+	0.575842i
$448$	2.43767	−	1.02848i	0.115169	−	0.0485909i
$449$	−6.06505	+	22.6351i	−0.286228	+	1.06822i	0.661710	+	0.749760i	$0.269831\pi$
$449$	−6.06505	+	22.6351i	−0.286228	+	1.06822i	−0.947938	+	0.318456i	$0.896836\pi$
$450$	9.56322	+	9.56322i	0.450815	+	0.450815i
$451$	18.4615	−	10.6588i	0.869319	−	0.501902i
$452$	−2.98679	−	1.72442i	−0.140487	−	0.0811101i
$453$	−3.37383	−	12.5913i	−0.158516	−	0.591591i
$454$	−3.19672			−0.150030
$455$	−40.7963	−	4.62444i	−1.91256	−	0.216797i
$456$	−4.30401			−0.201554
$457$	−3.74406	−	13.9730i	−0.175140	−	0.653630i	−0.996528	−	0.0832607i	$-0.973467\pi$
$457$	−3.74406	−	13.9730i	−0.175140	−	0.653630i	0.821388	−	0.570370i	$-0.193200\pi$
$458$	17.1197	+	9.88408i	0.799953	+	0.461853i
$459$	−1.72212	+	0.994265i	−0.0803815	+	0.0464083i
$460$	3.20330	+	3.20330i	0.149355	+	0.149355i
$461$	9.91797	−	37.0144i	0.461926	−	1.72393i	−0.204959	−	0.978771i	$-0.565706\pi$
$461$	9.91797	−	37.0144i	0.461926	−	1.72393i	0.666885	−	0.745161i	$-0.267627\pi$
$462$	−5.07702	+	2.14204i	−0.236204	+	0.0996568i
$463$	4.95612	+	4.95612i	0.230330	+	0.230330i	0.812831	−	0.582500i	$-0.197926\pi$
$463$	4.95612	+	4.95612i	0.230330	+	0.230330i	−0.582500	+	0.812831i	$0.697926\pi$
$464$	−2.33721	−	4.04816i	−0.108502	−	0.187931i
$465$	−17.4539	+	30.2310i	−0.809405	+	1.40193i
$466$	17.3494	−	4.64875i	0.803695	−	0.215349i
$467$	19.6330			0.908505			0.454253	−	0.890873i	$-0.349906\pi$
$467$	19.6330			0.908505			0.454253	+	0.890873i	$0.349906\pi$
$468$	0.893156	−	3.49318i	0.0412862	−	0.161472i
$469$	−28.3724	+	22.0677i	−1.31011	+	1.01899i
$470$	−1.31359	−	4.90238i	−0.0605913	−	0.226130i
$471$	2.56043	−	4.43480i	0.117978	−	0.204345i
$472$	3.92465	+	6.79770i	0.180647	+	0.312889i
$473$	13.0678	−	13.0678i	0.600858	−	0.600858i
$474$	0.738996	−	2.75797i	0.0339432	−	0.126678i
$475$	56.2259	+	15.0657i	2.57982	+	0.691261i
$476$	0.652534	−	5.22053i	0.0299088	−	0.239283i
$477$	−3.30561	−	5.72548i	−0.151353	−	0.262152i
$478$	8.36893	+	4.83180i	0.382786	+	0.221001i
$479$	−2.07197	−	7.73269i	−0.0946706	−	0.353315i	0.902299	−	0.431111i	$-0.141878\pi$
$479$	−2.07197	−	7.73269i	−0.0946706	−	0.353315i	−0.996969	+	0.0777959i	$0.975212\pi$
$480$		−	4.30400i		−	0.196450i
$481$	4.14102	+	6.98607i	0.188814	+	0.318537i
$482$			3.78060i			0.172201i
$483$	−1.68075	+	2.22036i	−0.0764768	+	0.101030i
$484$	3.33111	−	5.76965i	0.151414	−	0.262257i
$485$	−18.6650	+	10.7762i	−0.847534	+	0.489324i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	7.27652	+	1.94974i	0.329731	+	0.0883510i	0.419886	−	0.907577i	$-0.362070\pi$
$487$	7.27652	+	1.94974i	0.329731	+	0.0883510i	−0.0901559	+	0.995928i	$0.528737\pi$
$488$	−10.1978	−	2.73250i	−0.461635	−	0.123695i
$489$	−15.2955	+	15.2955i	−0.691684	+	0.691684i
$490$	−8.17830	−	28.9968i	−0.369458	−	1.30994i
$491$	−21.9776	−	12.6887i	−0.991833	−	0.572635i	−0.0860114	−	0.996294i	$-0.527412\pi$
$491$	−21.9776	−	12.6887i	−0.991833	−	0.572635i	−0.905822	+	0.423659i	$0.860745\pi$
$492$	−9.88660	+	2.64911i	−0.445722	+	0.119431i
$493$	−9.29520			−0.418635
$494$	−4.18820	−	14.9425i	−0.188436	−	0.672294i
$495$			8.96410i			0.402906i
$496$	7.83418	−	2.09916i	0.351765	−	0.0942552i
$497$	−1.27223	−	9.19756i	−0.0570674	−	0.412567i
$498$	11.7566	−	6.78766i	0.526824	−	0.304162i
$499$	−4.75574	+	4.75574i	−0.212896	+	0.212896i	−0.805497	−	0.592600i	$-0.798101\pi$
$499$	−4.75574	+	4.75574i	−0.212896	+	0.212896i	0.592600	+	0.805497i	$0.298101\pi$
$500$	−9.49587	+	35.4391i	−0.424668	+	1.58488i
$501$	0.493450	−	1.84158i	0.0220457	−	0.0822757i
$502$	−5.55234	+	5.55234i	−0.247813	+	0.247813i
$503$	−10.2713	+	5.93013i	−0.457974	+	0.264411i	−0.711192	−	0.702998i	$-0.751844\pi$
$503$	−10.2713	+	5.93013i	−0.457974	+	0.264411i	0.253218	+	0.967409i	$0.418511\pi$
$504$	2.62080	−	0.362516i	0.116740	−	0.0161477i
$505$	49.9416	−	13.3818i	2.22237	−	0.595483i
$506$			2.19217i			0.0974538i
$507$	12.9966	−	0.298358i	0.577198	−	0.0132505i
$508$	17.5531			0.778794
$509$	−1.34971	+	0.361654i	−0.0598249	+	0.0160300i	−0.288607	−	0.957448i	$-0.593192\pi$
$509$	−1.34971	+	0.361654i	−0.0598249	+	0.0160300i	0.228782	+	0.973478i	$0.426526\pi$
$510$	−7.41200	−	4.27932i	−0.328209	−	0.189491i
$511$	−14.5152	−	5.90127i	−0.642113	−	0.261057i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−4.15735	−	1.11396i	−0.183552	−	0.0491825i
$514$	−1.44214	−	0.386420i	−0.0636101	−	0.0170443i
$515$	−20.5799	−	20.5799i	−0.906858	−	0.906858i
$516$	−7.68448	+	4.43663i	−0.338290	+	0.195312i
$517$	1.22799	−	2.12694i	0.0540069	−	0.0935427i
$518$	−3.59674	+	4.75149i	−0.158032	+	0.208769i
$519$		−	15.0853i		−	0.662171i
$520$	14.9424	−	4.18819i	0.655270	−	0.183664i
$521$		−	32.9940i		−	1.44549i	−0.691113	−	0.722747i	$-0.742879\pi$
$521$		−	32.9940i		−	1.44549i	0.691113	−	0.722747i	$-0.257121\pi$
$522$	−1.20983	−	4.51513i	−0.0529527	−	0.197622i
