LMFDB - Embedded newform 546.2.i.a.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(79,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.i (of order $3$, degree $2$, 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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.79
Dual form			546.2.i.a.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +3.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(2.00000 - 3.46410i) q^{19} +3.00000 q^{20} +(2.50000 - 0.866025i) q^{21} +3.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} +(-0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} -9.00000 q^{29} +(-1.50000 + 2.59808i) q^{30} +(-2.50000 - 4.33013i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +6.00000 q^{34} +(-6.00000 - 5.19615i) q^{35} +1.00000 q^{36} +(2.00000 - 3.46410i) q^{37} +(2.00000 + 3.46410i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-1.50000 + 2.59808i) q^{40} -12.0000 q^{41} +(-0.500000 + 2.59808i) q^{42} -4.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(-1.50000 - 2.59808i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(6.00000 - 10.3923i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +4.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(4.50000 + 7.79423i) q^{53} +(-0.500000 + 0.866025i) q^{54} +9.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} -4.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(4.50000 + 7.79423i) q^{59} +(-1.50000 - 2.59808i) q^{60} +(-4.00000 + 6.92820i) q^{61} +5.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.50000 + 2.59808i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +6.00000 q^{69} +(7.50000 - 2.59808i) q^{70} +6.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-2.00000 + 3.46410i) q^{75} -4.00000 q^{76} +(7.50000 - 2.59808i) q^{77} +1.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.00000 - 10.3923i) q^{82} +3.00000 q^{83} +(-2.00000 - 1.73205i) q^{84} +18.0000 q^{85} +(2.00000 - 3.46410i) q^{86} +(4.50000 + 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{88} +3.00000 q^{90} +(-0.500000 + 2.59808i) q^{91} +6.00000 q^{92} +(-2.50000 + 4.33013i) q^{93} +(6.00000 + 10.3923i) q^{94} +(6.00000 + 10.3923i) q^{95} +(-0.500000 + 0.866025i) q^{96} +5.00000 q^{97} +(5.50000 - 4.33013i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} - 3 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - q^3 - q^4 - 3 * q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - q^{3} - q^{4} - 3 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + 2 q^{13} - 4 q^{14} + 6 q^{15} - q^{16} - 6 q^{17} - q^{18} + 4 q^{19} + 6 q^{20} + 5 q^{21} + 6 q^{22} - 6 q^{23} - q^{24} - 4 q^{25} - q^{26} + 2 q^{27} + 5 q^{28} - 18 q^{29} - 3 q^{30} - 5 q^{31} - q^{32} - 3 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 4 q^{37} + 4 q^{38} - q^{39} - 3 q^{40} - 24 q^{41} - q^{42} - 8 q^{43} - 3 q^{44} - 3 q^{45} - 6 q^{46} + 12 q^{47} + 2 q^{48} - 13 q^{49} + 8 q^{50} - 6 q^{51} - q^{52} + 9 q^{53} - q^{54} + 18 q^{55} - q^{56} - 8 q^{57} + 9 q^{58} + 9 q^{59} - 3 q^{60} - 8 q^{61} + 10 q^{62} - 4 q^{63} + 2 q^{64} - 3 q^{65} - 3 q^{66} + 4 q^{67} - 6 q^{68} + 12 q^{69} + 15 q^{70} + 12 q^{71} - q^{72} - 14 q^{73} + 4 q^{74} - 4 q^{75} - 8 q^{76} + 15 q^{77} + 2 q^{78} + q^{79} - 3 q^{80} - q^{81} + 12 q^{82} + 6 q^{83} - 4 q^{84} + 36 q^{85} + 4 q^{86} + 9 q^{87} - 3 q^{88} + 6 q^{90} - q^{91} + 12 q^{92} - 5 q^{93} + 12 q^{94} + 12 q^{95} - q^{96} + 10 q^{97} + 11 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 - 3 * q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9 - 3 * q^10 - 3 * q^11 - q^12 + 2 * q^13 - 4 * q^14 + 6 * q^15 - q^16 - 6 * q^17 - q^18 + 4 * q^19 + 6 * q^20 + 5 * q^21 + 6 * q^22 - 6 * q^23 - q^24 - 4 * q^25 - q^26 + 2 * q^27 + 5 * q^28 - 18 * q^29 - 3 * q^30 - 5 * q^31 - q^32 - 3 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 4 * q^37 + 4 * q^38 - q^39 - 3 * q^40 - 24 * q^41 - q^42 - 8 * q^43 - 3 * q^44 - 3 * q^45 - 6 * q^46 + 12 * q^47 + 2 * q^48 - 13 * q^49 + 8 * q^50 - 6 * q^51 - q^52 + 9 * q^53 - q^54 + 18 * q^55 - q^56 - 8 * q^57 + 9 * q^58 + 9 * q^59 - 3 * q^60 - 8 * q^61 + 10 * q^62 - 4 * q^63 + 2 * q^64 - 3 * q^65 - 3 * q^66 + 4 * q^67 - 6 * q^68 + 12 * q^69 + 15 * q^70 + 12 * q^71 - q^72 - 14 * q^73 + 4 * q^74 - 4 * q^75 - 8 * q^76 + 15 * q^77 + 2 * q^78 + q^79 - 3 * q^80 - q^81 + 12 * q^82 + 6 * q^83 - 4 * q^84 + 36 * q^85 + 4 * q^86 + 9 * q^87 - 3 * q^88 + 6 * q^90 - q^91 + 12 * q^92 - 5 * q^93 + 12 * q^94 + 12 * q^95 - q^96 + 10 * q^97 + 11 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$	1.00000			0.408248
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$	3.00000			0.774597
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	3.00000			0.670820
$21$	2.50000	−	0.866025i	0.545545	−	0.188982i
$22$	3.00000			0.639602
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	1.00000			0.192450
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$	−1.50000	+	2.59808i	−0.273861	+	0.474342i
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$	6.00000			1.02899
$35$	−6.00000	−	5.19615i	−1.01419	−	0.878310i
$36$	1.00000			0.166667
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	2.00000	+	3.46410i	0.324443	+	0.561951i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	−12.0000			−1.87409			−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000			−1.87409			−0.937043	+	0.349215i	$0.886448\pi$
$42$	−0.500000	+	2.59808i	−0.0771517	+	0.400892i
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	6.00000	−	10.3923i	0.875190	−	1.51587i	0.0186297	−	0.999826i	$-0.494070\pi$
$47$	6.00000	−	10.3923i	0.875190	−	1.51587i	0.856560	−	0.516047i	$-0.172597\pi$
$48$	1.00000			0.144338
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	4.00000			0.565685
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	9.00000			1.21356
$56$	−0.500000	+	2.59808i	−0.0668153	+	0.347183i
$57$	−4.00000			−0.529813
$58$	4.50000	−	7.79423i	0.590879	−	1.02343i
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	0.994769	+	0.102151i	$0.0325726\pi$
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	−0.408919	+	0.912571i	$0.634094\pi$
$60$	−1.50000	−	2.59808i	−0.193649	−	0.335410i
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	5.00000			0.635001
$63$	−2.00000	−	1.73205i	−0.251976	−	0.218218i
$64$	1.00000			0.125000
$65$	−1.50000	+	2.59808i	−0.186052	+	0.322252i
$66$	−1.50000	−	2.59808i	−0.184637	−	0.319801i
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	6.00000			0.722315
$70$	7.50000	−	2.59808i	0.896421	−	0.310530i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	−0.906208	−	0.422833i	$-0.861036\pi$
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	0.0869195	−	0.996215i	$-0.472298\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$	−4.00000			−0.458831
$77$	7.50000	−	2.59808i	0.854704	−	0.296078i
$78$	1.00000			0.113228
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.00000	−	10.3923i	0.662589	−	1.14764i
$83$	3.00000			0.329293			0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000			0.329293			0.164646	+	0.986353i	$0.447352\pi$
$84$	−2.00000	−	1.73205i	−0.218218	−	0.188982i
$85$	18.0000			1.95237
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$	4.50000	+	7.79423i	0.482451	+	0.835629i
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$	3.00000			0.316228
$91$	−0.500000	+	2.59808i	−0.0524142	+	0.272352i
$92$	6.00000			0.625543
$93$	−2.50000	+	4.33013i	−0.259238	+	0.449013i
$94$	6.00000	+	10.3923i	0.618853	+	1.07188i
