LMFDB - Embedded newform 273.2.bj.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(25,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("273.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bj (of order $6$, 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:	$2.17991597518$
Analytic rank:	$0$
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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	273.25
Dual form			273.2.bj.b.142.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.00000 - 1.73205i) q^{5} -1.73205i q^{6} +(-0.500000 + 2.59808i) q^{7} +1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.00000 - 1.73205i) q^{5} -1.73205i q^{6} +(-0.500000 + 2.59808i) q^{7} +1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.00000 - 5.19615i) q^{10} +(-4.50000 - 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.00000 + 3.46410i) q^{13} +(1.50000 + 4.33013i) q^{14} -3.46410i q^{15} +(2.50000 + 4.33013i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.50000 - 0.866025i) q^{18} +(-4.50000 + 2.59808i) q^{19} -3.46410i q^{20} +(2.00000 + 1.73205i) q^{21} -9.00000 q^{22} +(-3.00000 - 5.19615i) q^{23} +(1.50000 + 0.866025i) q^{24} +(3.50000 - 6.06218i) q^{25} +(1.50000 + 6.06218i) q^{26} -1.00000 q^{27} +(2.00000 + 1.73205i) q^{28} +3.00000 q^{29} +(-3.00000 - 5.19615i) q^{30} +(-3.00000 - 1.73205i) q^{31} +(4.50000 + 2.59808i) q^{32} +(-4.50000 + 2.59808i) q^{33} -5.19615i q^{34} +(3.00000 + 8.66025i) q^{35} -1.00000 q^{36} +(3.00000 - 1.73205i) q^{37} +(-4.50000 + 7.79423i) q^{38} +(2.50000 + 2.59808i) q^{39} +(3.00000 + 5.19615i) q^{40} +10.3923i q^{41} +(4.50000 + 0.866025i) q^{42} +8.00000 q^{43} +(-4.50000 + 2.59808i) q^{44} +(-3.00000 - 1.73205i) q^{45} +(-9.00000 - 5.19615i) q^{46} +(1.50000 - 0.866025i) q^{47} +5.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} -12.1244i q^{50} +(-1.50000 - 2.59808i) q^{51} +(2.50000 + 2.59808i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(-1.50000 + 0.866025i) q^{54} -18.0000 q^{55} +(-4.50000 - 0.866025i) q^{56} +5.19615i q^{57} +(4.50000 - 2.59808i) q^{58} +(7.50000 + 4.33013i) q^{59} +(-3.00000 - 1.73205i) q^{60} +(-0.500000 - 0.866025i) q^{61} -6.00000 q^{62} +(2.50000 - 0.866025i) q^{63} -1.00000 q^{64} +(3.00000 + 12.1244i) q^{65} +(-4.50000 + 7.79423i) q^{66} +(-1.50000 - 0.866025i) q^{67} +(-1.50000 - 2.59808i) q^{68} -6.00000 q^{69} +(12.0000 + 10.3923i) q^{70} -12.1244i q^{71} +(1.50000 - 0.866025i) q^{72} +(9.00000 + 5.19615i) q^{73} +(3.00000 - 5.19615i) q^{74} +(-3.50000 - 6.06218i) q^{75} +5.19615i q^{76} +(9.00000 - 10.3923i) q^{77} +(6.00000 + 1.73205i) q^{78} +(-2.00000 - 3.46410i) q^{79} +(15.0000 + 8.66025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(9.00000 + 15.5885i) q^{82} +3.46410i q^{83} +(2.50000 - 0.866025i) q^{84} -10.3923i q^{85} +(12.0000 - 6.92820i) q^{86} +(1.50000 - 2.59808i) q^{87} +(4.50000 - 7.79423i) q^{88} +(-3.00000 + 1.73205i) q^{89} -6.00000 q^{90} +(-8.50000 - 4.33013i) q^{91} -6.00000 q^{92} +(-3.00000 + 1.73205i) q^{93} +(1.50000 - 2.59808i) q^{94} +(-9.00000 + 15.5885i) q^{95} +(4.50000 - 2.59808i) q^{96} -17.3205i q^{97} +(-12.0000 + 1.73205i) q^{98} +5.19615i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + q^{3} + q^{4} + 6 q^{5} - q^{7} - q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + q^3 + q^4 + 6 * q^5 - q^7 - q^9	$ 2 q + 3 q^{2} + q^{3} + q^{4} + 6 q^{5} - q^{7} - q^{9} + 6 q^{10} - 9 q^{11} - q^{12} - 2 q^{13} + 3 q^{14} + 5 q^{16} + 3 q^{17} - 3 q^{18} - 9 q^{19} + 4 q^{21} - 18 q^{22} - 6 q^{23} + 3 q^{24} + 7 q^{25} + 3 q^{26} - 2 q^{27} + 4 q^{28} + 6 q^{29} - 6 q^{30} - 6 q^{31} + 9 q^{32} - 9 q^{33} + 6 q^{35} - 2 q^{36} + 6 q^{37} - 9 q^{38} + 5 q^{39} + 6 q^{40} + 9 q^{42} + 16 q^{43} - 9 q^{44} - 6 q^{45} - 18 q^{46} + 3 q^{47} + 10 q^{48} - 13 q^{49} - 3 q^{51} + 5 q^{52} - 3 q^{53} - 3 q^{54} - 36 q^{55} - 9 q^{56} + 9 q^{58} + 15 q^{59} - 6 q^{60} - q^{61} - 12 q^{62} + 5 q^{63} - 2 q^{64} + 6 q^{65} - 9 q^{66} - 3 q^{67} - 3 q^{68} - 12 q^{69} + 24 q^{70} + 3 q^{72} + 18 q^{73} + 6 q^{74} - 