$523$	−27.5778	−	15.9220i	−1.20589	−	0.696222i	−0.244032	−	0.969767i	$-0.578470\pi$
$523$	−27.5778	−	15.9220i	−1.20589	−	0.696222i	−0.961859	+	0.273545i	$0.911804\pi$
$524$	−4.24225	−	7.34779i	−0.185323	−	0.320990i
$525$	−35.5060	−	4.43803i	−1.54961	−	0.193692i
$526$	10.9954	+	2.94620i	0.479421	+	0.128461i
$527$	4.17425	−	15.5785i	0.181833	−	0.678610i
$528$	1.47272	−	1.47272i	0.0640917	−	0.0640917i
$529$	−10.9461	−	18.9592i	−0.475916	−	0.824311i
$530$	14.2273	−	24.6425i	0.617997	−	1.07040i
$531$	2.03155	+	7.58185i	0.0881617	+	0.329024i
$532$	8.98858	−	6.99121i	0.389704	−	0.303107i
$533$	−18.8176	−	31.7460i	−0.815081	−	1.37507i
$534$	3.94753			0.170827
$535$	−72.1057	+	19.3207i	−3.11740	+	0.835305i
$536$	6.79279	−	11.7654i	0.293404	−	0.508190i
$537$	5.51659	+	9.55501i	0.238058	+	0.412329i
$538$	13.4180	+	13.4180i	0.578492	+	0.578492i
$539$	7.12353	−	12.7203i	0.306832	−	0.547903i
$540$	1.11396	−	4.15735i	0.0479371	−	0.178904i
$541$	9.95760	+	9.95760i	0.428111	+	0.428111i	0.887984	−	0.459874i	$-0.152105\pi$
$541$	9.95760	+	9.95760i	0.428111	+	0.428111i	−0.459874	+	0.887984i	$0.652105\pi$
$542$	−25.7827	+	14.8857i	−1.10746	+	0.639394i
$543$	−9.23365	−	5.33105i	−0.396254	−	0.228777i
$544$	0.514669	+	1.92077i	0.0220663	+	0.0823524i
$545$	26.2358			1.12382
$546$	3.80884	+	8.74601i	0.163003	+	0.374295i
$547$	−25.2471			−1.07949			−0.539743	−	0.841830i	$-0.681479\pi$
$547$	−25.2471			−1.07949			−0.539743	+	0.841830i	$0.681479\pi$
$548$	−4.21490	−	15.7302i	−0.180052	−	0.671961i
$549$	−9.14314	−	5.27879i	−0.390220	−	0.225293i
$550$	−24.3940	+	14.0839i	−1.04017	+	0.600540i
$551$	−14.2261	−	14.2261i	−0.606051	−	0.606051i
$552$	0.272418	−	1.01668i	0.0115949	−	0.0432727i
$553$	2.93657	+	6.96018i	0.124876	+	0.295977i
$554$	−23.4384	−	23.4384i	−0.995804	−	0.995804i
$555$	4.84718	+	8.39555i	0.205751	+	0.356371i
$556$	1.98069	−	3.43066i	0.0840000	−	0.145492i
$557$	11.8245	−	3.16837i	0.501021	−	0.134248i	0.000547107	−	1.00000i	$-0.499826\pi$
$557$	11.8245	−	3.16837i	0.501021	−	0.134248i	0.500474	+	0.865752i	$0.333159\pi$
$558$	8.11054			0.343347
$559$	−22.8806	−	22.3614i	−0.967747	−	0.945786i
$560$	6.99119	+	8.98856i	0.295432	+	0.379836i
$561$	−1.07192	−	4.00046i	−0.0452565	−	0.168899i
$562$	4.99320	−	8.64848i	0.210626	−	0.364814i
$563$	−1.08194	−	1.87398i	−0.0455984	−	0.0789787i	0.842325	−	0.538969i	$-0.181186\pi$
$563$	−1.08194	−	1.87398i	−0.0455984	−	0.0789787i	−0.887924	+	0.459991i	$0.847853\pi$
$564$	−0.833826	+	0.833826i	−0.0351104	+	0.0351104i
$565$	3.84187	−	14.3381i	0.161629	−	0.603207i
$566$	−22.9712	−	6.15511i	−0.965551	−	0.258719i
$567$	2.62532	+	0.328149i	0.110253	+	0.0137810i
$568$	1.75473	+	3.03927i	0.0736267	+	0.127525i
$569$	32.3405	+	18.6718i	1.35579	+	0.782763i	0.989053	−	0.147564i	$-0.0471431\pi$
$569$	32.3405	+	18.6718i	1.35579	+	0.782763i	0.366732	+	0.930326i	$0.380476\pi$
$570$	−4.79449	−	17.8933i	−0.200819	−	0.749466i
$571$			7.23701i			0.302860i	0.988468	+	0.151430i	$0.0483877\pi$
$571$			7.23701i			0.302860i	−0.988468	+	0.151430i	$0.951612\pi$
$572$	6.54600	+	3.67982i	0.273702	+	0.153861i
$573$			0.596308i			0.0249111i
$574$	16.3443	−	21.5917i	0.682198	−	0.901220i
$575$	−7.11753	+	12.3279i	−0.296821	+	0.514110i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	−18.7126	−	18.7126i	−0.779016	−	0.779016i	0.200647	−	0.979664i	$-0.435695\pi$
$577$	−18.7126	−	18.7126i	−0.779016	−	0.779016i	−0.979664	+	0.200647i	$0.935695\pi$
$578$	−12.6012	−	3.37649i	−0.524142	−	0.140443i
$579$	17.6852	+	4.73873i	0.734970	+	0.196935i
$580$	14.2261	−	14.2261i	0.590705	−	0.590705i
$581$	−13.5271	+	33.2722i	−0.561200	+	1.38036i
$582$	4.33666	+	2.50377i	0.179760	+	0.103785i
$583$	13.3002	−	3.56379i	0.550839	−	0.147597i
$584$	5.92229			0.245066
$585$	15.5173	−	0.178089i	0.641561	−	0.00736307i
$586$			26.0235i			1.07502i
$587$	21.4264	−	5.74119i	0.884363	−	0.236964i	0.212074	−	0.977254i	$-0.431978\pi$
$587$	21.4264	−	5.74119i	0.884363	−	0.236964i	0.672288	+	0.740289i	$0.265311\pi$
$588$	−4.88447	+	5.01417i	−0.201432	+	0.206781i
$589$	30.2311	−	17.4539i	1.24565	−	0.719177i
$590$	−23.8885	+	23.8885i	−0.983474	+	0.983474i
$591$	1.02956	−	3.84238i	0.0423506	−	0.158055i
$592$	0.582965	−	2.17565i	0.0239597	−	0.0894189i
$593$	−14.5024	+	14.5024i	−0.595541	+	0.595541i	−0.939123	−	0.343582i	$-0.888360\pi$
$593$	−14.5024	+	14.5024i	−0.595541	+	0.595541i	0.343582	+	0.939123i	$0.388360\pi$
$594$	1.80370	−	1.04137i	0.0740068	−	0.0427278i
$595$	22.4305	−	3.10264i	0.919559	−	0.127196i
$596$	16.6309	−	4.45624i	0.681229	−	0.182535i
$597$		−	11.3202i		−	0.463306i
$598$	3.79475	−	0.0435516i	0.155179	−	0.00178096i
$599$	24.1646			0.987340			0.493670	−	0.869649i	$-0.335655\pi$
$599$	24.1646			0.987340			0.493670	+	0.869649i	$0.335655\pi$
$600$	13.0636	−	3.50038i	0.533319	−	0.142903i
$601$	20.1514	+	11.6344i	0.821993	+	0.474578i	0.851103	−	0.524998i	$-0.175934\pi$