$95$	6.00000	+	10.3923i	0.615587	+	1.06623i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	5.00000			0.507673			0.253837	−	0.967247i	$-0.418307\pi$
$97$	5.00000			0.507673			0.253837	+	0.967247i	$0.418307\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$	3.00000			0.301511
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.0623905	−	0.998052i	$-0.519872\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$	1.00000			0.0980581
$105$	−1.50000	+	7.79423i	−0.146385	+	0.760639i
$106$	−9.00000			−0.874157
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	0.939577	+	0.342337i	$0.111218\pi$
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	−0.173316	+	0.984866i	$0.555448\pi$
$110$	−4.50000	+	7.79423i	−0.429058	+	0.743151i
$111$	−4.00000			−0.379663
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$	2.00000	−	3.46410i	0.187317	−	0.324443i
$115$	−9.00000	−	15.5885i	−0.839254	−	1.45363i
$116$	4.50000	+	7.79423i	0.417815	+	0.723676i
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$	−9.00000			−0.828517
$119$	15.0000	−	5.19615i	1.37505	−	0.476331i
$120$	3.00000			0.273861
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−4.00000	−	6.92820i	−0.362143	−	0.627250i
$123$	6.00000	+	10.3923i	0.541002	+	0.937043i
$124$	−2.50000	+	4.33013i	−0.224507	+	0.388857i
$125$	−3.00000			−0.268328
$126$	2.50000	−	0.866025i	0.222718	−	0.0771517i
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$	−1.50000	−	2.59808i	−0.131559	−	0.227866i
$131$	−10.5000	+	18.1865i	−0.917389	+	1.58896i	−0.114024	+	0.993478i	$0.536374\pi$
$131$	−10.5000	+	18.1865i	−0.917389	+	1.58896i	−0.803365	+	0.595487i	$0.796959\pi$
$132$	3.00000			0.261116
$133$	8.00000	+	6.92820i	0.693688	+	0.600751i
$134$	−4.00000			−0.345547
$135$	−1.50000	+	2.59808i	−0.129099	+	0.223607i
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$	−3.00000	+	5.19615i	−0.255377	+	0.442326i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	−1.50000	+	7.79423i	−0.126773	+	0.658733i
$141$	−12.0000			−1.01058
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−1.50000	−	2.59808i	−0.125436	−	0.217262i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	13.5000	−	23.3827i	1.12111	−	1.94183i
$146$	14.0000			1.15865
$147$	1.00000	+	6.92820i	0.0824786	+	0.571429i
$148$	−4.00000			−0.328798
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$	−2.00000	−	3.46410i	−0.163299	−	0.282843i
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	0.935857	+	0.352381i	$0.114628\pi$
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	−0.162758	+	0.986666i	$0.552039\pi$
$152$	2.00000	−	3.46410i	0.162221	−	0.280976i
$153$	6.00000			0.485071
$154$	−1.50000	+	7.79423i	−0.120873	+	0.628077i
$155$	15.0000			1.20483
$156$	−0.500000	+	0.866025i	−0.0400320	+	0.0693375i
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	0.823359	−	0.567521i	$-0.192098\pi$
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	−0.903167	+	0.429289i	$0.858764\pi$
$158$	0.500000	+	0.866025i	0.0397779	+	0.0688973i
$159$	4.50000	−	7.79423i	0.356873	−	0.618123i
$160$	3.00000			0.237171
$161$	−12.0000	−	10.3923i	−0.945732	−	0.819028i
$162$	1.00000			0.0785674
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	0.665771	+	0.746156i	$0.268103\pi$
$164$	6.00000	+	10.3923i	0.468521	+	0.811503i
$165$	−4.50000	−	7.79423i	−0.350325	−	0.606780i
$166$	−1.50000	+	2.59808i	−0.116423	+	0.201650i
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$	2.50000	−	0.866025i	0.192879	−	0.0668153i
$169$	1.00000			0.0769231
$170$	−9.00000	+	15.5885i	−0.690268	+	1.19558i
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$	−9.00000			−0.682288
$175$	10.0000	−	3.46410i	0.755929	−	0.261861i
$176$	3.00000			0.226134
$177$	4.50000	−	7.79423i	0.338241	−	0.585850i
$178$		0			0
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$	−1.50000	+	2.59808i	−0.111803	+	0.193649i
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	−2.00000	−	1.73205i	−0.148250	−	0.128388i
$183$	8.00000			0.591377
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	6.00000	+	10.3923i	0.441129	+	0.764057i
$186$	−2.50000	−	4.33013i	−0.183309	−	0.317500i
$187$	−9.00000	+	15.5885i	−0.658145	+	1.13994i
$188$	−12.0000			−0.875190
$189$	−0.500000	+	2.59808i	−0.0363696	+	0.188982i
$190$	−12.0000			−0.870572
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	0.883460	−	0.468507i	$-0.155208\pi$
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	−0.847469	+	0.530845i	$0.821875\pi$
$194$	−2.50000	+	4.33013i	−0.179490	+	0.310885i
$195$	3.00000			0.214834
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	−1.50000	+	2.59808i	−0.106600	+	0.184637i
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$	−2.00000	−	3.46410i	−0.141421	−	0.244949i
$201$	2.00000	−	3.46410i	0.141069	−	0.244339i
$202$	18.0000			1.26648
$203$	4.50000	−	23.3827i	0.315838	−	1.64114i
$204$	6.00000			0.420084
$205$	18.0000	−	31.1769i	1.25717	−	2.17749i
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$	−3.00000	−	5.19615i	−0.208514	−	0.361158i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	−12.0000			−0.830057
$210$	−6.00000	−	5.19615i	−0.414039	−	0.358569i
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$	−3.00000	−	5.19615i	−0.205557	−	0.356034i
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$	6.00000	−	10.3923i	0.409197	−	0.708749i
$216$	1.00000			0.0680414
$217$	12.5000	−	4.33013i	0.848555	−	0.293948i
$218$	−16.0000			−1.08366
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$	−4.50000	−	7.79423i	−0.303390	−	0.525487i
$221$	−3.00000	−	5.19615i	−0.201802	−	0.349531i
$222$	2.00000	−	3.46410i	0.134231	−	0.232495i
$223$	−1.00000			−0.0669650			−0.0334825	−	0.999439i	$-0.510660\pi$
$223$	−1.00000			−0.0669650			−0.0334825	+	0.999439i	$0.510660\pi$
$224$	2.50000	−	0.866025i	0.167038	−	0.0578638i
$225$	4.00000			0.266667
$226$	6.00000	−	10.3923i	0.399114	−	0.691286i
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$	2.00000	+	3.46410i	0.132453	+	0.229416i
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	0.0137585	+	0.999905i	$0.495620\pi$
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	−0.872823	+	0.488037i	$0.837713\pi$
$230$	18.0000			1.18688
$231$	−6.00000	−	5.19615i	−0.394771	−	0.341882i
$232$	−9.00000			−0.590879
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$	18.0000	+	31.1769i	1.17419	+	2.03376i
$236$	4.50000	−	7.79423i	0.292925	−	0.507361i
$237$	−1.00000			−0.0649570
$238$	−3.00000	+	15.5885i	−0.194461	+	1.01045i
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$	−1.50000	+	2.59808i	−0.0968246	+	0.167705i
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	0.450910	−	0.892570i	$-0.351100\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	8.00000			0.512148
$245$	16.5000	−	12.9904i	1.05415	−	0.829925i
$246$	−12.0000			−0.765092
$247$	2.00000	−	3.46410i	0.127257	−	0.220416i
$248$	−2.50000	−	4.33013i	−0.158750	−	0.274963i
$249$	−1.50000	−	2.59808i	−0.0950586	−	0.164646i
$250$	1.50000	−	2.59808i	0.0948683	−	0.164317i
$251$	−3.00000			−0.189358			−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000			−0.189358			−0.0946792	+	0.995508i	$0.530183\pi$
$252$	−0.500000	+	2.59808i	−0.0314970	+	0.163663i
$253$	18.0000			1.13165
$254$	3.50000	−	6.06218i	0.219610	−	0.380375i
$255$	−9.00000	−	15.5885i	−0.563602	−	0.976187i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.0000	−	25.9808i	0.935674	−	1.62064i	0.162247	−	0.986750i	$-0.448126\pi$
$257$	15.0000	−	25.9808i	0.935674	−	1.62064i	0.773427	−	0.633885i	$-0.218541\pi$
$258$	−4.00000			−0.249029