7 q^{75} + 18 q^{77} + 12 q^{78} - 4 q^{79} + 30 q^{80} - q^{81} + 18 q^{82} + 5 q^{84} + 24 q^{86} + 3 q^{87} + 9 q^{88} - 6 q^{89} - 12 q^{90} - 17 q^{91} - 12 q^{92} - 6 q^{93} + 3 q^{94} - 18 q^{95} + 9 q^{96} - 24 q^{98}+O(q^{100}) $ 2 * q + 3 * q^2 + q^3 + q^4 + 6 * q^5 - q^7 - q^9 + 6 * q^10 - 9 * q^11 - q^12 - 2 * q^13 + 3 * q^14 + 5 * q^16 + 3 * q^17 - 3 * q^18 - 9 * q^19 + 4 * q^21 - 18 * q^22 - 6 * q^23 + 3 * q^24 + 7 * q^25 + 3 * q^26 - 2 * q^27 + 4 * q^28 + 6 * q^29 - 6 * q^30 - 6 * q^31 + 9 * q^32 - 9 * q^33 + 6 * q^35 - 2 * q^36 + 6 * q^37 - 9 * q^38 + 5 * q^39 + 6 * q^40 + 9 * q^42 + 16 * q^43 - 9 * q^44 - 6 * q^45 - 18 * q^46 + 3 * q^47 + 10 * q^48 - 13 * q^49 - 3 * q^51 + 5 * q^52 - 3 * q^53 - 3 * q^54 - 36 * q^55 - 9 * q^56 + 9 * q^58 + 15 * q^59 - 6 * q^60 - q^61 - 12 * q^62 + 5 * q^63 - 2 * q^64 + 6 * q^65 - 9 * q^66 - 3 * q^67 - 3 * q^68 - 12 * q^69 + 24 * q^70 + 3 * q^72 + 18 * q^73 + 6 * q^74 - 7 * q^75 + 18 * q^77 + 12 * q^78 - 4 * q^79 + 30 * q^80 - q^81 + 18 * q^82 + 5 * q^84 + 24 * q^86 + 3 * q^87 + 9 * q^88 - 6 * q^89 - 12 * q^90 - 17 * q^91 - 12 * q^92 - 6 * q^93 + 3 * q^94 - 18 * q^95 + 9 * q^96 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.50000	−	0.866025i	1.06066	−	0.612372i	0.135045	−	0.990839i	$-0.456882\pi$
$2$	1.50000	−	0.866025i	1.06066	−	0.612372i	0.925615	+	0.378467i	$0.123549\pi$
$3$	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
$5$	3.00000	−	1.73205i	1.34164	−	0.774597i	0.354593	−	0.935021i	$-0.384620\pi$
$5$	3.00000	−	1.73205i	1.34164	−	0.774597i	0.987048	+	0.160424i	$0.0512862\pi$
$6$		−	1.73205i		−	0.707107i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$			1.73205i			0.612372i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	3.00000	−	5.19615i	0.948683	−	1.64317i
$11$	−4.50000	−	2.59808i	−1.35680	−	0.783349i	−0.367610	−	0.929980i	$-0.619824\pi$
$11$	−4.50000	−	2.59808i	−1.35680	−	0.783349i	−0.989191	+	0.146631i	$0.953157\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$	1.50000	+	4.33013i	0.400892	+	1.15728i
$15$		−	3.46410i		−	0.894427i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	−1.50000	−	0.866025i	−0.353553	−	0.204124i
$19$	−4.50000	+	2.59808i	−1.03237	+	0.596040i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−4.50000	+	2.59808i	−1.03237	+	0.596040i	−0.114708	+	0.993399i	$0.536593\pi$
$20$		−	3.46410i		−	0.774597i
$21$	2.00000	+	1.73205i	0.436436	+	0.377964i
$22$	−9.00000			−1.91881
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	3.50000	−	6.06218i	0.700000	−	1.21244i
$26$	1.50000	+	6.06218i	0.294174	+	1.18889i
$27$	−1.00000			−0.192450
$28$	2.00000	+	1.73205i	0.377964	+	0.327327i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	−3.00000	−	5.19615i	−0.547723	−	0.948683i
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	0.205783	−	0.978598i	$-0.434026\pi$
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	−0.744599	+	0.667512i	$0.767359\pi$
$32$	4.50000	+	2.59808i	0.795495	+	0.459279i
$33$	−4.50000	+	2.59808i	−0.783349	+	0.452267i
$34$		−	5.19615i		−	0.891133i
$35$	3.00000	+	8.66025i	0.507093	+	1.46385i
$36$	−1.00000			−0.166667
$37$	3.00000	−	1.73205i	0.493197	−	0.284747i	−0.232703	−	0.972548i	$-0.574757\pi$
$37$	3.00000	−	1.73205i	0.493197	−	0.284747i	0.725900	+	0.687800i	$0.241424\pi$
$38$	−4.50000	+	7.79423i	−0.729996	+	1.26439i
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$	3.00000	+	5.19615i	0.474342	+	0.821584i
$41$			10.3923i			1.62301i	0.584349	+	0.811503i	$0.301350\pi$
$41$			10.3923i			1.62301i	−0.584349	+	0.811503i	$0.698650\pi$
$42$	4.50000	+	0.866025i	0.694365	+	0.133631i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	−4.50000	+	2.59808i	−0.678401	+	0.391675i
$45$	−3.00000	−	1.73205i	−0.447214	−	0.258199i
$46$	−9.00000	−	5.19615i	−1.32698	−	0.766131i
$47$	1.50000	−	0.866025i	0.218797	−	0.126323i	−0.386596	−	0.922249i	$-0.626349\pi$
$47$	1.50000	−	0.866025i	0.218797	−	0.126323i	0.605393	+	0.795926i	$0.293016\pi$
$48$	5.00000			0.721688
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		−	12.1244i		−	1.71464i