$601$	20.1514	+	11.6344i	0.821993	+	0.474578i	−0.0291101	+	0.999576i	$0.509267\pi$
$602$	8.84178	−	21.7478i	0.360364	−	0.886375i
$603$	9.60645	−	9.60645i	0.391205	−	0.391205i
$604$	−12.5913	−	3.37383i	−0.512333	−	0.137279i
$605$	27.6971	+	7.42143i	1.12605	+	0.301724i
$606$	−8.49437	−	8.49437i	−0.345060	−	0.345060i
$607$	−14.9344	+	8.62238i	−0.606169	+	0.349972i	−0.771464	−	0.636272i	$-0.780475\pi$
$607$	−14.9344	+	8.62238i	−0.606169	+	0.349972i	0.165296	+	0.986244i	$0.447142\pi$
$608$	−2.15200	+	3.72738i	−0.0872753	+	0.151165i
$609$	9.86077	+	7.46432i	0.399579	+	0.302469i
$610$		−	45.4399i		−	1.83981i
$611$	−3.70623	−	2.08345i	−0.149938	−	0.0842874i
$612$			1.98853i			0.0803815i
$613$	6.16332	+	23.0018i	0.248934	+	0.929034i	0.971365	+	0.237591i	$0.0763579\pi$
$613$	6.16332	+	23.0018i	0.248934	+	0.929034i	−0.722431	+	0.691443i	$0.756975\pi$
$614$	7.68344	+	4.43604i	0.310079	+	0.179024i
$615$	−22.0265	−	38.1510i	−0.888194	−	1.53840i
$616$	−0.683447	+	5.46785i	−0.0275369	+	0.220306i
$617$	−4.59036	−	1.22998i	−0.184801	−	0.0495173i	0.165232	−	0.986255i	$-0.447163\pi$
$617$	−4.59036	−	1.22998i	−0.184801	−	0.0495173i	−0.350033	+	0.936737i	$0.613830\pi$
$618$	−1.75017	+	6.53174i	−0.0704024	+	0.262745i
$619$	−5.95823	+	5.95823i	−0.239481	+	0.239481i	−0.816635	−	0.577154i	$-0.804163\pi$
$619$	−5.95823	+	5.95823i	−0.239481	+	0.239481i	0.577154	+	0.816635i	$0.304163\pi$
$620$	17.4539	+	30.2310i	0.700965	+	1.21411i
$621$	0.526272	−	0.911529i	0.0211185	−	0.0365784i
$622$	0.664740	+	2.48085i	0.0266537	+	0.0994728i
$623$	−8.24411	+	6.41217i	−0.330293	+	0.256898i
$624$	−2.57860	−	2.52008i	−0.103227	−	0.100884i
$625$	−90.2883			−3.61153
$626$	−1.12935	+	0.302609i	−0.0451380	+	0.0120947i
$627$	4.48206	−	7.76315i	0.178996	−	0.310030i
$628$	−2.56043	−	4.43480i	−0.102172	−	0.176968i
$629$	−3.16711	−	3.16711i	−0.126281	−	0.126281i
$630$	4.42656	+	10.4917i	0.176359	+	0.418001i
$631$	−10.7175	+	39.9983i	−0.426657	+	1.59231i	0.333620	+	0.942708i	$0.391730\pi$
$631$	−10.7175	+	39.9983i	−0.426657	+	1.59231i	−0.760277	+	0.649599i	$0.774937\pi$
$632$	−2.01897	−	2.01897i	−0.0803105	−	0.0803105i
$633$	1.73226	−	1.00012i	0.0688510	−	0.0397511i
$634$	6.29841	+	3.63639i	0.250142	+	0.144419i
$635$	19.5535	+	72.9745i	0.775955	+	2.89590i
$636$	−6.61122			−0.262152
$637$	−22.1610	−	12.0785i	−0.878052	−	0.478566i
$638$	9.73556			0.385434
$639$	0.908313	+	3.38987i	0.0359323	+	0.134101i
$640$	−3.72738	−	2.15200i	−0.147337	−	0.0850653i
$641$	9.98634	−	5.76561i	0.394437	−	0.227728i	−0.289644	−	0.957134i	$-0.593537\pi$
$641$	9.98634	−	5.76561i	0.394437	−	0.227728i	0.684081	+	0.729406i	$0.260204\pi$
$642$	12.2642	+	12.2642i	0.484028	+	0.484028i
$643$	−2.50134	+	9.33513i	−0.0986432	+	0.368142i	−0.997547	−	0.0700053i	$-0.977698\pi$
$643$	−2.50134	+	9.33513i	−0.0986432	+	0.368142i	0.898903	+	0.438147i	$0.144365\pi$
$644$	1.08252	+	2.56575i	0.0426571	+	0.101105i
$645$	−27.0048	−	27.0048i	−1.06331	−	1.06331i
$646$	4.27932	+	7.41201i	0.168368	+	0.291622i
$647$	18.7193	−	32.4227i	0.735930	−	1.27467i	−0.218385	−	0.975863i	$-0.570079\pi$
$647$	18.7193	−	32.4227i	0.735930	−	1.27467i	0.954314	−	0.298805i	$-0.0965880\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	−16.3480			−0.641716
$650$	24.8646	+	41.9475i	0.975268	+	1.64532i
$651$	−16.9382	+	13.1743i	−0.663861	+	0.516343i
$652$	5.59853	+	20.8940i	0.219255	+	0.818271i
$653$	4.82503	−	8.35720i	0.188818	−	0.327042i	−0.756038	−	0.654527i	$-0.772868\pi$
$653$	4.82503	−	8.35720i	0.188818	−	0.327042i	0.944856	+	0.327485i	$0.106201\pi$
$654$	−3.04784	−	5.27901i	−0.119180	−	0.206426i
$655$	25.8216	−	25.8216i	1.00893	−	1.00893i
$656$	−2.64911	+	9.88660i	−0.103430	+	0.386007i
$657$	5.72049	+	1.53280i	0.223178	+	0.0598003i
$658$	0.386956	−	3.09580i	0.0150851	−	0.120687i
$659$	21.2814	+	36.8605i	0.829007	+	1.43588i	0.898818	+	0.438323i	$0.144427\pi$
$659$	21.2814	+	36.8605i	0.829007	+	1.43588i	−0.0698102	+	0.997560i	$0.522239\pi$
$660$	7.76314	+	4.48205i	0.302180	+	0.174463i
$661$	9.64240	+	35.9859i	0.375046	+	1.39969i	0.853278	+	0.521456i	$0.174611\pi$
$661$	9.64240	+	35.9859i	0.375046	+	1.39969i	−0.478232	+	0.878233i	$0.658722\pi$
$662$		−	11.6684i		−	0.453504i
$663$	−6.90369	+	1.93502i	−0.268117	+	0.0751500i
$664$		−	13.5753i		−	0.526824i
$665$	39.0778	+	29.5807i	1.51537	+	1.14709i
$666$	1.12620	−	1.95064i	0.0436394	−	0.0755857i
$667$	4.26086	−	2.46001i	0.164981	−	0.0952519i
$668$	−1.34813	−	1.34813i	−0.0521607	−	0.0521607i
$669$	4.91474	+	1.31690i	0.190015	+	0.0509144i
$670$	56.4799	+	15.1338i	2.18201	+	0.584668i
$671$	15.5483	−	15.5483i	0.600236	−	0.600236i
$672$	0.996451	−	2.45094i	0.0384389	−	0.0945469i
$673$	−19.6533	−	11.3468i	−0.757579	−	0.437389i	0.0708467	−	0.997487i	$-0.477430\pi$
$673$	−19.6533	−	11.3468i	−0.757579	−	0.437389i	−0.828426	+	0.560099i	$0.810763\pi$
$674$	−20.3767	+	5.45992i	−0.784881	+	0.210308i
$675$	13.5244			0.520556