$259$	8.00000	+	6.92820i	0.497096	+	0.430498i
$260$	3.00000			0.186052
$261$	4.50000	−	7.79423i	0.278543	−	0.482451i
$262$	−10.5000	−	18.1865i	−0.648692	−	1.12357i
$263$	−3.00000	−	5.19615i	−0.184988	−	0.320408i	0.758585	−	0.651575i	$-0.225891\pi$
$263$	−3.00000	−	5.19615i	−0.184988	−	0.320408i	−0.943572	+	0.331166i	$0.892558\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$	−27.0000			−1.65860
$266$	−10.0000	+	3.46410i	−0.613139	+	0.212398i
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	0.816668	−	0.577108i	$-0.195819\pi$
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	−0.908124	+	0.418701i	$0.862486\pi$
$270$	−1.50000	−	2.59808i	−0.0912871	−	0.158114i
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	−0.739921	−	0.672694i	$-0.765137\pi$
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	0.952531	+	0.304443i	$0.0984703\pi$
$272$	6.00000			0.363803
$273$	2.50000	−	0.866025i	0.151307	−	0.0524142i
$274$	−12.0000			−0.724947
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$	−3.00000	−	5.19615i	−0.180579	−	0.312772i
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	2.00000	−	3.46410i	0.119952	−	0.207763i
$279$	5.00000			0.299342
$280$	−6.00000	−	5.19615i	−0.358569	−	0.310530i
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	6.00000	−	10.3923i	0.357295	−	0.618853i
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	0.834772	−	0.550596i	$-0.185599\pi$
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	−0.894216	+	0.447636i	$0.852266\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	6.00000	−	10.3923i	0.355409	−	0.615587i
$286$	3.00000			0.177394
$287$	6.00000	−	31.1769i	0.354169	−	1.84032i
$288$	1.00000			0.0589256
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	13.5000	+	23.3827i	0.792747	+	1.37308i
$291$	−2.50000	−	4.33013i	−0.146553	−	0.253837i
$292$	−7.00000	+	12.1244i	−0.409644	+	0.709524i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$	−6.50000	−	2.59808i	−0.379088	−	0.151523i
$295$	−27.0000			−1.57200
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	−1.50000	−	2.59808i	−0.0870388	−	0.150756i
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$	4.00000			0.230940
$301$	2.00000	−	10.3923i	0.115278	−	0.599002i
$302$	−19.0000			−1.09333
$303$	−9.00000	+	15.5885i	−0.517036	+	0.895533i
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$	−12.0000	−	20.7846i	−0.687118	−	1.19012i
$306$	−3.00000	+	5.19615i	−0.171499	+	0.297044i
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	−6.00000	−	5.19615i	−0.341882	−	0.296078i
$309$	8.00000			0.455104
$310$	−7.50000	+	12.9904i	−0.425971	+	0.737804i
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	0.999928	+	0.0119847i	$0.00381495\pi$
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	−0.489585	+	0.871956i	$0.662852\pi$
$312$	−0.500000	−	0.866025i	−0.0283069	−	0.0490290i
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	−0.462093	−	0.886831i	$-0.652902\pi$
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	0.999065	−	0.0432311i	$-0.0137652\pi$
$314$	2.00000			0.112867
$315$	7.50000	−	2.59808i	0.422577	−	0.146385i
$316$	−1.00000			−0.0562544
$317$	7.50000	−	12.9904i	0.421242	−	0.729612i	−0.574819	−	0.818280i	$-0.694928\pi$
$317$	7.50000	−	12.9904i	0.421242	−	0.729612i	0.996061	+	0.0886679i	$0.0282610\pi$
$318$	4.50000	+	7.79423i	0.252347	+	0.437079i
$319$	13.5000	+	23.3827i	0.755855	+	1.30918i
$320$	−1.50000	+	2.59808i	−0.0838525	+	0.145237i
$321$	3.00000			0.167444
$322$	15.0000	−	5.19615i	0.835917	−	0.289570i
$323$	−24.0000			−1.33540
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−2.00000	−	3.46410i	−0.110940	−	0.192154i
$326$	−4.00000	−	6.92820i	−0.221540	−	0.383718i
$327$	8.00000	−	13.8564i	0.442401	−	0.766261i
$328$	−12.0000			−0.662589
$329$	24.0000	+	20.7846i	1.32316	+	1.14589i
$330$	9.00000			0.495434
$331$	−16.0000	+	27.7128i	−0.879440	+	1.52323i	−0.0274825	+	0.999622i	$0.508749\pi$
$331$	−16.0000	+	27.7128i	−0.879440	+	1.52323i	−0.851957	+	0.523612i	$0.824584\pi$
$332$	−1.50000	−	2.59808i	−0.0823232	−	0.142588i
$333$	2.00000	+	3.46410i	0.109599	+	0.189832i
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	−12.0000			−0.655630
$336$	−0.500000	+	2.59808i	−0.0272772	+	0.141737i
$337$	−31.0000			−1.68868			−0.844339	−	0.535810i	$-0.820006\pi$
$337$	−31.0000			−1.68868			−0.844339	+	0.535810i	$0.820006\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$	6.00000	+	10.3923i	0.325875	+	0.564433i
$340$	−9.00000	−	15.5885i	−0.488094	−	0.845403i
$341$	−7.50000	+	12.9904i	−0.406148	+	0.703469i
$342$	−4.00000			−0.216295
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−4.00000			−0.215666
$345$	−9.00000	+	15.5885i	−0.484544	+	0.839254i
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$	4.50000	−	7.79423i	0.241225	−	0.417815i
$349$	−34.0000			−1.81998			−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000			−1.81998			−0.909989	+	0.414632i	$0.863910\pi$
$350$	−2.00000	+	10.3923i	−0.106904	+	0.555492i
$351$	1.00000			0.0533761
$352$	−1.50000	+	2.59808i	−0.0799503	+	0.138478i
$353$	15.0000	+	25.9808i	0.798369	+	1.38282i	0.920677	+	0.390324i	$0.127637\pi$
$353$	15.0000	+	25.9808i	0.798369	+	1.38282i	−0.122308	+	0.992492i	$0.539030\pi$
$354$	4.50000	+	7.79423i	0.239172	+	0.414259i
$355$	−9.00000	+	15.5885i	−0.477670	+	0.827349i
$356$		0			0
$357$	−12.0000	−	10.3923i	−0.635107	−	0.550019i
$358$	12.0000			0.634220
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	0.934268	+	0.356572i	$0.116054\pi$
$360$	−1.50000	−	2.59808i	−0.0790569	−	0.136931i
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	8.00000	−	13.8564i	0.420471	−	0.728277i
$363$	−2.00000			−0.104973
$364$	2.50000	−	0.866025i	0.131036	−	0.0453921i
$365$	42.0000			2.19838
$366$	−4.00000	+	6.92820i	−0.209083	+	0.362143i
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	0.942799	−	0.333363i	$-0.108183\pi$
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	−0.760100	+	0.649806i	$0.774850\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$	6.00000	−	10.3923i	0.312348	−	0.541002i
$370$	−12.0000			−0.623850
$371$	−22.5000	+	7.79423i	−1.16814	+	0.404656i
$372$	5.00000			0.259238
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$	−9.00000	−	15.5885i	−0.465379	−	0.806060i
$375$	1.50000	+	2.59808i	0.0774597	+	0.134164i
$376$	6.00000	−	10.3923i	0.309426	−	0.535942i
$377$	−9.00000			−0.463524
$378$	−2.00000	−	1.73205i	−0.102869	−	0.0890871i
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	6.00000	−	10.3923i	0.307794	−	0.533114i
$381$	3.50000	+	6.06218i	0.179310	+	0.310575i
$382$	−3.00000	−	5.19615i	−0.153493	−	0.265858i
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	−0.779143	−	0.626846i	$-0.784346\pi$
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	0.932436	+	0.361335i	$0.117679\pi$
$384$	1.00000			0.0510310
$385$	−4.50000	+	23.3827i	−0.229341	+	1.19169i
$386$	−1.00000			−0.0508987
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$	−2.50000	−	4.33013i	−0.126918	−	0.219829i
$389$	−15.0000	−	25.9808i	−0.760530	−	1.31728i	−0.942578	−	0.333987i	$-0.891606\pi$
$389$	−15.0000	−	25.9808i	−0.760530	−	1.31728i	0.182047	−	0.983290i	$-0.441728\pi$
$390$	−1.50000	+	2.59808i	−0.0759555	+	0.131559i
$391$	36.0000			1.82060
$392$	−6.50000	−	2.59808i	−0.328300	−	0.131223i
$393$	21.0000			1.05931
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	1.50000	+	2.59808i	0.0754732	+	0.130723i
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	−0.890028	−	0.455905i	$-0.849316\pi$