$51$	−1.50000	−	2.59808i	−0.210042	−	0.363803i
$52$	2.50000	+	2.59808i	0.346688	+	0.360288i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$	−1.50000	+	0.866025i	−0.204124	+	0.117851i
$55$	−18.0000			−2.42712
$56$	−4.50000	−	0.866025i	−0.601338	−	0.115728i
$57$			5.19615i			0.688247i
$58$	4.50000	−	2.59808i	0.590879	−	0.341144i
$59$	7.50000	+	4.33013i	0.976417	+	0.563735i	0.901186	−	0.433432i	$-0.142697\pi$
$59$	7.50000	+	4.33013i	0.976417	+	0.563735i	0.0752304	+	0.997166i	$0.476031\pi$
$60$	−3.00000	−	1.73205i	−0.387298	−	0.223607i
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	−6.00000			−0.762001
$63$	2.50000	−	0.866025i	0.314970	−	0.109109i
$64$	−1.00000			−0.125000
$65$	3.00000	+	12.1244i	0.372104	+	1.50384i
$66$	−4.50000	+	7.79423i	−0.553912	+	0.959403i
$67$	−1.50000	−	0.866025i	−0.183254	−	0.105802i	0.405567	−	0.914066i	$-0.367074\pi$
$67$	−1.50000	−	0.866025i	−0.183254	−	0.105802i	−0.588821	+	0.808264i	$0.700408\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	−6.00000			−0.722315
$70$	12.0000	+	10.3923i	1.43427	+	1.24212i
$71$		−	12.1244i		−	1.43890i	−0.694546	−	0.719448i	$-0.744395\pi$
$71$		−	12.1244i		−	1.43890i	0.694546	−	0.719448i	$-0.255605\pi$
$72$	1.50000	−	0.866025i	0.176777	−	0.102062i
$73$	9.00000	+	5.19615i	1.05337	+	0.608164i	0.923591	−	0.383379i	$-0.125240\pi$
$73$	9.00000	+	5.19615i	1.05337	+	0.608164i	0.129779	+	0.991543i	$0.458573\pi$
$74$	3.00000	−	5.19615i	0.348743	−	0.604040i
$75$	−3.50000	−	6.06218i	−0.404145	−	0.700000i
$76$			5.19615i			0.596040i
$77$	9.00000	−	10.3923i	1.02565	−	1.18431i
$78$	6.00000	+	1.73205i	0.679366	+	0.196116i
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$	15.0000	+	8.66025i	1.67705	+	0.968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	9.00000	+	15.5885i	0.993884	+	1.72146i
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$	2.50000	−	0.866025i	0.272772	−	0.0944911i
$85$		−	10.3923i		−	1.12720i
$86$	12.0000	−	6.92820i	1.29399	−	0.747087i
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$	4.50000	−	7.79423i	0.479702	−	0.830868i
$89$	−3.00000	+	1.73205i	−0.317999	+	0.183597i	−0.650500	−	0.759506i	$-0.725441\pi$
$89$	−3.00000	+	1.73205i	−0.317999	+	0.183597i	0.332501	+	0.943103i	$0.392107\pi$
$90$	−6.00000			−0.632456
$91$	−8.50000	−	4.33013i	−0.891042	−	0.453921i
$92$	−6.00000			−0.625543
$93$	−3.00000	+	1.73205i	−0.311086	+	0.179605i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	−9.00000	+	15.5885i	−0.923381	+	1.59934i
$96$	4.50000	−	2.59808i	0.459279	−	0.265165i
$97$		−	17.3205i		−	1.75863i	−0.476240	−	0.879316i	$-0.658000\pi$
$97$		−	17.3205i		−	1.75863i	0.476240	−	0.879316i	$-0.342000\pi$
$98$	−12.0000	+	1.73205i	−1.21218	+	0.174964i
$99$			5.19615i			0.522233i
$100$	−3.50000	−	6.06218i	−0.350000	−	0.606218i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$	−4.50000	−	2.59808i	−0.445566	−	0.257248i
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$	−6.00000	−	1.73205i	−0.588348	−	0.169842i
$105$	9.00000	+	1.73205i	0.878310	+	0.169031i
$106$			5.19615i			0.504695i
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−12.0000	−	6.92820i	−1.14939	−	0.663602i	−0.200653	−	0.979662i	$-0.564306\pi$
$109$	−12.0000	−	6.92820i	−1.14939	−	0.663602i	−0.948739	+	0.316061i	$0.897640\pi$
$110$	−27.0000	+	15.5885i	−2.57435	+	1.48630i
$111$		−	3.46410i		−	0.328798i
$112$	−12.5000	+	4.33013i	−1.18114	+	0.409159i
$113$	9.00000			0.846649			0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000			0.846649			0.423324	+	0.905978i	$0.360863\pi$
$114$	4.50000	+	7.79423i	0.421464	+	0.729996i
$115$	−18.0000	−	10.3923i	−1.67851	−	0.969087i
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$	3.50000	−	0.866025i	0.323575	−	0.0800641i
$118$	15.0000			1.38086
$119$	6.00000	+	5.19615i	0.550019	+	0.476331i
$120$	6.00000			0.547723
$121$	8.00000	+	13.8564i	0.727273	+	1.25967i
$122$	−1.50000	−	0.866025i	−0.135804	−	0.0784063i
$123$	9.00000	+	5.19615i	0.811503	+	0.468521i
$124$	−3.00000	+	1.73205i	−0.269408	+	0.155543i
$125$		−	6.92820i		−	0.619677i
$126$	3.00000	−	3.46410i	0.267261	−	0.308607i