$676$	6.23990	−	11.4045i	0.239996	−	0.438636i
$677$			0.606031i			0.0232916i	0.999932	+	0.0116458i	$0.00370706\pi$
$677$			0.606031i			0.0232916i	−0.999932	+	0.0116458i	$0.996293\pi$
$678$	−3.33133	+	0.892628i	−0.127939	+	0.0342812i
$679$	−13.1238	+	1.81531i	−0.503644	+	0.0696654i
$680$	−7.41200	+	4.27932i	−0.284237	+	0.164104i
$681$	−2.26042	+	2.26042i	−0.0866196	+	0.0866196i
$682$	−4.37200	+	16.3165i	−0.167413	+	0.624792i
$683$	7.79907	−	29.1065i	0.298423	−	1.11373i	−0.640037	−	0.768344i	$-0.721081\pi$
$683$	7.79907	−	29.1065i	0.298423	−	1.11373i	0.938460	−	0.345387i	$-0.112252\pi$
$684$	−3.04339	+	3.04339i	−0.116367	+	0.116367i
$685$	60.7007	−	35.0456i	2.31926	−	1.33902i
$686$	2.05608	−	18.4058i	0.0785014	−	0.702736i
$687$	19.0946	−	5.11638i	0.728504	−	0.195202i
$688$			8.87327i			0.338290i
$689$	−6.43332	−	22.9525i	−0.245090	−	0.874422i
$690$	4.53015			0.172460
$691$	−3.20434	+	0.858600i	−0.121899	+	0.0326627i	−0.319253	−	0.947670i	$-0.603432\pi$
$691$	−3.20434	+	0.858600i	−0.121899	+	0.0326627i	0.197354	+	0.980332i	$0.436765\pi$
$692$	−13.0642	−	7.54265i	−0.496628	−	0.286728i
$693$	−2.07534	+	5.10465i	−0.0788358	+	0.193910i
$694$	−2.83937	+	2.83937i	−0.107781	+	0.107781i
$695$	16.4688	+	4.41281i	0.624699	+	0.167388i
$696$	−4.51513	−	1.20983i	−0.171146	−	0.0458583i
$697$	14.3920	+	14.3920i	0.545134	+	0.545134i
$698$	−20.1402	+	11.6280i	−0.762318	+	0.440125i
$699$	8.98070	−	15.5550i	0.339681	−	0.588345i
$700$	−21.5965	+	28.5301i	−0.816269	+	1.07834i
$701$			19.1737i			0.724180i	0.932143	+	0.362090i	$0.117937\pi$
$701$			19.1737i			0.724180i	−0.932143	+	0.362090i	$0.882063\pi$
$702$	−1.83849	−	3.10160i	−0.0693894	−	0.117063i
$703$		−	9.69437i		−	0.365630i
$704$	−0.539051	−	2.01177i	−0.0203163	−	0.0758213i
$705$	−4.39535	−	2.53766i	−0.165539	−	0.0955737i
$706$	−0.464951	−	0.805320i	−0.0174987	−	0.0303086i
$707$	31.5376	+	3.94201i	1.18609	+	0.148254i
$708$	7.58185	+	2.03155i	0.284943	+	0.0763503i
$709$	3.41413	−	12.7417i	0.128220	−	0.478524i	−0.871714	−	0.490015i	$-0.836991\pi$
$709$	3.41413	−	12.7417i	0.128220	−	0.478524i	0.999934	+	0.0114911i	$0.00365780\pi$
$710$	−10.6806	+	10.6806i	−0.400837	+	0.400837i
$711$	−1.42763	−	2.47273i	−0.0535403	−	0.0927345i
$712$	1.97377	−	3.41866i	0.0739700	−	0.128120i
$713$	2.20946	+	8.24581i	0.0827449	+	0.308808i
$714$	−3.23006	−	4.15288i	−0.120882	−	0.155418i
$715$	−8.00634	+	31.3132i	−0.299420	+	1.17105i
$716$	11.0332			0.412329
$717$	9.33432	−	2.50112i	0.348597	−	0.0934062i
$718$	17.9165	−	31.0323i	0.668639	−	1.15812i
$719$	−0.801273	−	1.38784i	−0.0298824	−	0.0517579i	0.850697	−	0.525656i	$-0.176180\pi$
$719$	−0.801273	−	1.38784i	−0.0298824	−	0.0517579i	−0.880580	+	0.473898i	$0.842847\pi$
$720$	−3.04339	−	3.04339i	−0.113420	−	0.113420i
$721$	−6.95472	−	16.4839i	−0.259007	−	0.613893i
$722$	0.123069	−	0.459298i	0.00458014	−	0.0170933i
$723$	2.67329	+	2.67329i	0.0994205	+	0.0994205i
$724$	−9.23365	+	5.33105i	−0.343166	+	0.198127i
$725$	54.7491	+	31.6094i	2.03333	+	1.17394i
$726$	−1.72431	−	6.43521i	−0.0639951	−	0.238833i
$727$	−19.8575			−0.736475			−0.368237	−	0.929732i	$-0.620039\pi$
$727$	−19.8575			−0.736475			−0.368237	+	0.929732i	$0.620039\pi$
$728$	9.47869	+	1.07445i	0.351304	+	0.0398218i
$729$	−1.00000			−0.0370370
$730$	6.59718	+	24.6210i	0.244173	+	0.911265i
$731$	15.2808	+	8.82238i	0.565181	+	0.326307i
$732$	−9.14314	+	5.27879i	−0.337940	+	0.195110i
$733$	−1.88875	−	1.88875i	−0.0697627	−	0.0697627i	0.671365	−	0.741127i	$-0.265709\pi$
$733$	−1.88875	−	1.88875i	−0.0697627	−	0.0697627i	−0.741127	+	0.671365i	$0.765709\pi$
$734$	4.60267	−	17.1774i	0.169888	−	0.634029i
$735$	−26.2867	−	14.7209i	−0.969601	−	0.542988i
$736$	−0.744260	−	0.744260i	−0.0274338	−	0.0274338i
$737$	14.1476	+	24.5043i	0.521132	+	0.902628i
$738$	−5.11768	+	8.86408i	−0.188384	+	0.326291i
$739$	−3.79946	+	1.01806i	−0.139765	+	0.0374501i	−0.328024	−	0.944670i	$-0.606383\pi$
$739$	−3.79946	+	1.01806i	−0.139765	+	0.0374501i	0.188258	+	0.982120i	$0.439716\pi$
$740$	9.69435			0.356371
$741$	−13.5274	−	7.60442i	−0.496942	−	0.279355i
$742$	13.8070	−	10.7389i	0.506871	−	0.394238i
$743$	5.64117	+	21.0531i	0.206955	+	0.772365i	0.988845	+	0.148949i	$0.0475890\pi$
$743$	5.64117	+	21.0531i	0.206955	+	0.772365i	−0.781890	+	0.623416i	$0.785744\pi$
$744$	4.05527	−	7.02394i	0.148673	−	0.257510i
$745$	37.0523	+	64.1764i	1.35749	+	2.35124i
$746$	−16.8270	+	16.8270i	−0.616079	+	0.616079i
$747$	3.51355	−	13.1127i	0.128554	−	0.479770i
$748$	−4.00046	−	1.07192i	−0.146271	−	0.0391933i
$749$	−45.5340	−	5.69147i	−1.66378	−	0.207962i
$750$	18.3446	+	31.7738i	0.669850	+	1.16021i
$751$	−45.7093	−	26.3903i	−1.66796	−	0.962995i	−0.968738	−	0.248085i	$-0.920199\pi$
$751$	−45.7093	−	26.3903i	−1.66796	−	0.962995i	−0.699217	−	0.714909i	$-0.746468\pi$
$752$	0.305202	+	1.13903i	0.0111296	+	0.0415361i
$753$			7.85219i			0.286150i