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	0.839840	+	0.542834i	$0.182649\pi$
$398$	8.00000			0.401004
$399$	2.00000	−	10.3923i	0.100125	−	0.520266i
$400$	4.00000			0.200000
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$	2.00000	+	3.46410i	0.0997509	+	0.172774i
$403$	−2.50000	−	4.33013i	−0.124534	−	0.215699i
$404$	−9.00000	+	15.5885i	−0.447767	+	0.775555i
$405$	3.00000			0.149071
$406$	18.0000	+	15.5885i	0.893325	+	0.773642i
$407$	−12.0000			−0.594818
$408$	−3.00000	+	5.19615i	−0.148522	+	0.257248i
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	−0.766426	+	0.642333i	$0.777967\pi$
$410$	18.0000	+	31.1769i	0.888957	+	1.53972i
$411$	6.00000	−	10.3923i	0.295958	−	0.512615i
$412$	8.00000			0.394132
$413$	−22.5000	+	7.79423i	−1.10715	+	0.383529i
$414$	6.00000			0.294884
$415$	−4.50000	+	7.79423i	−0.220896	+	0.382604i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	2.00000	+	3.46410i	0.0979404	+	0.169638i
$418$	6.00000	−	10.3923i	0.293470	−	0.508304i
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$	7.50000	−	2.59808i	0.365963	−	0.126773i
$421$	8.00000			0.389896			0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000			0.389896			0.194948	+	0.980814i	$0.437546\pi$
$422$	−4.00000	+	6.92820i	−0.194717	+	0.337260i
$423$	6.00000	+	10.3923i	0.291730	+	0.505291i
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$	−12.0000	+	20.7846i	−0.582086	+	1.00820i
$426$	6.00000			0.290701
$427$	−16.0000	−	13.8564i	−0.774294	−	0.670559i
$428$	3.00000			0.145010
$429$	−1.50000	+	2.59808i	−0.0724207	+	0.125436i
$430$	6.00000	+	10.3923i	0.289346	+	0.501161i
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	−0.959985	−	0.280052i	$-0.909648\pi$
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	0.237460	−	0.971397i	$-0.423685\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$	−2.50000	+	12.9904i	−0.120004	+	0.623558i
$435$	−27.0000			−1.29455
$436$	8.00000	−	13.8564i	0.383131	−	0.663602i
$437$	12.0000	+	20.7846i	0.574038	+	0.994263i
$438$	−7.00000	−	12.1244i	−0.334473	−	0.579324i
$439$	0.500000	−	0.866025i	0.0238637	−	0.0413331i	−0.853847	−	0.520524i	$-0.825737\pi$
$439$	0.500000	−	0.866025i	0.0238637	−	0.0413331i	0.877711	+	0.479191i	$0.159070\pi$
$440$	9.00000			0.429058
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$	6.00000			0.285391
$443$	1.50000	−	2.59808i	0.0712672	−	0.123438i	−0.828190	−	0.560448i	$-0.810629\pi$
$443$	1.50000	−	2.59808i	0.0712672	−	0.123438i	0.899457	+	0.437009i	$0.143962\pi$
$444$	2.00000	+	3.46410i	0.0949158	+	0.164399i
$445$		0			0
$446$	0.500000	−	0.866025i	0.0236757	−	0.0410075i
$447$	6.00000			0.283790
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$	−2.00000	+	3.46410i	−0.0942809	+	0.163299i
$451$	18.0000	+	31.1769i	0.847587	+	1.46806i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$	9.50000	−	16.4545i	0.446349	−	0.773099i
$454$	−3.00000			−0.140797
$455$	−6.00000	−	5.19615i	−0.281284	−	0.243599i
$456$	−4.00000			−0.187317
$457$	9.50000	−	16.4545i	0.444391	−	0.769708i	−0.553618	−	0.832771i	$-0.686753\pi$
$457$	9.50000	−	16.4545i	0.444391	−	0.769708i	0.998010	+	0.0630623i	$0.0200867\pi$
$458$	−13.0000	−	22.5167i	−0.607450	−	1.05213i
$459$	−3.00000	−	5.19615i	−0.140028	−	0.242536i
$460$	−9.00000	+	15.5885i	−0.419627	+	0.726816i
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$	7.50000	−	2.59808i	0.348932	−	0.120873i
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$	4.50000	−	7.79423i	0.208907	−	0.361838i
$465$	−7.50000	−	12.9904i	−0.347804	−	0.602414i
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	−0.0627555	−	0.998029i	$-0.519989\pi$
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	0.895696	−	0.444667i	$-0.146678\pi$
$468$	1.00000			0.0462250
$469$	−10.0000	+	3.46410i	−0.461757	+	0.159957i
$470$	−36.0000			−1.66056
$471$	−1.00000	+	1.73205i	−0.0460776	+	0.0798087i
$472$	4.50000	+	7.79423i	0.207129	+	0.358758i
$473$	6.00000	+	10.3923i	0.275880	+	0.477839i
$474$	0.500000	−	0.866025i	0.0229658	−	0.0397779i
$475$	−16.0000			−0.734130
$476$	−12.0000	−	10.3923i	−0.550019	−	0.476331i
$477$	−9.00000			−0.412082
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$	−3.00000	−	5.19615i	−0.137073	−	0.237418i	0.789314	−	0.613990i	$-0.210436\pi$
$479$	−3.00000	−	5.19615i	−0.137073	−	0.237418i	−0.926388	+	0.376571i	$0.877103\pi$
$480$	−1.50000	−	2.59808i	−0.0684653	−	0.118585i
$481$	2.00000	−	3.46410i	0.0911922	−	0.157949i
$482$	17.0000			0.774329
$483$	−3.00000	+	15.5885i	−0.136505	+	0.709299i
$484$	−2.00000			−0.0909091
$485$	−7.50000	+	12.9904i	−0.340557	+	0.589863i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	−0.999698	−	0.0245553i	$-0.992183\pi$
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	0.478584	−	0.878042i	$-0.341150\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$	8.00000			0.361773
$490$	3.00000	+	20.7846i	0.135526	+	0.938953i
$491$	−15.0000			−0.676941			−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000			−0.676941			−0.338470	+	0.940977i	$0.609909\pi$
$492$	6.00000	−	10.3923i	0.270501	−	0.468521i
$493$	27.0000	+	46.7654i	1.21602	+	2.10621i
$494$	2.00000	+	3.46410i	0.0899843	+	0.155857i
$495$	−4.50000	+	7.79423i	−0.202260	+	0.350325i
$496$	5.00000			0.224507
$497$	−3.00000	+	15.5885i	−0.134568	+	0.699238i
$498$	3.00000			0.134433
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	−0.629519	−	0.776985i	$-0.716748\pi$
$499$	8.00000	−	13.8564i	0.358129	−	0.620298i	0.987648	+	0.156687i	$0.0500814\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$	1.50000	−	2.59808i	0.0669483	−	0.115958i
$503$	30.0000			1.33763			0.668817	−	0.743427i	$-0.266801\pi$
$503$	30.0000			1.33763			0.668817	+	0.743427i	$0.266801\pi$
$504$	−2.00000	−	1.73205i	−0.0890871	−	0.0771517i
$505$	54.0000			2.40297
$506$	−9.00000	+	15.5885i	−0.400099	+	0.692991i
$507$	−0.500000	−	0.866025i	−0.0222058	−	0.0384615i
$508$	3.50000	+	6.06218i	0.155287	+	0.268966i
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	−0.948353	−	0.317217i	$-0.897252\pi$
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	0.748894	+	0.662690i	$0.230585\pi$
$510$	18.0000			0.797053
$511$	35.0000	−	12.1244i	1.54831	−	0.536350i
$512$	1.00000			0.0441942
$513$	2.00000	−	3.46410i	0.0883022	−	0.152944i
$514$	15.0000	+	25.9808i	0.661622	+	1.14596i
$515$	−12.0000	−	20.7846i	−0.528783	−	0.915879i
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$	−36.0000			−1.58328
$518$	−10.0000	+	3.46410i	−0.439375	+	0.152204i
$519$	6.00000			0.263371
$520$	−1.50000	+	2.59808i	−0.0657794	+	0.113933i
$521$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$521$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$522$	4.50000	+	7.79423i	0.196960	+	0.341144i
$523$	−4.00000	+	6.92820i	−0.174908	+	0.302949i	−0.940129	−	0.340818i	$-0.889296\pi$
$523$	−4.00000	+	6.92820i	−0.174908	+	0.302949i	0.765222	+	0.643767i	$0.222629\pi$
$524$	21.0000			0.917389
$525$	−8.00000	−	6.92820i	−0.349149	−	0.302372i
$526$	6.00000			0.261612
$527$	−15.0000	+	25.9808i	−0.653410	+	1.13174i
$528$	−1.50000	−	2.59808i	−0.0652791	−	0.113067i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	13.5000	−	23.3827i	0.586403	−	1.01568i
$531$	−9.00000			−0.390567
$532$	2.00000	−	10.3923i	0.0867110	−	0.450564i
$533$	−12.0000			−0.519778
$534$		0			0
$535$	−4.50000	−	7.79423i	−0.194552	−	0.336974i
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$	3.00000			0.129339
$539$	3.00000	+	20.7846i	0.129219	+	0.895257i
$540$	3.00000			0.129099
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	−0.996867	−	0.0790969i	$-0.974796\pi$