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$	−10.5000	+	6.06218i	−0.928078	+	0.535826i
$129$	4.00000	−	6.92820i	0.352180	−	0.609994i
$130$	15.0000	+	15.5885i	1.31559	+	1.36720i
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	0.966803	−	0.255524i	$-0.0822479\pi$
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	−0.704692	+	0.709514i	$0.748915\pi$
$132$			5.19615i			0.452267i
$133$	−4.50000	−	12.9904i	−0.390199	−	1.12641i
$134$	−3.00000			−0.259161
$135$	−3.00000	+	1.73205i	−0.258199	+	0.149071i
$136$	4.50000	+	2.59808i	0.385872	+	0.222783i
$137$	−9.00000	−	5.19615i	−0.768922	−	0.443937i	0.0635680	−	0.997978i	$-0.479752\pi$
$137$	−9.00000	−	5.19615i	−0.768922	−	0.443937i	−0.832490	+	0.554040i	$0.813085\pi$
$138$	−9.00000	+	5.19615i	−0.766131	+	0.442326i
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$	9.00000	+	1.73205i	0.760639	+	0.146385i
$141$		−	1.73205i		−	0.145865i
$142$	−10.5000	−	18.1865i	−0.881140	−	1.52618i
$143$	13.5000	−	12.9904i	1.12893	−	1.08631i
$144$	2.50000	−	4.33013i	0.208333	−	0.360844i
$145$	9.00000	−	5.19615i	0.747409	−	0.431517i
$146$	18.0000			1.48969
$147$	−5.50000	+	4.33013i	−0.453632	+	0.357143i
$148$		−	3.46410i		−	0.284747i
$149$	−3.00000	+	1.73205i	−0.245770	+	0.141895i	−0.617826	−	0.786315i	$-0.711986\pi$
$149$	−3.00000	+	1.73205i	−0.245770	+	0.141895i	0.372056	+	0.928210i	$0.378653\pi$
$150$	−10.5000	−	6.06218i	−0.857321	−	0.494975i
$151$	7.50000	+	4.33013i	0.610341	+	0.352381i	0.773099	−	0.634285i	$-0.218706\pi$
$151$	7.50000	+	4.33013i	0.610341	+	0.352381i	−0.162758	+	0.986666i	$0.552039\pi$
$152$	−4.50000	−	7.79423i	−0.364998	−	0.632195i
$153$	−3.00000			−0.242536
$154$	4.50000	−	23.3827i	0.362620	−	1.88423i
$155$	−12.0000			−0.963863
$156$	3.50000	−	0.866025i	0.280224	−	0.0693375i
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	0.297097	+	0.954847i	$0.403982\pi$
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	−0.975470	+	0.220131i	$0.929352\pi$
$158$	−6.00000	−	3.46410i	−0.477334	−	0.275589i
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$	18.0000			1.42302
$161$	15.0000	−	5.19615i	1.18217	−	0.409514i
$162$			1.73205i			0.136083i
$163$	−10.5000	+	6.06218i	−0.822423	+	0.474826i	−0.851251	−	0.524758i	$-0.824156\pi$
$163$	−10.5000	+	6.06218i	−0.822423	+	0.474826i	0.0288280	+	0.999584i	$0.490822\pi$
$164$	9.00000	+	5.19615i	0.702782	+	0.405751i
$165$	−9.00000	+	15.5885i	−0.700649	+	1.21356i
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$			8.66025i			0.670151i	0.942191	+	0.335075i	$0.108762\pi$
$167$			8.66025i			0.670151i	−0.942191	+	0.335075i	$0.891238\pi$
$168$	−3.00000	+	3.46410i	−0.231455	+	0.267261i
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	−9.00000	−	15.5885i	−0.690268	−	1.19558i
$171$	4.50000	+	2.59808i	0.344124	+	0.198680i
$172$	4.00000	−	6.92820i	0.304997	−	0.528271i
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	−0.996544	−	0.0830722i	$-0.973527\pi$
$173$	−7.50000	−	12.9904i	−0.570214	−	0.987640i	0.426329	−	0.904568i	$-0.359807\pi$
$174$		−	5.19615i		−	0.393919i
$175$	14.0000	+	12.1244i	1.05830	+	0.916515i
$176$		−	25.9808i		−	1.95837i
$177$	7.50000	−	4.33013i	0.563735	−	0.325472i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$	−3.00000	+	1.73205i	−0.223607	+	0.129099i
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	−16.5000	+	0.866025i	−1.22306	+	0.0641941i
$183$	−1.00000			−0.0739221
$184$	9.00000	−	5.19615i	0.663489	−	0.383065i
$185$	6.00000	−	10.3923i	0.441129	−	0.764057i
$186$	−3.00000	+	5.19615i	−0.219971	+	0.381000i
$187$	−13.5000	+	7.79423i	−0.987218	+	0.569970i
$188$		−	1.73205i		−	0.126323i
$189$	0.500000	−	2.59808i	0.0363696	−	0.188982i
$190$			31.1769i			2.26181i
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	3.00000	+	1.73205i	0.215945	+	0.124676i	0.604071	−	0.796930i	$-0.293544\pi$
$193$	3.00000	+	1.73205i	0.215945	+	0.124676i	−0.388126	+	0.921606i	$0.626878\pi$
$194$	−15.0000	−	25.9808i	−1.07694	−	1.86531i
$195$	12.0000	+	3.46410i	0.859338	+	0.248069i
$196$	−5.50000	+	4.33013i	−0.392857	+	0.309295i