$754$	−0.193415	−	16.8527i	−0.00704377	−	0.613740i
$755$		−	56.1047i		−	2.04186i
$756$	1.59685	−	2.10952i	0.0580767	−	0.0767226i
$757$	−2.62912	+	4.55376i	−0.0955569	+	0.165509i	−0.909841	−	0.414957i	$-0.863797\pi$
$757$	−2.62912	+	4.55376i	−0.0955569	+	0.165509i	0.814284	+	0.580467i	$0.197130\pi$
$758$	−11.1681	+	6.44789i	−0.405643	+	0.234198i
$759$	1.55010	+	1.55010i	0.0562650	+	0.0562650i
$760$	−17.8933	−	4.79449i	−0.649057	−	0.173914i
$761$	−35.3805	−	9.48018i	−1.28254	−	0.343656i	−0.447719	−	0.894174i	$-0.647764\pi$
$761$	−35.3805	−	9.48018i	−1.28254	−	0.343656i	−0.834823	+	0.550518i	$0.814430\pi$
$762$	12.4119	−	12.4119i	0.449637	−	0.449637i
$763$	14.9401	+	6.07405i	0.540869	+	0.219895i
$764$	0.516418	+	0.298154i	0.0186833	+	0.0107868i
$765$	−8.26701	+	2.21514i	−0.298894	+	0.0800885i
$766$	−17.0514			−0.616093
$767$	0.324785	+	28.2992i	0.0117273	+	1.02183i
$768$			1.00000i			0.0360844i
$769$	−31.3561	+	8.40185i	−1.13073	+	0.302979i	−0.775219	−	0.631693i	$-0.782360\pi$
$769$	−31.3561	+	8.40185i	−1.13073	+	0.302979i	−0.355513	+	0.934671i	$0.615694\pi$
$770$	−23.4931	+	3.24963i	−0.846632	+	0.117108i
$771$	−1.29299	+	0.746507i	−0.0465658	+	0.0268848i
$772$	12.9464	−	12.9464i	0.465953	−	0.465953i
$773$	4.89978	−	18.2862i	0.176233	−	0.657710i	−0.820105	−	0.572212i	$-0.806085\pi$
$773$	4.89978	−	18.2862i	0.176233	−	0.657710i	0.996338	−	0.0854977i	$-0.0272480\pi$
$774$	−2.29657	+	8.57092i	−0.0825485	+	0.308075i
$775$	−77.5629	+	77.5629i	−2.78614	+	2.78614i
$776$	4.33666	−	2.50377i	0.155677	−	0.0898801i
$777$	0.816532	+	5.90309i	0.0292929	+	0.211772i
$778$	10.5828	−	2.83564i	0.379410	−	0.101663i
$779$			44.0531i			1.57837i
$780$	7.60441	−	13.5274i	0.272282	−	0.484359i
$781$	−7.30926			−0.261546
$782$	−2.02170	+	0.541712i	−0.0722957	+	0.0193716i
$783$	−4.04816	−	2.33721i	−0.144669	−	0.0835249i
$784$	1.90016	+	6.73716i	0.0678629	+	0.240613i
$785$	15.5848	−	15.5848i	0.556245	−	0.556245i
$786$	−8.19539	−	2.19595i	−0.292320	−	0.0783269i
$787$	−0.0736327	−	0.0197298i	−0.00262472	−	0.000703292i	0.257506	−	0.966277i	$-0.417099\pi$
$787$	−0.0736327	−	0.0197298i	−0.00262472	−	0.000703292i	−0.260131	+	0.965573i	$0.583766\pi$
$788$	−2.81282	−	2.81282i	−0.100203	−	0.100203i
$789$	9.85819	−	5.69163i	0.350961	−	0.202627i
$790$	6.14452	−	10.6426i	0.218612	−	0.378648i
$791$	5.50728	−	7.27542i	0.195816	−	0.258684i
$792$		−	2.08273i		−	0.0740068i
$793$	−27.2238	−	26.6060i	−0.966745	−	0.944807i
$794$			20.0107i			0.710154i
$795$	−7.36462	−	27.4851i	−0.261196	−	0.974797i
$796$	−9.80361	−	5.66011i	−0.347480	−	0.200617i
$797$	−8.29289	−	14.3637i	−0.293749	−	0.508788i	0.680944	−	0.732335i	$-0.261570\pi$
$797$	−8.29289	−	14.3637i	−0.293749	−	0.508788i	−0.974693	+	0.223547i	$0.928236\pi$
$798$	1.41236	−	11.2994i	0.0499969	−	0.399995i
$799$	2.26499	+	0.606902i	0.0801296	+	0.0214707i
$800$	3.50038	−	13.0636i	0.123757	−	0.461868i
$801$	2.79133	−	2.79133i	0.0986267	−	0.0986267i
$802$	12.8014	+	22.1727i	0.452033	+	0.782944i
$803$	−6.16728	+	10.6820i	−0.217639	+	0.376961i
$804$	−3.51620	−	13.1227i	−0.124007	−	0.462800i
$805$	−9.46085	+	7.35853i	−0.333451	+	0.259354i
$806$	28.3315	+	7.24398i	0.997936	+	0.255158i
$807$	18.9759			0.667984
$808$	−11.6035	+	3.10916i	−0.408211	+	0.109380i
$809$	4.96420	−	8.59825i	0.174532	−	0.302299i	−0.765467	−	0.643475i	$-0.777492\pi$
$809$	4.96420	−	8.59825i	0.174532	−	0.302299i	0.939999	+	0.341176i	$0.110825\pi$
$810$	−2.15200	−	3.72738i	−0.0756136	−	0.130967i
$811$	−9.10336	−	9.10336i	−0.319662	−	0.319662i	0.528975	−	0.848637i	$-0.322576\pi$
$811$	−9.10336	−	9.10336i	−0.319662	−	0.319662i	−0.848637	+	0.528975i	$0.822576\pi$
$812$	11.3947	−	4.80752i	0.399875	−	0.168711i
$813$	−7.70538	+	28.7569i	−0.270240	+	1.00855i
$814$	3.31715	+	3.31715i	0.116266	+	0.116266i
$815$	−80.6270	+	46.5500i	−2.82424	+	1.63058i
$816$	1.72212	+	0.994265i	0.0602862	+	0.0348062i
$817$	9.88446	+	36.8893i	0.345814	+	1.29059i
$818$	−32.3674			−1.13170
$819$	8.87762	+	3.49110i	0.310209	+	0.121989i
$820$	−44.0530			−1.53840
$821$	−2.00015	−	7.46466i	−0.0698057	−	0.260518i	0.922200	−	0.386714i	$-0.126390\pi$
$821$	−2.00015	−	7.46466i	−0.0698057	−	0.260518i	−0.992005	+	0.126196i	$0.959723\pi$
$822$	−14.1033	−	8.14256i	−0.491910	−	0.284004i
$823$	4.61054	−	2.66189i	0.160713	−	0.0927878i	−0.417486	−	0.908683i	$-0.637089\pi$
$823$	4.61054	−	2.66189i	0.160713	−	0.0927878i	0.578200	+	0.815895i	$0.303756\pi$
$824$	4.78157	+	4.78157i	0.166574	+	0.166574i
$825$	−7.29037	+	27.2080i	−0.253818	+	0.947262i
$826$	−19.1340	+	8.07282i	−0.665758	+	0.280889i
$827$	−4.15086	−	4.15086i	−0.144340	−	0.144340i	0.631244	−	0.775584i	$-0.282545\pi$
$827$	−4.15086	−	4.15086i	−0.144340	−	0.144340i	−0.775584	+	0.631244i	$0.782545\pi$
$828$	−0.526272	−	0.911529i	−0.0182892	−	0.0316778i
$829$	−23.7170	+	41.0790i	−0.823724	+	1.42673i	0.0791670	+	0.996861i	$0.474774\pi$