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	0.566933	+	0.823764i	$0.308130\pi$
$542$	3.50000	+	6.06218i	0.150338	+	0.260393i
$543$	8.00000	+	13.8564i	0.343313	+	0.594635i
$544$	−3.00000	+	5.19615i	−0.128624	+	0.222783i
$545$	−48.0000			−2.05609
$546$	−0.500000	+	2.59808i	−0.0213980	+	0.111187i
$547$	44.0000			1.88130			0.940652	−	0.339372i	$-0.110215\pi$
$547$	44.0000			1.88130			0.940652	+	0.339372i	$0.110215\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$	−4.00000	−	6.92820i	−0.170716	−	0.295689i
$550$	−6.00000	−	10.3923i	−0.255841	−	0.443129i
$551$	−18.0000	+	31.1769i	−0.766826	+	1.32818i
$552$	6.00000			0.255377
$553$	2.00000	+	1.73205i	0.0850487	+	0.0736543i
$554$	2.00000			0.0849719
$555$	6.00000	−	10.3923i	0.254686	−	0.441129i
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	10.5000	+	18.1865i	0.444899	+	0.770588i	0.998045	−	0.0624962i	$-0.0199061\pi$
$557$	10.5000	+	18.1865i	0.444899	+	0.770588i	−0.553146	+	0.833084i	$0.686573\pi$
$558$	−2.50000	+	4.33013i	−0.105833	+	0.183309i
$559$	−4.00000			−0.169182
$560$	7.50000	−	2.59808i	0.316933	−	0.109789i
$561$	18.0000			0.759961
$562$		0			0
$563$	−16.5000	−	28.5788i	−0.695392	−	1.20445i	−0.970048	−	0.242912i	$-0.921897\pi$
$563$	−16.5000	−	28.5788i	−0.695392	−	1.20445i	0.274656	−	0.961542i	$-0.411436\pi$
$564$	6.00000	+	10.3923i	0.252646	+	0.437595i
$565$	18.0000	−	31.1769i	0.757266	−	1.31162i
$566$	2.00000			0.0840663
$567$	2.50000	−	0.866025i	0.104990	−	0.0363696i
$568$	6.00000			0.251754
$569$	−6.00000	+	10.3923i	−0.251533	+	0.435668i	−0.963948	−	0.266090i	$-0.914268\pi$
$569$	−6.00000	+	10.3923i	−0.251533	+	0.435668i	0.712415	+	0.701758i	$0.247601\pi$
$570$	6.00000	+	10.3923i	0.251312	+	0.435286i
$571$	20.0000	+	34.6410i	0.836974	+	1.44968i	0.892413	+	0.451219i	$0.149011\pi$
$571$	20.0000	+	34.6410i	0.836974	+	1.44968i	−0.0554391	+	0.998462i	$0.517656\pi$
$572$	−1.50000	+	2.59808i	−0.0627182	+	0.108631i
$573$	6.00000			0.250654
$574$	24.0000	+	20.7846i	1.00174	+	0.867533i
$575$	24.0000			1.00087
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−8.50000	−	14.7224i	−0.353860	−	0.612903i	0.633062	−	0.774101i	$-0.281798\pi$
$577$	−8.50000	−	14.7224i	−0.353860	−	0.612903i	−0.986922	+	0.161198i	$0.948464\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$	0.500000	−	0.866025i	0.0207793	−	0.0359908i
$580$	−27.0000			−1.12111
$581$	−1.50000	+	7.79423i	−0.0622305	+	0.323359i
$582$	5.00000			0.207257
$583$	13.5000	−	23.3827i	0.559113	−	0.968412i
$584$	−7.00000	−	12.1244i	−0.289662	−	0.501709i
$585$	−1.50000	−	2.59808i	−0.0620174	−	0.107417i
$586$	−10.5000	+	18.1865i	−0.433751	+	0.751279i
$587$	33.0000			1.36206			0.681028	−	0.732257i	$-0.261533\pi$
$587$	33.0000			1.36206			0.681028	+	0.732257i	$0.261533\pi$
$588$	5.50000	−	4.33013i	0.226816	−	0.178571i
$589$	−20.0000			−0.824086
$590$	13.5000	−	23.3827i	0.555786	−	0.962650i
$591$	9.00000	+	15.5885i	0.370211	+	0.641223i
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	6.00000	−	10.3923i	0.246390	−	0.426761i	−0.716131	−	0.697966i	$-0.754089\pi$
$593$	6.00000	−	10.3923i	0.246390	−	0.426761i	0.962522	+	0.271205i	$0.0874221\pi$
$594$	3.00000			0.123091
$595$	−9.00000	+	46.7654i	−0.368964	+	1.91719i
$596$	6.00000			0.245770
$597$	−4.00000	+	6.92820i	−0.163709	+	0.283552i
$598$	−3.00000	−	5.19615i	−0.122679	−	0.212486i
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	0.798206	−	0.602384i	$-0.205782\pi$
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	−0.920783	+	0.390075i	$0.872449\pi$
$600$	−2.00000	+	3.46410i	−0.0816497	+	0.141421i
$601$	−37.0000			−1.50926			−0.754631	−	0.656150i	$-0.772184\pi$
$601$	−37.0000			−1.50926			−0.754631	+	0.656150i	$0.772184\pi$
$602$	8.00000	+	6.92820i	0.326056	+	0.282372i
$603$	−4.00000			−0.162893
$604$	9.50000	−	16.4545i	0.386550	−	0.669523i
$605$	3.00000	+	5.19615i	0.121967	+	0.211254i
$606$	−9.00000	−	15.5885i	−0.365600	−	0.633238i
$607$	−2.50000	+	4.33013i	−0.101472	+	0.175754i	−0.912291	−	0.409542i	$-0.865689\pi$
$607$	−2.50000	+	4.33013i	−0.101472	+	0.175754i	0.810819	+	0.585296i	$0.199022\pi$
$608$	−4.00000			−0.162221
$609$	−22.5000	+	7.79423i	−0.911746	+	0.315838i
$610$	24.0000			0.971732
$611$	6.00000	−	10.3923i	0.242734	−	0.420428i
$612$	−3.00000	−	5.19615i	−0.121268	−	0.210042i
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	−1.00000	+	1.73205i	−0.0403567	+	0.0698999i
$615$	−36.0000			−1.45166
$616$	7.50000	−	2.59808i	0.302184	−	0.104679i
$617$	48.0000			1.93241			0.966204	−	0.257780i	$-0.0829910\pi$
$617$	48.0000			1.93241			0.966204	+	0.257780i	$0.0829910\pi$
$618$	−4.00000	+	6.92820i	−0.160904	+	0.278693i
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	0.592025	−	0.805919i	$-0.298329\pi$
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	−0.993959	+	0.109749i	$0.964995\pi$
$620$	−7.50000	−	12.9904i	−0.301207	−	0.521706i
$621$	−3.00000	+	5.19615i	−0.120386	+	0.208514i
$622$	−18.0000			−0.721734
$623$		0			0
$624$	1.00000			0.0400320
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	9.50000	+	16.4545i	0.379696	+	0.657653i
$627$	6.00000	+	10.3923i	0.239617	+	0.415029i
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$	−24.0000			−0.956943
$630$	−1.50000	+	7.79423i	−0.0597614	+	0.310530i
$631$	−13.0000			−0.517522			−0.258761	−	0.965941i	$-0.583314\pi$
$631$	−13.0000			−0.517522			−0.258761	+	0.965941i	$0.583314\pi$
$632$	0.500000	−	0.866025i	0.0198889	−	0.0344486i
$633$	−4.00000	−	6.92820i	−0.158986	−	0.275371i
$634$	7.50000	+	12.9904i	0.297863	+	0.515914i
$635$	10.5000	−	18.1865i	0.416680	−	0.721711i
$636$	−9.00000			−0.356873
$637$	−6.50000	−	2.59808i	−0.257539	−	0.102940i
$638$	−27.0000			−1.06894
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$641$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$642$	−1.50000	+	2.59808i	−0.0592003	+	0.102538i
$643$	8.00000			0.315489			0.157745	−	0.987480i	$-0.449578\pi$
$643$	8.00000			0.315489			0.157745	+	0.987480i	$0.449578\pi$
$644$	−3.00000	+	15.5885i	−0.118217	+	0.614271i
$645$	−12.0000			−0.472500
$646$	12.0000	−	20.7846i	0.472134	−	0.817760i
$647$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$647$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	13.5000	−	23.3827i	0.529921	−	0.917851i
$650$	4.00000			0.156893
$651$	−10.0000	−	8.66025i	−0.391931	−	0.339422i
$652$	8.00000			0.313304
$653$	−4.50000	+	7.79423i	−0.176099	+	0.305012i	−0.940541	−	0.339680i	$-0.889681\pi$
$653$	−4.50000	+	7.79423i	−0.176099	+	0.305012i	0.764442	+	0.644692i	$0.223014\pi$
$654$	8.00000	+	13.8564i	0.312825	+	0.541828i
$655$	−31.5000	−	54.5596i	−1.23081	−	2.13182i
$656$	6.00000	−	10.3923i	0.234261	−	0.405751i
$657$	14.0000			0.546192
$658$	−30.0000	+	10.3923i	−1.16952	+	0.405134i
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$	−4.50000	+	7.79423i	−0.175162	+	0.303390i
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	0.697174	−	0.716902i	$-0.254441\pi$
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	−0.969442	+	0.245319i	$0.921107\pi$
$662$	−16.0000	−	27.7128i	−0.621858	−	1.07709i
$663$	−3.00000	+	5.19615i	−0.116510	+	0.201802i
$664$	3.00000			0.116423
$665$	−30.0000	+	10.3923i	−1.16335	+	0.402996i
$666$	−4.00000			−0.154997
$667$	27.0000	−	46.7654i	1.04544	−	1.81076i
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$	0.500000	+	0.866025i	0.0193311	+	0.0334825i
$670$	6.00000	−	10.3923i	0.231800	−	0.401490i
$671$	24.0000			0.926510
$672$	−2.00000	−	1.73205i	−0.0771517	−	0.0668153i
$673$	−31.0000			−1.19496			−0.597481	−	0.801883i	$-0.703832\pi$