$197$		−	24.2487i		−	1.72765i	−0.503793	−	0.863825i	$-0.668062\pi$
$197$		−	24.2487i		−	1.72765i	0.503793	−	0.863825i	$-0.331938\pi$
$198$	4.50000	+	7.79423i	0.319801	+	0.553912i
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	−0.828403	−	0.560133i	$-0.810750\pi$
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	0.899291	+	0.437351i	$0.144083\pi$
$200$	10.5000	+	6.06218i	0.742462	+	0.428661i
$201$	−1.50000	+	0.866025i	−0.105802	+	0.0610847i
$202$		−	10.3923i		−	0.731200i
$203$	−1.50000	+	7.79423i	−0.105279	+	0.547048i
$204$	−3.00000			−0.210042
$205$	18.0000	+	31.1769i	1.25717	+	2.17749i
$206$	6.00000	+	3.46410i	0.418040	+	0.241355i
$207$	−3.00000	+	5.19615i	−0.208514	+	0.361158i
$208$	−17.5000	+	4.33013i	−1.21341	+	0.300240i
$209$	27.0000			1.86763
$210$	15.0000	−	5.19615i	1.03510	−	0.358569i
$211$	−14.0000			−0.963800			−0.481900	−	0.876226i	$-0.660053\pi$
$211$	−14.0000			−0.963800			−0.481900	+	0.876226i	$0.660053\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$	−10.5000	−	6.06218i	−0.719448	−	0.415374i
$214$	−18.0000	−	10.3923i	−1.23045	−	0.710403i
$215$	24.0000	−	13.8564i	1.63679	−	0.944999i
$216$		−	1.73205i		−	0.117851i
$217$	6.00000	−	6.92820i	0.407307	−	0.470317i
$218$	−24.0000			−1.62549
$219$	9.00000	−	5.19615i	0.608164	−	0.351123i
$220$	−9.00000	+	15.5885i	−0.606780	+	1.05097i
$221$	7.50000	+	7.79423i	0.504505	+	0.524297i
$222$	−3.00000	−	5.19615i	−0.201347	−	0.348743i
$223$			25.9808i			1.73980i	0.493228	+	0.869900i	$0.335817\pi$
$223$			25.9808i			1.73980i	−0.493228	+	0.869900i	$0.664183\pi$
$224$	−9.00000	+	10.3923i	−0.601338	+	0.694365i
$225$	−7.00000			−0.466667
$226$	13.5000	−	7.79423i	0.898007	−	0.518464i
$227$	−21.0000	−	12.1244i	−1.39382	−	0.804722i	−0.400083	−	0.916479i	$-0.631019\pi$
$227$	−21.0000	−	12.1244i	−1.39382	−	0.804722i	−0.993736	+	0.111757i	$0.964352\pi$
$228$	4.50000	+	2.59808i	0.298020	+	0.172062i
$229$	−6.00000	+	3.46410i	−0.396491	+	0.228914i	−0.684969	−	0.728572i	$-0.740184\pi$
$229$	−6.00000	+	3.46410i	−0.396491	+	0.228914i	0.288478	+	0.957487i	$0.406851\pi$
$230$	−36.0000			−2.37377
$231$	−4.50000	−	12.9904i	−0.296078	−	0.854704i
$232$			5.19615i			0.341144i
$233$	13.5000	+	23.3827i	0.884414	+	1.53185i	0.846383	+	0.532574i	$0.178775\pi$
$233$	13.5000	+	23.3827i	0.884414	+	1.53185i	0.0380310	+	0.999277i	$0.487891\pi$
$234$	4.50000	−	4.33013i	0.294174	−	0.283069i
$235$	3.00000	−	5.19615i	0.195698	−	0.338960i
$236$	7.50000	−	4.33013i	0.488208	−	0.281867i
$237$	−4.00000			−0.259828
$238$	13.5000	+	2.59808i	0.875075	+	0.168408i
$239$			15.5885i			1.00833i	0.863606	+	0.504167i	$0.168200\pi$
$239$			15.5885i			1.00833i	−0.863606	+	0.504167i	$0.831800\pi$
$240$	15.0000	−	8.66025i	0.968246	−	0.559017i
$241$	6.00000	+	3.46410i	0.386494	+	0.223142i	0.680640	−	0.732618i	$-0.261702\pi$
$241$	6.00000	+	3.46410i	0.386494	+	0.223142i	−0.294146	+	0.955761i	$0.595035\pi$
$242$	24.0000	+	13.8564i	1.54278	+	0.890724i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−1.00000			−0.0640184
$245$	−24.0000	+	3.46410i	−1.53330	+	0.221313i
$246$	18.0000			1.14764
$247$	−4.50000	−	18.1865i	−0.286328	−	1.15718i
$248$	3.00000	−	5.19615i	0.190500	−	0.329956i
$249$	3.00000	+	1.73205i	0.190117	+	0.109764i
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$	0.500000	−	2.59808i	0.0314970	−	0.163663i
$253$			31.1769i			1.96008i
$254$	−3.00000	+	1.73205i	−0.188237	+	0.108679i
$255$	−9.00000	−	5.19615i	−0.563602	−	0.325396i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$		−	13.8564i		−	0.862662i
$259$	3.00000	+	8.66025i	0.186411	+	0.538122i
$260$	12.0000	+	3.46410i	0.744208	+	0.214834i
$261$	−1.50000	−	2.59808i	−0.0928477	−	0.160817i
$262$	9.00000	+	5.19615i	0.556022	+	0.321019i
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.133281	+	0.991078i	$0.542551\pi$
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.791658	+	0.610964i	$0.790782\pi$
$264$	−4.50000	−	7.79423i	−0.276956	−	0.479702i
$265$			10.3923i			0.638394i
$266$	−18.0000	−	15.5885i	−1.10365	−	0.955790i
$267$			3.46410i			0.212000i