$829$	−23.7170	+	41.0790i	−0.823724	+	1.42673i	−0.902891	+	0.429870i	$0.858559\pi$
$830$	56.4373	−	15.1223i	1.95897	−	0.524904i
$831$	−33.1470			−1.14986
$832$	−3.47176	+	0.973091i	−0.120361	+	0.0337359i
$833$	13.4914	+	3.42622i	0.467451	+	0.118712i
$834$	−1.02528	−	3.82640i	−0.0355026	−	0.132497i
$835$	4.10288	−	7.10640i	0.141986	−	0.245927i
$836$	−4.48206	−	7.76315i	−0.155015	−	0.268494i
$837$	5.73502	−	5.73502i	0.198231	−	0.198231i
$838$	−6.76543	+	25.2489i	−0.233708	+	0.872210i
$839$	−30.0745	−	8.05843i	−1.03829	−	0.278208i	−0.300883	−	0.953661i	$-0.597281\pi$
$839$	−30.0745	−	8.05843i	−1.03829	−	0.278208i	−0.737403	+	0.675453i	$0.763948\pi$
$840$	11.2994	+	1.41235i	0.389866	+	0.0487308i
$841$	3.57495	+	6.19199i	0.123274	+	0.213517i
$842$	−17.5412	−	10.1274i	−0.604508	−	0.349013i
$843$	−2.58467	−	9.64613i	−0.0890208	−	0.332230i
$844$		−	2.00024i		−	0.0688510i
$845$	54.3636	+	13.2373i	1.87017	+	0.455376i
$846$			1.17921i			0.0405420i
$847$	14.0541	+	10.6385i	0.482904	+	0.365544i
$848$	−3.30561	+	5.72548i	−0.113515	+	0.196614i
$849$	−20.5954	+	11.8908i	−0.706832	+	0.408090i
$850$	−19.0168	−	19.0168i	−0.652269	−	0.652269i
$851$	2.28997	+	0.613596i	0.0784992	+	0.0210338i
$852$	3.38987	+	0.908313i	0.116135	+	0.0311183i
$853$	3.19682	−	3.19682i	0.109457	−	0.109457i	−0.650257	−	0.759714i	$-0.725339\pi$
$853$	3.19682	−	3.19682i	0.109457	−	0.109457i	0.759714	+	0.650257i	$0.225339\pi$
$854$	10.5201	−	25.8760i	0.359991	−	0.885457i
$855$	−16.0427	−	9.26224i	−0.548647	−	0.316762i
$856$	16.7532	−	4.48900i	0.572611	−	0.153431i
$857$	51.4392			1.75713			0.878565	−	0.477623i	$-0.158501\pi$
$857$	51.4392			1.75713			0.878565	+	0.477623i	$0.158501\pi$
$858$	7.23075	−	2.02669i	0.246854	−	0.0691901i
$859$		−	38.4423i		−	1.31164i	−0.754919	−	0.655818i	$-0.772324\pi$
$859$		−	38.4423i		−	1.31164i	0.754919	−	0.655818i	$-0.227676\pi$
$860$	−36.8893	+	9.88445i	−1.25791	+	0.337057i
$861$	−3.71048	−	26.8248i	−0.126453	−	0.914187i
$862$	−15.1069	+	8.72195i	−0.514542	+	0.297071i
$863$	−11.7566	+	11.7566i	−0.400201	+	0.400201i	−0.878304	−	0.478103i	$-0.841325\pi$
$863$	−11.7566	+	11.7566i	−0.400201	+	0.400201i	0.478103	+	0.878304i	$0.341325\pi$
$864$	−0.258819	+	0.965926i	−0.00880520	+	0.0328615i
$865$	16.8044	−	62.7148i	0.571366	−	2.13237i
$866$	−4.97923	+	4.97923i	−0.169201	+	0.169201i
$867$	−11.2980	+	6.52288i	−0.383699	+	0.221528i
$868$	2.94020	+	21.2561i	0.0997969	+	0.721479i
$869$	5.74412	−	1.53913i	0.194856	−	0.0522115i
$870$		−	20.1187i		−	0.682087i
$871$	42.1371	−	24.9769i	1.42776	−	0.846312i
$872$	−6.09568			−0.206426
$873$	4.83691	−	1.29605i	0.163705	−	0.0438646i
$874$	−3.92323	−	2.26508i	−0.132705	−	0.0766174i
$875$	−89.9229	−	36.5590i	−3.03995	−	1.23592i
$876$	4.18769	−	4.18769i	0.141489	−	0.141489i
$877$	−44.5674	−	11.9418i	−1.50494	−	0.403246i	−0.590186	−	0.807267i	$-0.700945\pi$
$877$	−44.5674	−	11.9418i	−1.50494	−	0.403246i	−0.914750	+	0.404021i	$0.867612\pi$
$878$	−2.33412	−	0.625426i	−0.0787728	−	0.0211071i
$879$	18.4014	+	18.4014i	0.620663	+	0.620663i
$880$	7.76314	−	4.48205i	0.261695	−	0.151090i
$881$	−17.3427	+	30.0384i	−0.584290	+	1.01202i	0.410674	+	0.911782i	$0.365293\pi$
$881$	−17.3427	+	30.0384i	−0.584290	+	1.01202i	−0.994964	+	0.100237i	$0.968040\pi$
$882$	0.0917094	+	6.99940i	0.00308802	+	0.235682i
$883$			1.08651i			0.0365640i	0.999833	+	0.0182820i	$0.00581966\pi$
$883$			1.08651i			0.0365640i	−0.999833	+	0.0182820i	$0.994180\pi$
$884$	−1.77607	+	6.94628i	−0.0597356	+	0.233629i
$885$			33.7834i			1.13562i
$886$	5.64753	+	21.0769i	0.189733	+	0.708092i
$887$	−11.4530	−	6.61237i	−0.384553	−	0.222022i	0.295245	−	0.955422i	$-0.404599\pi$
$887$	−11.4530	−	6.61237i	−0.384553	−	0.222022i	−0.679797	+	0.733400i	$0.737932\pi$
$888$	−1.12620	−	1.95064i	−0.0377929	−	0.0654591i
$889$	−5.76004	+	46.0826i	−0.193186	+	1.54556i
$890$	16.4113	+	4.39739i	0.550107	+	0.147401i
$891$	0.539051	−	2.01177i	0.0180589	−	0.0673967i
$892$	3.59784	−	3.59784i	0.120465	−	0.120465i
$893$	2.53766	+	4.39536i	0.0849196	+	0.147085i
$894$	8.60880	−	14.9109i	0.287921	−	0.498694i
$895$	12.2905	+	45.8687i	0.410826	+	1.53322i
$896$	−1.62435	−	2.08842i	−0.0542656	−	0.0697692i
$897$	2.65250	−	2.71409i	0.0885643	−	0.0906208i
$898$	23.4336			0.781988
$899$	36.6202	−	9.81235i	1.22135	−	0.327260i
$900$	6.76222	−	11.7125i	0.225407	−	0.390417i
$901$	6.57330	+	11.3853i	0.218988	+	0.379299i
$902$	−15.0738	−	15.0738i	−0.501902	−	0.501902i
$903$	−9.12594	−	21.6301i	−0.303692	−	0.719805i
$904$	−0.892628	+	3.33133i	−0.0296884	+	0.110798i
$905$	−32.4489	−	32.4489i	−1.07864	−	1.07864i
$906$	−11.2891	+	6.51774i	−0.375054	+	0.216537i
$907$	25.1361	+	14.5123i	0.834631	+	0.481875i	0.855436	−	0.517909i	$-0.173289\pi$
$907$	25.1361	+	14.5123i	0.834631	+	0.481875i	−0.0208044	+	0.999784i	$0.506623\pi$
$908$	0.827373	+	3.08780i	0.0274573	+	0.102472i
$909$	−12.0129			−0.398441