$673$	−31.0000			−1.19496			−0.597481	+	0.801883i	$0.703832\pi$
$674$	15.5000	−	26.8468i	0.597038	−	1.03410i
$675$	−2.00000	−	3.46410i	−0.0769800	−	0.133333i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−4.50000	+	7.79423i	−0.172949	+	0.299557i	−0.939450	−	0.342687i	$-0.888663\pi$
$677$	−4.50000	+	7.79423i	−0.172949	+	0.299557i	0.766501	+	0.642244i	$0.221996\pi$
$678$	−12.0000			−0.460857
$679$	−2.50000	+	12.9904i	−0.0959412	+	0.498525i
$680$	18.0000			0.690268
$681$	1.50000	−	2.59808i	0.0574801	−	0.0995585i
$682$	−7.50000	−	12.9904i	−0.287190	−	0.497427i
$683$	19.5000	+	33.7750i	0.746147	+	1.29236i	0.949657	+	0.313291i	$0.101432\pi$
$683$	19.5000	+	33.7750i	0.746147	+	1.29236i	−0.203510	+	0.979073i	$0.565235\pi$
$684$	2.00000	−	3.46410i	0.0764719	−	0.132453i
$685$	−36.0000			−1.37549
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$	26.0000			0.991962
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	4.50000	+	7.79423i	0.171436	+	0.296936i
$690$	−9.00000	−	15.5885i	−0.342624	−	0.593442i
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	−0.181584	−	0.983375i	$-0.558123\pi$
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	0.942420	−	0.334431i	$-0.108544\pi$
$692$	6.00000			0.228086
$693$	−1.50000	+	7.79423i	−0.0569803	+	0.296078i
$694$	12.0000			0.455514
$695$	6.00000	−	10.3923i	0.227593	−	0.394203i
$696$	4.50000	+	7.79423i	0.170572	+	0.295439i
$697$	36.0000	+	62.3538i	1.36360	+	2.36182i
$698$	17.0000	−	29.4449i	0.643459	−	1.11450i
$699$	−6.00000			−0.226941
$700$	−8.00000	−	6.92820i	−0.302372	−	0.261861i
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$	−0.500000	+	0.866025i	−0.0188713	+	0.0326860i
$703$	−8.00000	−	13.8564i	−0.301726	−	0.522604i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$	18.0000	−	31.1769i	0.677919	−	1.17419i
$706$	−30.0000			−1.12906
$707$	45.0000	−	15.5885i	1.69240	−	0.586264i
$708$	−9.00000			−0.338241
$709$	17.0000	−	29.4449i	0.638448	−	1.10583i	−0.347325	−	0.937745i	$-0.612910\pi$
$709$	17.0000	−	29.4449i	0.638448	−	1.10583i	0.985773	−	0.168080i	$-0.0537568\pi$
$710$	−9.00000	−	15.5885i	−0.337764	−	0.585024i
$711$	0.500000	+	0.866025i	0.0187515	+	0.0324785i
$712$		0			0
$713$	30.0000			1.12351
$714$	15.0000	−	5.19615i	0.561361	−	0.194461i
$715$	9.00000			0.336581
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	−3.00000	−	5.19615i	−0.112037	−	0.194054i
$718$	3.00000	+	5.19615i	0.111959	+	0.193919i
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	−0.647965	−	0.761670i	$-0.724380\pi$
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	0.983608	+	0.180319i	$0.0577130\pi$
$720$	3.00000			0.111803
$721$	−16.0000	−	13.8564i	−0.595871	−	0.516040i
$722$	−3.00000			−0.111648
$723$	−8.50000	+	14.7224i	−0.316118	+	0.547533i
$724$	8.00000	+	13.8564i	0.297318	+	0.514969i
$725$	18.0000	+	31.1769i	0.668503	+	1.15788i
$726$	1.00000	−	1.73205i	0.0371135	−	0.0642824i
$727$	−37.0000			−1.37225			−0.686127	−	0.727482i	$-0.740691\pi$
$727$	−37.0000			−1.37225			−0.686127	+	0.727482i	$0.740691\pi$
$728$	−0.500000	+	2.59808i	−0.0185312	+	0.0962911i
$729$	1.00000			0.0370370
$730$	−21.0000	+	36.3731i	−0.777245	+	1.34623i
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	−4.00000	−	6.92820i	−0.147844	−	0.256074i
$733$	−25.0000	+	43.3013i	−0.923396	+	1.59937i	−0.129275	+	0.991609i	$0.541265\pi$
$733$	−25.0000	+	43.3013i	−0.923396	+	1.59937i	−0.794121	+	0.607760i	$0.792068\pi$
$734$	−7.00000			−0.258375
$735$	−19.5000	−	7.79423i	−0.719268	−	0.287494i
$736$	6.00000			0.221163
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$	6.00000	+	10.3923i	0.220863	+	0.382546i
$739$	−19.0000	−	32.9090i	−0.698926	−	1.21058i	−0.968839	−	0.247691i	$-0.920328\pi$
$739$	−19.0000	−	32.9090i	−0.698926	−	1.21058i	0.269913	−	0.962885i	$-0.413005\pi$
$740$	6.00000	−	10.3923i	0.220564	−	0.382029i
$741$	−4.00000			−0.146944
$742$	4.50000	−	23.3827i	0.165200	−	0.858405i
$743$	−36.0000			−1.32071			−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000			−1.32071			−0.660356	+	0.750953i	$0.729595\pi$
$744$	−2.50000	+	4.33013i	−0.0916544	+	0.158750i
$745$	−9.00000	−	15.5885i	−0.329734	−	0.571117i
$746$	−7.00000	−	12.1244i	−0.256288	−	0.443904i
$747$	−1.50000	+	2.59808i	−0.0548821	+	0.0950586i
$748$	18.0000			0.658145
$749$	−6.00000	−	5.19615i	−0.219235	−	0.189863i
$750$	−3.00000			−0.109545
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	−0.431390	−	0.902165i	$-0.641977\pi$
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	0.996993	−	0.0774878i	$-0.0246899\pi$
$752$	6.00000	+	10.3923i	0.218797	+	0.378968i
$753$	1.50000	+	2.59808i	0.0546630	+	0.0946792i
$754$	4.50000	−	7.79423i	0.163880	−	0.283849i
$755$	−57.0000			−2.07444
$756$	2.50000	−	0.866025i	0.0909241	−	0.0314970i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	8.00000	−	13.8564i	0.290573	−	0.503287i
$759$	−9.00000	−	15.5885i	−0.326679	−	0.565825i
$760$	6.00000	+	10.3923i	0.217643	+	0.376969i
$761$	−18.0000	+	31.1769i	−0.652499	+	1.13016i	0.330015	+	0.943976i	$0.392946\pi$
$761$	−18.0000	+	31.1769i	−0.652499	+	1.13016i	−0.982514	+	0.186187i	$0.940387\pi$
$762$	−7.00000			−0.253583
$763$	−40.0000	+	13.8564i	−1.44810	+	0.501636i
$764$	6.00000			0.217072
$765$	−9.00000	+	15.5885i	−0.325396	+	0.563602i
$766$	3.00000	+	5.19615i	0.108394	+	0.187745i
$767$	4.50000	+	7.79423i	0.162486	+	0.281433i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−1.00000			−0.0360609			−0.0180305	−	0.999837i	$-0.505740\pi$
$769$	−1.00000			−0.0360609			−0.0180305	+	0.999837i	$0.505740\pi$
$770$	−18.0000	−	15.5885i	−0.648675	−	0.561769i
$771$	−30.0000			−1.08042
$772$	0.500000	−	0.866025i	0.0179954	−	0.0311689i
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$	2.00000	+	3.46410i	0.0718885	+	0.124515i
$775$	−10.0000	+	17.3205i	−0.359211	+	0.622171i
$776$	5.00000			0.179490
$777$	2.00000	−	10.3923i	0.0717496	−	0.372822i
$778$	30.0000			1.07555
$779$	−24.0000	+	41.5692i	−0.859889	+	1.48937i
$780$	−1.50000	−	2.59808i	−0.0537086	−	0.0930261i
$781$	−9.00000	−	15.5885i	−0.322045	−	0.557799i
$782$	−18.0000	+	31.1769i	−0.643679	+	1.11488i
$783$	−9.00000			−0.321634
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	6.00000			0.214149
$786$	−10.5000	+	18.1865i	−0.374523	+	0.648692i
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	−0.996531	−	0.0832226i	$-0.973479\pi$
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	0.426193	−	0.904632i	$-0.359855\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$	−3.00000	+	5.19615i	−0.106803	+	0.184988i
$790$	−3.00000			−0.106735
$791$	6.00000	−	31.1769i	0.213335	−	1.10852i
$792$	3.00000			0.106600
$793$	−4.00000	+	6.92820i	−0.142044	+	0.246028i
$794$	−1.00000	−	1.73205i	−0.0354887	−	0.0614682i
$795$	13.5000	+	23.3827i	0.478796	+	0.829298i
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$	9.00000			0.318796			0.159398	−	0.987214i	$-0.449045\pi$
$797$	9.00000			0.318796			0.159398	+	0.987214i	$0.449045\pi$
$798$	8.00000	+	6.92820i	0.283197	+	0.245256i
$799$	−72.0000			−2.54718
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$		0			0
$802$	−9.00000	−	15.5885i	−0.317801	−	0.550448i
$803$	−21.0000	+	36.3731i	−0.741074	+	1.28358i
$804$	−4.00000			−0.141069
$805$	45.0000	−	15.5885i	1.58604	−	0.549421i
$806$	5.00000			0.176117
$807$	−1.50000	+	2.59808i	−0.0528025	+	0.0914566i
$808$	−9.00000	−	15.5885i	−0.316619	−	0.548400i
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	0.952012	−	0.306062i	$-0.0990113\pi$
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	−0.741063	+	0.671436i	$0.765678\pi$