$268$	−1.50000	+	0.866025i	−0.0916271	+	0.0529009i
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	−0.908124	−	0.418701i	$-0.862486\pi$
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	0.816668	+	0.577108i	$0.195819\pi$
$270$	−3.00000	+	5.19615i	−0.182574	+	0.316228i
$271$	16.5000	−	9.52628i	1.00230	−	0.578680i	0.0933746	−	0.995631i	$-0.470235\pi$
$271$	16.5000	−	9.52628i	1.00230	−	0.578680i	0.908929	+	0.416951i	$0.136901\pi$
$272$	15.0000			0.909509
$273$	−8.00000	+	5.19615i	−0.484182	+	0.314485i
$274$	−18.0000			−1.08742
$275$	−31.5000	+	18.1865i	−1.89952	+	1.09669i
$276$	−3.00000	+	5.19615i	−0.180579	+	0.312772i
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	−0.425684	−	0.904872i	$-0.639967\pi$
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	0.996484	−	0.0837823i	$-0.0267000\pi$
$278$	21.0000	−	12.1244i	1.25950	−	0.727171i
$279$			3.46410i			0.207390i
$280$	−15.0000	+	5.19615i	−0.896421	+	0.310530i
$281$		−	6.92820i		−	0.413302i	−0.978415	−	0.206651i	$-0.933744\pi$
$281$		−	6.92820i		−	0.413302i	0.978415	−	0.206651i	$-0.0662565\pi$
$282$	−1.50000	−	2.59808i	−0.0893237	−	0.154713i
$283$	−11.0000	+	19.0526i	−0.653882	+	1.13256i	0.328291	+	0.944577i	$0.393527\pi$
$283$	−11.0000	+	19.0526i	−0.653882	+	1.13256i	−0.982173	+	0.187980i	$0.939806\pi$
$284$	−10.5000	−	6.06218i	−0.623060	−	0.359724i
$285$	9.00000	+	15.5885i	0.533114	+	0.923381i
$286$	9.00000	−	31.1769i	0.532181	−	1.84353i
$287$	−27.0000	−	5.19615i	−1.59376	−	0.306719i
$288$		−	5.19615i		−	0.306186i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	9.00000	−	15.5885i	0.528498	−	0.915386i
$291$	−15.0000	−	8.66025i	−0.879316	−	0.507673i
$292$	9.00000	−	5.19615i	0.526685	−	0.304082i
$293$		−	10.3923i		−	0.607125i	−0.952812	−	0.303562i	$-0.901824\pi$
$293$		−	10.3923i		−	0.607125i	0.952812	−	0.303562i	$-0.0981761\pi$
$294$	−4.50000	+	11.2583i	−0.262445	+	0.656599i
$295$	30.0000			1.74667
$296$	3.00000	+	5.19615i	0.174371	+	0.302020i
$297$	4.50000	+	2.59808i	0.261116	+	0.150756i
$298$	−3.00000	+	5.19615i	−0.173785	+	0.301005i
$299$	21.0000	−	5.19615i	1.21446	−	0.300501i
$300$	−7.00000			−0.404145
$301$	−4.00000	+	20.7846i	−0.230556	+	1.19800i
$302$	15.0000			0.863153
$303$	−3.00000	−	5.19615i	−0.172345	−	0.298511i
$304$	−22.5000	−	12.9904i	−1.29046	−	0.745049i
$305$	−3.00000	−	1.73205i	−0.171780	−	0.0991769i
$306$	−4.50000	+	2.59808i	−0.257248	+	0.148522i
$307$		−	12.1244i		−	0.691974i	−0.938239	−	0.345987i	$-0.887544\pi$
$307$		−	12.1244i		−	0.691974i	0.938239	−	0.345987i	$-0.112456\pi$
$308$	−4.50000	−	12.9904i	−0.256411	−	0.740196i
$309$	4.00000			0.227552
$310$	−18.0000	+	10.3923i	−1.02233	+	0.590243i
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	0.489585	+	0.871956i	$0.337148\pi$
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	−0.999928	+	0.0119847i	$0.996185\pi$
$312$	−4.50000	+	4.33013i	−0.254762	+	0.245145i
$313$	1.00000	+	1.73205i	0.0565233	+	0.0979013i	0.892903	−	0.450250i	$-0.148665\pi$
$313$	1.00000	+	1.73205i	0.0565233	+	0.0979013i	−0.836379	+	0.548151i	$0.815332\pi$
$314$			29.4449i			1.66167i
$315$	6.00000	−	6.92820i	0.338062	−	0.390360i
$316$	−4.00000			−0.225018
$317$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$317$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$318$	4.50000	+	2.59808i	0.252347	+	0.145693i
$319$	−13.5000	−	7.79423i	−0.755855	−	0.436393i
$320$	−3.00000	+	1.73205i	−0.167705	+	0.0968246i
$321$	−12.0000			−0.669775
$322$	18.0000	−	20.7846i	1.00310	−	1.15828i
$323$			15.5885i			0.867365i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	17.5000	+	18.1865i	0.970725	+	1.00881i
$326$	−10.5000	+	18.1865i	−0.581541	+	1.00726i
$327$	−12.0000	+	6.92820i	−0.663602	+	0.383131i
$328$	−18.0000			−0.993884
$329$	1.50000	+	4.33013i	0.0826977	+	0.238728i
$330$			31.1769i			1.71623i
$331$	27.0000	−	15.5885i	1.48405	−	0.856819i	0.484219	−	0.874947i	$-0.339104\pi$
$331$	27.0000	−	15.5885i	1.48405	−	0.856819i	0.999836	+	0.0181280i	$0.00577063\pi$
$332$	3.00000	+	1.73205i	0.164646	+	0.0950586i
$333$	−3.00000	−	1.73205i	−0.164399	−	0.0949158i