$910$	6.09200	+	40.6031i	0.201948	+	1.34598i
$911$	11.0947			0.367584			0.183792	−	0.982965i	$-0.441163\pi$
$911$	11.0947			0.367584			0.183792	+	0.982965i	$0.441163\pi$
$912$	1.11396	+	4.15735i	0.0368869	+	0.137664i
$913$	24.4858	+	14.1369i	0.810362	+	0.467863i
$914$	−12.5279	+	7.23297i	−0.414385	+	0.239245i
$915$	−32.1308	−	32.1308i	−1.06221	−	1.06221i
$916$	5.11638	−	19.0946i	0.169050	−	0.630903i
$917$	20.6824	−	8.72610i	0.682993	−	0.288161i
$918$	1.40610	+	1.40610i	0.0464083	+	0.0464083i
$919$	17.0810	+	29.5852i	0.563451	+	0.975925i	0.997192	+	0.0748876i	$0.0238598\pi$
$919$	17.0810	+	29.5852i	0.563451	+	0.975925i	−0.433741	+	0.901037i	$0.642807\pi$
$920$	2.26507	−	3.92322i	0.0746773	−	0.129345i
$921$	8.56977	−	2.29626i	0.282383	−	0.0756644i
$922$	−38.3201			−1.26201
$923$	0.145212	+	12.6527i	0.00477972	+	0.416468i
$924$	3.38308	+	4.34962i	0.111295	+	0.143092i
$925$	7.88427	+	29.4245i	0.259233	+	0.967472i
$926$	3.50450	−	6.06998i	0.115165	−	0.199472i
$927$	3.38108	+	5.85620i	0.111049	+	0.192343i
$928$	−3.30531	+	3.30531i	−0.108502	+	0.108502i
$929$	5.64383	−	21.0631i	0.185168	−	0.691056i	−0.809426	−	0.587221i	$-0.800222\pi$
$929$	5.64383	−	21.0631i	0.185168	−	0.691056i	0.994595	−	0.103835i	$-0.0331115\pi$
$930$	33.7183	+	9.03480i	1.10567	+	0.296263i
$931$	15.4046	+	25.8921i	0.504865	+	0.848578i
$932$	−8.98070	−	15.5550i	−0.294173	−	0.509522i
$933$	2.22426	+	1.28418i	0.0728192	+	0.0420422i
$934$	−5.08139	−	18.9640i	−0.166268	−	0.620521i
$935$		−	17.8254i		−	0.582952i
$936$	−3.60531	+	0.0413775i	−0.117843	+	0.00135247i
$937$			42.7694i			1.39721i	0.715506	+	0.698607i	$0.246196\pi$
$937$			42.7694i			1.39721i	−0.715506	+	0.698607i	$0.753804\pi$
$938$	28.6591	+	21.6941i	0.935751	+	0.708337i
$939$	−0.584596	+	1.01255i	−0.0190776	+	0.0330433i
$940$	−4.39535	+	2.53766i	−0.143361	+	0.0827693i
$941$	19.6030	+	19.6030i	0.639040	+	0.639040i	0.950319	−	0.311279i	$-0.100757\pi$
$941$	19.6030	+	19.6030i	0.639040	+	0.639040i	−0.311279	+	0.950319i	$0.600757\pi$
$942$	−4.94637	−	1.32538i	−0.161162	−	0.0431831i
$943$	−10.4061	−	2.78830i	−0.338868	−	0.0907995i
$944$	5.55030	−	5.55030i	0.180647	−	0.180647i
$945$	10.5488	+	4.28873i	0.343154	+	0.139512i
$946$	−16.0047	−	9.24033i	−0.520359	−	0.300429i
$947$	−15.5080	+	4.15536i	−0.503943	+	0.135031i	−0.501829	−	0.864967i	$-0.667339\pi$
$947$	−15.5080	+	4.15536i	−0.503943	+	0.135031i	−0.00211374	+	0.999998i	$0.500673\pi$
$948$	−2.85526			−0.0927345
$949$	18.6137	+	10.4636i	0.604225	+	0.339664i
$950$		−	58.2093i		−	1.88856i
$951$	7.02497	−	1.88233i	0.227800	−	0.0610389i
$952$	−5.21153	+	0.720874i	−0.168907	+	0.0233636i
$953$	7.79284	−	4.49920i	0.252435	−	0.145743i	−0.368444	−	0.929650i	$-0.620109\pi$
$953$	7.79284	−	4.49920i	0.252435	−	0.145743i	0.620879	+	0.783907i	$0.286776\pi$
$954$	−4.67484	+	4.67484i	−0.151353	+	0.151353i
$955$	−0.664262	+	2.47906i	−0.0214950	+	0.0802205i
$956$	2.50112	−	9.33432i	0.0808922	−	0.301894i
$957$	6.88408	−	6.88408i	0.222531	−	0.222531i
$958$	−6.93294	+	4.00273i	−0.223993	+	0.129322i
$959$	42.6800	−	5.90361i	1.37821	−	0.190638i
$960$	−4.15735	+	1.11396i	−0.134178	+	0.0359528i
$961$			34.7809i			1.12196i
$962$	5.67624	−	5.80805i	0.183009	−	0.187259i
$963$	17.3442			0.558908
$964$	3.65178	−	0.978490i	0.117616	−	0.0315151i
$965$	68.2446	+	39.4011i	2.19687	+	1.26837i
$966$	2.57972	+	1.04881i	0.0830010	+	0.0337448i
$967$	41.0307	−	41.0307i	1.31946	−	1.31946i	0.405256	−	0.914203i	$-0.367183\pi$
$967$	41.0307	−	41.0307i	1.31946	−	1.31946i	0.914203	−	0.405256i	$-0.132817\pi$
$968$	−6.43521	−	1.72431i	−0.206835	−	0.0554214i
$969$	8.26702	+	2.21514i	0.265575	+	0.0711606i
$970$	15.2399	+	15.2399i	0.489324	+	0.489324i
$971$	8.65603	−	4.99756i	0.277785	−	0.160379i	−0.354635	−	0.935005i	$-0.615395\pi$
$971$	8.65603	−	4.99756i	0.277785	−	0.160379i	0.632420	+	0.774625i	$0.282062\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	8.35662	+	6.32572i	0.267901	+	0.202793i
$974$		−	7.53321i		−	0.241380i
$975$	47.2432	+	12.0794i	1.51299	+	0.386852i
$976$			10.5576i			0.337940i
$977$	−11.1595	−	41.6477i	−0.357023	−	1.33243i	−0.877920	−	0.478808i	$-0.841069\pi$
$977$	−11.1595	−	41.6477i	−0.357023	−	1.33243i	0.520897	−	0.853619i	$-0.325597\pi$
$978$	18.7330	+	10.8155i	0.599016	+	0.345842i
$979$	4.11083	+	7.12017i	0.131383	+	0.227562i
$980$	−25.8920	+	15.4046i	−0.827091	+	0.492080i
$981$	−5.88798	−	1.57768i	−0.187989	−	0.0503714i
$982$	−6.56818	+	24.5128i	−0.209599	+	0.782234i
$983$	−6.14884	+	6.14884i	−0.196118	+	0.196118i	−0.798333	−	0.602216i	$-0.794285\pi$
$983$	−6.14884	+	6.14884i	−0.196118	+	0.196118i	0.602216	+	0.798333i	$0.294285\pi$
$984$	5.11768	+	8.86408i	0.163146	+	0.282577i
$985$	8.56051	−	14.8272i	0.272760	−	0.472435i
$986$	2.40578	+	8.97848i	0.0766155	+	0.285933i
$987$	−1.91544	−	2.46268i	−0.0609692	−	0.0783880i
$988$	−13.3493	+	7.91288i	−0.424699	+	0.251742i