$810$	−1.50000	+	2.59808i	−0.0527046	+	0.0912871i
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	−22.5000	+	7.79423i	−0.789595	+	0.273524i
$813$	−7.00000			−0.245501
$814$	6.00000	−	10.3923i	0.210300	−	0.364250i
$815$	−12.0000	−	20.7846i	−0.420342	−	0.728053i
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$	−7.00000			−0.244749
$819$	−2.00000	−	1.73205i	−0.0698857	−	0.0605228i
$820$	−36.0000			−1.25717
$821$	19.5000	−	33.7750i	0.680555	−	1.17876i	−0.294257	−	0.955726i	$-0.595072\pi$
$821$	19.5000	−	33.7750i	0.680555	−	1.17876i	0.974812	−	0.223029i	$-0.0715945\pi$
$822$	6.00000	+	10.3923i	0.209274	+	0.362473i
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$	−4.00000	+	6.92820i	−0.139347	+	0.241355i
$825$	12.0000			0.417786
$826$	4.50000	−	23.3827i	0.156575	−	0.813588i
$827$	3.00000			0.104320			0.0521601	−	0.998639i	$-0.483389\pi$
$827$	3.00000			0.104320			0.0521601	+	0.998639i	$0.483389\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	23.0000	+	39.8372i	0.798823	+	1.38360i	0.920383	+	0.391018i	$0.127877\pi$
$829$	23.0000	+	39.8372i	0.798823	+	1.38360i	−0.121560	+	0.992584i	$0.538790\pi$
$830$	−4.50000	−	7.79423i	−0.156197	−	0.270542i
$831$	−1.00000	+	1.73205i	−0.0346896	+	0.0600842i
$832$	1.00000			0.0346688
$833$	6.00000	+	41.5692i	0.207888	+	1.44029i
$834$	−4.00000			−0.138509
$835$	−18.0000	+	31.1769i	−0.622916	+	1.07892i
$836$	6.00000	+	10.3923i	0.207514	+	0.359425i
$837$	−2.50000	−	4.33013i	−0.0864126	−	0.149671i
$838$	−12.0000	+	20.7846i	−0.414533	+	0.717992i
$839$	−48.0000			−1.65714			−0.828572	−	0.559883i	$-0.810846\pi$
$839$	−48.0000			−1.65714			−0.828572	+	0.559883i	$0.810846\pi$
$840$	−1.50000	+	7.79423i	−0.0517549	+	0.268926i
$841$	52.0000			1.79310
$842$	−4.00000	+	6.92820i	−0.137849	+	0.238762i
$843$		0			0
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	−1.50000	+	2.59808i	−0.0516016	+	0.0893765i
$846$	−12.0000			−0.412568
$847$	4.00000	+	3.46410i	0.137442	+	0.119028i
$848$	−9.00000			−0.309061
$849$	−1.00000	+	1.73205i	−0.0343199	+	0.0594438i
$850$	−12.0000	−	20.7846i	−0.411597	−	0.712906i
$851$	12.0000	+	20.7846i	0.411355	+	0.712487i
$852$	−3.00000	+	5.19615i	−0.102778	+	0.178017i
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$	20.0000	−	6.92820i	0.684386	−	0.237078i
$855$	−12.0000			−0.410391
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	0.810227	−	0.586116i	$-0.199344\pi$
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	−0.912705	+	0.408619i	$0.866010\pi$
$858$	−1.50000	−	2.59808i	−0.0512092	−	0.0886969i
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	−0.984655	−	0.174512i	$-0.944165\pi$
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	0.643459	+	0.765480i	$0.277499\pi$
$860$	−12.0000			−0.409197
$861$	−30.0000	+	10.3923i	−1.02240	+	0.354169i
$862$	30.0000			1.02180
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	−0.586235	−	0.810141i	$-0.699391\pi$
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	0.994720	+	0.102624i	$0.0327240\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−9.00000	−	15.5885i	−0.306009	−	0.530023i
$866$	−1.00000	+	1.73205i	−0.0339814	+	0.0588575i
$867$	19.0000			0.645274
$868$	−10.0000	−	8.66025i	−0.339422	−	0.293948i
$869$	−3.00000			−0.101768
$870$	13.5000	−	23.3827i	0.457693	−	0.792747i
$871$	2.00000	+	3.46410i	0.0677674	+	0.117377i
$872$	8.00000	+	13.8564i	0.270914	+	0.469237i
$873$	−2.50000	+	4.33013i	−0.0846122	+	0.146553i
$874$	−24.0000			−0.811812
$875$	1.50000	−	7.79423i	0.0507093	−	0.263493i
$876$	14.0000			0.473016
$877$	29.0000	−	50.2295i	0.979260	−	1.69613i	0.314169	−	0.949367i	$-0.398274\pi$
$877$	29.0000	−	50.2295i	0.979260	−	1.69613i	0.665092	−	0.746762i	$-0.268392\pi$
$878$	0.500000	+	0.866025i	0.0168742	+	0.0292269i
$879$	−10.5000	−	18.1865i	−0.354156	−	0.613417i
$880$	−4.50000	+	7.79423i	−0.151695	+	0.262743i
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$	1.00000	+	6.92820i	0.0336718	+	0.233285i
$883$	26.0000			0.874970			0.437485	−	0.899226i	$-0.355869\pi$
$883$	26.0000			0.874970			0.437485	+	0.899226i	$0.355869\pi$
$884$	−3.00000	+	5.19615i	−0.100901	+	0.174766i
$885$	13.5000	+	23.3827i	0.453798	+	0.786000i
$886$	1.50000	+	2.59808i	0.0503935	+	0.0872841i
$887$	18.0000	−	31.1769i	0.604381	−	1.04682i	−0.387768	−	0.921757i	$-0.626754\pi$
$887$	18.0000	−	31.1769i	0.604381	−	1.04682i	0.992149	−	0.125061i	$-0.0399128\pi$
$888$	−4.00000			−0.134231
$889$	3.50000	−	18.1865i	0.117386	−	0.609957i
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$	0.500000	+	0.866025i	0.0167412	+	0.0289967i
$893$	−24.0000	−	41.5692i	−0.803129	−	1.39106i
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$	36.0000			1.20335
$896$	−2.00000	−	1.73205i	−0.0668153	−	0.0578638i
$897$	6.00000			0.200334
$898$	6.00000	−	10.3923i	0.200223	−	0.346796i
$899$	22.5000	+	38.9711i	0.750417	+	1.29976i
$900$	−2.00000	−	3.46410i	−0.0666667	−	0.115470i
$901$	27.0000	−	46.7654i	0.899500	−	1.55798i
$902$	−36.0000			−1.19867
$903$	−10.0000	+	3.46410i	−0.332779	+	0.115278i
$904$	−12.0000			−0.399114
$905$	24.0000	−	41.5692i	0.797787	−	1.38181i
$906$	9.50000	+	16.4545i	0.315616	+	0.546664i
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	1.50000	−	2.59808i	0.0497792	−	0.0862202i
$909$	18.0000			0.597022
$910$	7.50000	−	2.59808i	0.248623	−	0.0861254i
$911$	54.0000			1.78910			0.894550	−	0.446968i	$-0.147496\pi$
$911$	54.0000			1.78910			0.894550	+	0.446968i	$0.147496\pi$
$912$	2.00000	−	3.46410i	0.0662266	−	0.114708i
$913$	−4.50000	−	7.79423i	−0.148928	−	0.257951i
$914$	9.50000	+	16.4545i	0.314232	+	0.544266i
$915$	−12.0000	+	20.7846i	−0.396708	+	0.687118i
$916$	26.0000			0.859064
$917$	−42.0000	−	36.3731i	−1.38696	−	1.20114i
$918$	6.00000			0.198030
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	−0.924427	−	0.381358i	$-0.875456\pi$
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	0.792480	+	0.609898i	$0.208790\pi$
$920$	−9.00000	−	15.5885i	−0.296721	−	0.513936i
$921$	−1.00000	−	1.73205i	−0.0329511	−	0.0570730i
$922$	−9.00000	+	15.5885i	−0.296399	+	0.513378i
$923$	6.00000			0.197492
$924$	−1.50000	+	7.79423i	−0.0493464	+	0.256411i
$925$	−16.0000			−0.526077
$926$	8.00000	−	13.8564i	0.262896	−	0.455350i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	4.50000	+	7.79423i	0.147720	+	0.255858i
$929$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$929$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$930$	15.0000			0.491869
$931$	−22.0000	+	17.3205i	−0.721021	+	0.567657i
$932$	−6.00000			−0.196537
$933$	9.00000	−	15.5885i	0.294647	−	0.510343i
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$	−27.0000	−	46.7654i	−0.882994	−	1.52939i
$936$	−0.500000	+	0.866025i	−0.0163430	+	0.0283069i
$937$	−13.0000			−0.424691			−0.212346	−	0.977195i	$-0.568110\pi$
$937$	−13.0000			−0.424691			−0.212346	+	0.977195i	$0.568110\pi$
$938$	2.00000	−	10.3923i	0.0653023	−	0.339321i
$939$	−19.0000			−0.620042
$940$	18.0000	−	31.1769i	0.587095	−	1.01688i
$941$	22.5000	+	38.9711i	0.733479	+	1.27042i	0.955387	+	0.295355i	$0.0954381\pi$
$941$	22.5000	+	38.9711i	0.733479	+	1.27042i	−0.221908	+	0.975068i	$0.571229\pi$
$942$	−1.00000	−	1.73205i	−0.0325818	−	0.0564333i
$943$	36.0000	−	62.3538i	1.17232	−	2.03052i
$944$	−9.00000			−0.292925
$945$	−6.00000	−	5.19615i	−0.195180	−	0.169031i
$946$	−12.0000			−0.390154
$947$	−30.0000	+	51.9615i	−0.974869	+	1.68852i	−0.294502	+	0.955651i	$0.595154\pi$
$947$	−30.0000	+	51.9615i	−0.974869	+	1.68852i	−0.680367	+	0.732872i	$0.738179\pi$