$334$	7.50000	+	12.9904i	0.410382	+	0.710802i
$335$	−6.00000			−0.327815
$336$	−2.50000	+	12.9904i	−0.136386	+	0.708683i
$337$	−17.0000			−0.926049			−0.463025	−	0.886345i	$-0.653236\pi$
$337$	−17.0000			−0.926049			−0.463025	+	0.886345i	$0.653236\pi$
$338$	−22.5000	−	0.866025i	−1.22384	−	0.0471056i
$339$	4.50000	−	7.79423i	0.244406	−	0.423324i
$340$	−9.00000	−	5.19615i	−0.488094	−	0.281801i
$341$	9.00000	+	15.5885i	0.487377	+	0.844162i
$342$	9.00000			0.486664
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$			13.8564i			0.747087i
$345$	−18.0000	+	10.3923i	−0.969087	+	0.559503i
$346$	−22.5000	−	12.9904i	−1.20961	−	0.698367i
$347$	3.00000	−	5.19615i	0.161048	−	0.278944i	−0.774197	−	0.632945i	$-0.781846\pi$
$347$	3.00000	−	5.19615i	0.161048	−	0.278944i	0.935245	+	0.354001i	$0.115179\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$			24.2487i			1.29800i	0.760787	+	0.649002i	$0.224813\pi$
$349$			24.2487i			1.29800i	−0.760787	+	0.649002i	$0.775187\pi$
$350$	31.5000	+	6.06218i	1.68375	+	0.324037i
$351$	1.00000	−	3.46410i	0.0533761	−	0.184900i
$352$	−13.5000	−	23.3827i	−0.719552	−	1.24630i
$353$	6.00000	+	3.46410i	0.319348	+	0.184376i	0.651102	−	0.758990i	$-0.274307\pi$
$353$	6.00000	+	3.46410i	0.319348	+	0.184376i	−0.331754	+	0.943366i	$0.607640\pi$
$354$	7.50000	−	12.9904i	0.398621	−	0.690431i
$355$	−21.0000	−	36.3731i	−1.11456	−	1.93048i
$356$			3.46410i			0.183597i
$357$	7.50000	−	2.59808i	0.396942	−	0.137505i
$358$		−	20.7846i		−	1.09850i
$359$	21.0000	−	12.1244i	1.10834	−	0.639899i	0.169939	−	0.985455i	$-0.445643\pi$
$359$	21.0000	−	12.1244i	1.10834	−	0.639899i	0.938398	+	0.345556i	$0.112310\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	4.00000	−	6.92820i	0.210526	−	0.364642i
$362$	7.50000	−	4.33013i	0.394191	−	0.227586i
$363$	16.0000			0.839782
$364$	−8.00000	+	5.19615i	−0.419314	+	0.272352i
$365$	36.0000			1.88433
$366$	−1.50000	+	0.866025i	−0.0784063	+	0.0452679i
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	15.0000	−	25.9808i	0.781929	−	1.35434i
$369$	9.00000	−	5.19615i	0.468521	−	0.270501i
$370$		−	20.7846i		−	1.08054i
$371$	−6.00000	−	5.19615i	−0.311504	−	0.269771i
$372$			3.46410i			0.179605i
$373$	−0.500000	−	0.866025i	−0.0258890	−	0.0448411i	0.852791	−	0.522253i	$-0.174908\pi$
$373$	−0.500000	−	0.866025i	−0.0258890	−	0.0448411i	−0.878680	+	0.477412i	$0.841575\pi$
$374$	−13.5000	+	23.3827i	−0.698068	+	1.20909i
$375$	−6.00000	−	3.46410i	−0.309839	−	0.178885i
$376$	1.50000	+	2.59808i	0.0773566	+	0.133986i
$377$	−3.00000	+	10.3923i	−0.154508	+	0.535231i
$378$	−1.50000	−	4.33013i	−0.0771517	−	0.222718i
$379$		−	17.3205i		−	0.889695i	−0.895606	−	0.444847i	$-0.853258\pi$
$379$		−	17.3205i		−	0.889695i	0.895606	−	0.444847i	$-0.146742\pi$
$380$	9.00000	+	15.5885i	0.461690	+	0.799671i
$381$	−1.00000	+	1.73205i	−0.0512316	+	0.0887357i
$382$	18.0000	+	10.3923i	0.920960	+	0.531717i
$383$	9.00000	−	5.19615i	0.459879	−	0.265511i	−0.252115	−	0.967697i	$-0.581126\pi$
$383$	9.00000	−	5.19615i	0.459879	−	0.265511i	0.711993	+	0.702186i	$0.247793\pi$
$384$			12.1244i			0.618718i
$385$	9.00000	−	46.7654i	0.458682	−	2.38338i
$386$	6.00000			0.305392
$387$	−4.00000	−	6.92820i	−0.203331	−	0.352180i
$388$	−15.0000	−	8.66025i	−0.761510	−	0.439658i
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	−0.466915	−	0.884302i	$-0.654634\pi$
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	0.999286	−	0.0377914i	$-0.0120322\pi$
$390$	21.0000	−	5.19615i	1.06338	−	0.263117i
$391$	−18.0000			−0.910299
$392$	4.50000	−	11.2583i	0.227284	−	0.568632i
$393$	6.00000			0.302660
$394$	−21.0000	−	36.3731i	−1.05796	−	1.83245i
$395$	−12.0000	−	6.92820i	−0.603786	−	0.348596i
$396$	4.50000	+	2.59808i	0.226134	+	0.130558i
$397$	3.00000	−	1.73205i	0.150566	−	0.0869291i	−0.422824	−	0.906212i	$-0.638961\pi$
$397$	3.00000	−	1.73205i	0.150566	−	0.0869291i	0.573390	+	0.819282i	$0.305628\pi$
$398$		−	3.46410i		−	0.173640i
$399$	−13.5000	−	2.59808i	−0.675845	−	0.130066i
$400$	35.0000			1.75000
$401$	−3.00000	+	1.73205i	−0.149813	+	0.0864945i	−0.573033	−	0.819533i	$-0.694233\pi$