$989$	−9.33950			−0.296979
$990$	8.65865	−	2.32008i	0.275190	−	0.0737369i
$991$	16.9678	−	29.3891i	0.539000	−	0.933575i	−0.459958	−	0.887940i	$-0.652136\pi$
$991$	16.9678	−	29.3891i	0.539000	−	0.933575i	0.998958	−	0.0456345i	$-0.0145310\pi$
$992$	−4.05527	−	7.02394i	−0.128755	−	0.223010i
$993$	−8.25078	−	8.25078i	−0.261831	−	0.261831i
$994$	−8.55489	+	3.60939i	−0.271345	+	0.114483i
$995$	12.6103	−	47.0621i	0.399772	−	1.49197i
$996$	−9.59920	−	9.59920i	−0.304162	−	0.304162i
$997$	9.72285	−	5.61349i	0.307926	−	0.177781i	−0.338072	−	0.941120i	$-0.609775\pi$
$997$	9.72285	−	5.61349i	0.307926	−	0.177781i	0.645998	+	0.763339i	$0.276441\pi$
$998$	5.82457	+	3.36282i	0.184373	+	0.106448i
$999$	−0.582965	−	2.17565i	−0.0184442	−	0.0688347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.a.97.1	✓	40
7.6	odd	2		546.2.bx.b.97.5	yes	40
13.11	odd	12		546.2.bx.b.349.5	yes	40
91.76	even	12	inner	546.2.bx.a.349.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.97.1	✓	40	1.1	even	1	trivial
546.2.bx.a.349.1	yes	40	91.76	even	12	inner
546.2.bx.b.97.5	yes	40	7.6	odd	2
546.2.bx.b.349.5	yes	40	13.11	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.bx (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-3.04339 - 3.04339i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-1.02848 - 2.43767i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-3.04339 - 3.04339i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-1.02848 - 2.43767i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.15200 + 3.72738i) q^{10} +(-2.01177 + 0.539051i) q^{11} +1.00000 q^{12} +(0.973091 + 3.47176i) q^{13} +(-2.08842 + 1.62435i) q^{14} +(1.11396 + 4.15735i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.994265 - 1.72212i) q^{17} +(0.707107 - 0.707107i) q^{18} +(1.11396 - 4.15735i) q^{19} +(4.15735 + 1.11396i) q^{20} +(-0.328149 + 2.62532i) q^{21} +(1.04137 + 1.80370i) q^{22} +(0.911529 + 0.526272i) q^{23} +(-0.258819 - 0.965926i) q^{24} +13.5244i q^{25} +(3.10160 - 1.83849i) q^{26} -1.00000i q^{27} +(2.10952 + 1.59685i) q^{28} +(2.33721 - 4.04816i) q^{29} +(3.72738 - 2.15200i) q^{30} +(5.73502 + 5.73502i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(2.01177 + 0.539051i) q^{33} +(-1.40610 + 1.40610i) q^{34} +(-4.28873 + 10.5488i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(2.17565 - 0.582965i) q^{37} -4.30401 q^{38} +(0.893156 - 3.49318i) q^{39} -4.30400i q^{40} +(-9.88660 + 2.64911i) q^{41} +(2.62080 - 0.362516i) q^{42} +(-7.68448 + 4.43663i) q^{43} +(1.47272 - 1.47272i) q^{44} +(1.11396 - 4.15735i) q^{45} +(0.272418 - 1.01668i) q^{46} +(-0.833826 + 0.833826i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-4.88447 + 5.01417i) q^{49} +(13.0636 - 3.50038i) q^{50} +1.98853i q^{51} +(-2.57860 - 2.52008i) q^{52} -6.61122 q^{53} +(-0.965926 + 0.258819i) q^{54} +(7.76314 + 4.48205i) q^{55} +(0.996451 - 2.45094i) q^{56} +(-3.04339 + 3.04339i) q^{57} +(-4.51513 - 1.20983i) q^{58} +(7.58185 + 2.03155i) q^{59} +(-3.04339 - 3.04339i) q^{60} +(-9.14314 + 5.27879i) q^{61} +(4.05527 - 7.02394i) q^{62} +(1.59685 - 2.10952i) q^{63} +1.00000i q^{64} +(7.60441 - 13.5274i) q^{65} -2.08273i q^{66} +(-3.51620 - 13.1227i) q^{67} +(1.72212 + 0.994265i) q^{68} +(-0.526272 - 0.911529i) q^{69} +(11.2994 + 1.41235i) q^{70} +(3.38987 + 0.908313i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(4.18769 - 4.18769i) q^{73} +(-1.12620 - 1.95064i) q^{74} +(6.76222 - 11.7125i) q^{75} +(1.11396 + 4.15735i) q^{76} +(3.38308 + 4.34962i) q^{77} +(-3.60531 + 0.0413775i) q^{78} -2.85526 q^{79} +(-4.15735 + 1.11396i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.11768 + 8.86408i) q^{82} +(-9.59920 - 9.59920i) q^{83} +(-1.02848 - 2.43767i) q^{84} +(-2.21514 + 8.26701i) q^{85} +(6.27435 + 6.27435i) q^{86} +(-4.04816 + 2.33721i) q^{87} +(-1.80370 - 1.04137i) q^{88} +(-1.02170 - 3.81303i) q^{89} -4.30400 q^{90} +(7.46220 - 5.94269i) q^{91} -1.05254 q^{92} +(-2.09916 - 7.83418i) q^{93} +(1.02122 + 0.589604i) q^{94} +(-16.0427 + 9.26224i) q^{95} +(0.707107 + 0.707107i) q^{96} +(1.29605 - 4.83691i) q^{97} +(6.10751 + 3.42028i) q^{98} +(-1.47272 - 1.47272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 + 20 * q^9	\( 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39} - 4 q^{41} + 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} + 32 q^{53} - 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} + 84 q^{59} - 48 q^{61} - 4 q^{62} - 4 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 36 q^{70} - 40 q^{71} - 48 q^{73} + 8 q^{74} + 36 q^{75} + 16 q^{76} - 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} + 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{89} - 48 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} + 8 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

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