$948$	0.500000	+	0.866025i	0.0162392	+	0.0281272i
$949$	−7.00000	−	12.1244i	−0.227230	−	0.393573i
$950$	8.00000	−	13.8564i	0.259554	−	0.449561i
$951$	−15.0000			−0.486408
$952$	15.0000	−	5.19615i	0.486153	−	0.168408i
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$	4.50000	−	7.79423i	0.145693	−	0.252347i
$955$	−9.00000	−	15.5885i	−0.291233	−	0.504431i
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$	13.5000	−	23.3827i	0.436393	−	0.755855i
$958$	6.00000			0.193851
$959$	−30.0000	+	10.3923i	−0.968751	+	0.335585i
$960$	3.00000			0.0968246
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	2.00000	+	3.46410i	0.0644826	+	0.111687i
$963$	−1.50000	−	2.59808i	−0.0483368	−	0.0837218i
$964$	−8.50000	+	14.7224i	−0.273767	+	0.474178i
$965$	−3.00000			−0.0965734
$966$	−12.0000	−	10.3923i	−0.386094	−	0.334367i
$967$	29.0000			0.932577			0.466289	−	0.884633i	$-0.345591\pi$
$967$	29.0000			0.932577			0.466289	+	0.884633i	$0.345591\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$	12.0000	+	20.7846i	0.385496	+	0.667698i
$970$	−7.50000	−	12.9904i	−0.240810	−	0.417096i
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	−0.469897	−	0.882721i	$-0.655709\pi$
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	0.999408	−	0.0344175i	$-0.0109576\pi$
$972$	1.00000			0.0320750
$973$	2.00000	−	10.3923i	0.0641171	−	0.333162i
$974$	23.0000			0.736968
$975$	−2.00000	+	3.46410i	−0.0640513	+	0.110940i
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$	−4.00000	+	6.92820i	−0.127906	+	0.221540i
$979$		0			0
$980$	−19.5000	−	7.79423i	−0.622905	−	0.248978i
$981$	−16.0000			−0.510841
$982$	7.50000	−	12.9904i	0.239335	−	0.414540i
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	0.686050	−	0.727554i	$-0.259343\pi$
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	−0.973106	+	0.230360i	$0.926010\pi$
$984$	6.00000	+	10.3923i	0.191273	+	0.331295i
$985$	27.0000	−	46.7654i	0.860292	−	1.49007i
$986$	−54.0000			−1.71971
$987$	6.00000	−	31.1769i	0.190982	−	0.992372i
$988$	−4.00000			−0.127257
$989$	12.0000	−	20.7846i	0.381578	−	0.660912i
$990$	−4.50000	−	7.79423i	−0.143019	−	0.247717i
$991$	−17.5000	−	30.3109i	−0.555906	−	0.962857i	−0.997832	−	0.0658059i	$-0.979038\pi$
$991$	−17.5000	−	30.3109i	−0.555906	−	0.962857i	0.441927	−	0.897051i	$-0.354295\pi$
$992$	−2.50000	+	4.33013i	−0.0793751	+	0.137482i
$993$	32.0000			1.01549
$994$	−12.0000	−	10.3923i	−0.380617	−	0.329624i
$995$	24.0000			0.760851
$996$	−1.50000	+	2.59808i	−0.0475293	+	0.0823232i
$997$	8.00000	+	13.8564i	0.253363	+	0.438837i	0.964449	−	0.264267i	$-0.0851301\pi$
$997$	8.00000	+	13.8564i	0.253363	+	0.438837i	−0.711087	+	0.703104i	$0.751797\pi$
$998$	8.00000	+	13.8564i	0.253236	+	0.438617i
$999$	2.00000	−	3.46410i	0.0632772	−	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.i.a.79.1	✓	2
3.2	odd	2		1638.2.j.j.1171.1		2
7.2	even	3		3822.2.a.bh.1.1		1
7.4	even	3	inner	546.2.i.a.235.1	yes	2
7.5	odd	6		3822.2.a.s.1.1		1
21.11	odd	6		1638.2.j.j.235.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.a.79.1	✓	2	1.1	even	1	trivial
546.2.i.a.235.1	yes	2	7.4	even	3	inner
1638.2.j.j.235.1		2	21.11	odd	6
1638.2.j.j.1171.1		2	3.2	odd	2
3822.2.a.s.1.1		1	7.5	odd	6
3822.2.a.bh.1.1		1	7.2	even	3

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +3.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(2.00000 - 3.46410i) q^{19} +3.00000 q^{20} +(2.50000 - 0.866025i) q^{21} +3.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} +(-0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} -9.00000 q^{29} +(-1.50000 + 2.59808i) q^{30} +(-2.50000 - 4.33013i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +6.00000 q^{34} +(-6.00000 - 5.19615i) q^{35} +1.00000 q^{36} +(2.00000 - 3.46410i) q^{37} +(2.00000 + 3.46410i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-1.50000 + 2.59808i) q^{40} -12.0000 q^{41} +(-0.500000 + 2.59808i) q^{42} -4.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(-1.50000 - 2.59808i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(6.00000 - 10.3923i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +4.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(4.50000 + 7.79423i) q^{53} +(-0.500000 + 0.866025i) q^{54} +9.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} -4.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(4.50000 + 7.79423i) q^{59} +(-1.50000 - 2.59808i) q^{60} +(-4.00000 + 6.92820i) q^{61} +5.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.50000 + 2.59808i) q^{65} +(-1.50000 - 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +6.00000 q^{69} +(7.50000 - 2.59808i) q^{70} +6.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-2.00000 + 3.46410i) q^{75} -4.00000 q^{76} +(7.50000 - 2.59808i) q^{77} +1.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.00000 - 10.3923i) q^{82} +3.00000 q^{83} +(-2.00000 - 1.73205i) q^{84} +18.0000 q^{85} +(2.00000 - 3.46410i) q^{86} +(4.50000 + 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{88} +3.00000 q^{90} +(-0.500000 + 2.59808i) q^{91} +6.00000 q^{92} +(-2.50000 + 4.33013i) q^{93} +(6.00000 + 10.3923i) q^{94} +(6.00000 + 10.3923i) q^{95} +(-0.500000 + 0.866025i) q^{96} +5.00000 q^{97} +(5.50000 - 4.33013i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} - 3 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 - 3 * q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - q^{3} - q^{4} - 3 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + 2 q^{13} - 4 q^{14} + 6 q^{15} - q^{16} - 6 q^{17} - q^{18} + 4 q^{19} + 6 q^{20} + 5 q^{21} + 6 q^{22} - 6 q^{23} - q^{24} - 4 q^{25} - q^{26} + 2 q^{27} + 5 q^{28} - 18 q^{29} - 3 q^{30} - 5 q^{31} - q^{32} - 3 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 4 q^{37} + 4 q^{38} - q^{39} - 3 q^{40} - 24 q^{41} - q^{42} - 8 q^{43} - 3 q^{44} - 3 q^{45} - 6 q^{46} + 12 q^{47} + 2 q^{48} - 13 q^{49} + 8 q^{50} - 6 q^{51} - q^{52} + 9 q^{53} - q^{54} + 18 q^{55} - q^{56} - 8 q^{57} + 9 q^{58} + 9 q^{59} - 3 q^{60} - 8 q^{61} + 10 q^{62} - 4 q^{63} + 2 q^{64} - 3 q^{65} - 3 q^{66} + 4 q^{67} - 6 q^{68} + 12 q^{69} + 15 q^{70} + 12 q^{71} - q^{72} - 14 q^{73} + 4 q^{74} - 4 q^{75} - 8 q^{76} + 15 q^{77} + 2 q^{78} + q^{79} - 3 q^{80} - q^{81} + 12 q^{82} + 6 q^{83} - 4 q^{84} + 36 q^{85} + 4 q^{86} + 9 q^{87} - 3 q^{88} + 6 q^{90} - q^{91} + 12 q^{92} - 5 q^{93} + 12 q^{94} + 12 q^{95} - q^{96} + 10 q^{97} + 11 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 - 3 * q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9 - 3 * q^10 - 3 * q^11 - q^12 + 2 * q^13 - 4 * q^14 + 6 * q^15 - q^16 - 6 * q^17 - q^18 + 4 * q^19 + 6 * q^20 + 5 * q^21 + 6 * q^22 - 6 * q^23 - q^24 - 4 * q^25 - q^26 + 2 * q^27 + 5 * q^28 - 18 * q^29 - 3 * q^30 - 5 * q^31 - q^32 - 3 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 4 * q^37 + 4 * q^38 - q^39 - 3 * q^40 - 24 * q^41 - q^42 - 8 * q^43 - 3 * q^44 - 3 * q^45 - 6 * q^46 + 12 * q^47 + 2 * q^48 - 13 * q^49 + 8 * q^50 - 6 * q^51 - q^52 + 9 * q^53 - q^54 + 18 * q^55 - q^56 - 8 * q^57 + 9 * q^58 + 9 * q^59 - 3 * q^60 - 8 * q^61 + 10 * q^62 - 4 * q^63 + 2 * q^64 - 3 * q^65 - 3 * q^66 + 4 * q^67 - 6 * q^68 + 12 * q^69 + 15 * q^70 + 12 * q^71 - q^72 - 14 * q^73 + 4 * q^74 - 4 * q^75 - 8 * q^76 + 15 * q^77 + 2 * q^78 + q^79 - 3 * q^80 - q^81 + 12 * q^82 + 6 * q^83 - 4 * q^84 + 36 * q^85 + 4 * q^86 + 9 * q^87 - 3 * q^88 + 6 * q^90 - q^91 + 12 * q^92 - 5 * q^93 + 12 * q^94 + 12 * q^95 - q^96 + 10 * q^97 + 11 * q^98 + 6 * q^99

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