$401$	−3.00000	+	1.73205i	−0.149813	+	0.0864945i	0.423220	+	0.906027i	$0.360900\pi$
$402$	−1.50000	+	2.59808i	−0.0748132	+	0.129580i
$403$	9.00000	−	8.66025i	0.448322	−	0.431398i
$404$	−3.00000	−	5.19615i	−0.149256	−	0.258518i
$405$			3.46410i			0.172133i
$406$	4.50000	+	12.9904i	0.223331	+	0.644702i
$407$	−18.0000			−0.892227
$408$	4.50000	−	2.59808i	0.222783	−	0.128624i
$409$	−3.00000	−	1.73205i	−0.148340	−	0.0856444i	0.423993	−	0.905666i	$-0.360628\pi$
$409$	−3.00000	−	1.73205i	−0.148340	−	0.0856444i	−0.572333	+	0.820021i	$0.693962\pi$
$410$	54.0000	+	31.1769i	2.66687	+	1.53972i
$411$	−9.00000	+	5.19615i	−0.443937	+	0.256307i
$412$	4.00000			0.197066
$413$	−15.0000	+	17.3205i	−0.738102	+	0.852286i
$414$			10.3923i			0.510754i
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$	−13.5000	+	12.9904i	−0.661892	+	0.636906i
$417$	7.00000	−	12.1244i	0.342791	−	0.593732i
$418$	40.5000	−	23.3827i	1.98092	−	1.14368i
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$	6.00000	−	6.92820i	0.292770	−	0.338062i
$421$			10.3923i			0.506490i	0.967402	+	0.253245i	$0.0814979\pi$
$421$			10.3923i			0.506490i	−0.967402	+	0.253245i	$0.918502\pi$
$422$	−21.0000	+	12.1244i	−1.02226	+	0.590204i
$423$	−1.50000	−	0.866025i	−0.0729325	−	0.0421076i
$424$	−4.50000	−	2.59808i	−0.218539	−	0.126174i
$425$	−10.5000	−	18.1865i	−0.509325	−	0.882176i
$426$	−21.0000			−1.01745
$427$	2.50000	−	0.866025i	0.120983	−	0.0419099i
$428$	−12.0000			−0.580042
$429$	−4.50000	−	18.1865i	−0.217262	−	0.878054i
$430$	24.0000	−	41.5692i	1.15738	−	2.00465i
$431$	3.00000	+	1.73205i	0.144505	+	0.0834300i	0.570509	−	0.821291i	$-0.306746\pi$
$431$	3.00000	+	1.73205i	0.144505	+	0.0834300i	−0.426004	+	0.904721i	$0.640079\pi$
$432$	−2.50000	−	4.33013i	−0.120281	−	0.208333i
$433$	19.0000			0.913082			0.456541	−	0.889702i	$-0.349088\pi$
$433$	19.0000			0.913082			0.456541	+	0.889702i	$0.349088\pi$
$434$	3.00000	−	15.5885i	0.144005	−	0.748270i
$435$		−	10.3923i		−	0.498273i
$436$	−12.0000	+	6.92820i	−0.574696	+	0.331801i
$437$	27.0000	+	15.5885i	1.29159	+	0.745697i
$438$	9.00000	−	15.5885i	0.430037	−	0.744845i
$439$	−1.00000	−	1.73205i	−0.0477274	−	0.0826663i	0.841175	−	0.540763i	$-0.181865\pi$
$439$	−1.00000	−	1.73205i	−0.0477274	−	0.0826663i	−0.888902	+	0.458097i	$0.848531\pi$
$440$		−	31.1769i		−	1.48630i
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$	18.0000	+	5.19615i	0.856173	+	0.247156i
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	0.785916	−	0.618333i	$-0.212192\pi$
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	−0.928450	+	0.371457i	$0.878858\pi$
$444$	−3.00000	−	1.73205i	−0.142374	−	0.0821995i
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	22.5000	+	38.9711i	1.06541	+	1.84534i
$447$			3.46410i			0.163846i
$448$	0.500000	−	2.59808i	0.0236228	−	0.122748i
$449$		−	6.92820i		−	0.326962i	−0.986546	−	0.163481i	$-0.947728\pi$
$449$		−	6.92820i		−	0.326962i	0.986546	−	0.163481i	$-0.0522723\pi$
$450$	−10.5000	+	6.06218i	−0.494975	+	0.285774i
$451$	27.0000	−	46.7654i	1.27138	−	2.20210i
$452$	4.50000	−	7.79423i	0.211662	−	0.366610i
$453$	7.50000	−	4.33013i	0.352381	−	0.203447i
$454$	−42.0000			−1.97116
$455$	−33.0000	+	1.73205i	−1.54706	+	0.0811998i
$456$	−9.00000			−0.421464
$457$	−15.0000	+	8.66025i	−0.701670	+	0.405110i	−0.807969	−	0.589225i	$-0.799433\pi$
$457$	−15.0000	+	8.66025i	−0.701670	+	0.405110i	0.106299	+	0.994334i	$0.466100\pi$
$458$	−6.00000	+	10.3923i	−0.280362	+	0.485601i
$459$	−1.50000	+	2.59808i	−0.0700140	+	0.121268i
$460$	−18.0000	+	10.3923i	−0.839254	+	0.484544i
$461$			6.92820i			0.322679i	0.986899	+	0.161339i	$0.0515813\pi$
$461$			6.92820i			0.322679i	−0.986899	+	0.161339i	$0.948419\pi$
$462$	−18.0000	−	15.5885i	−0.837436	−	0.725241i
$463$			31.1769i			1.44891i	0.689320	+	0.724457i	$0.257909\pi$
$463$			31.1769i			1.44891i	−0.689320	+	0.724457i	$0.742091\pi$
$464$	7.50000	+	12.9904i	0.348179	+	0.603063i
$465$	−6.00000	+	10.3923i	−0.278243	+	0.481932i
$466$	40.5000	+	23.3827i	1.87613	+	1.08318i
$467$	9.00000	+	15.5885i	0.416470	+	0.721348i	0.995582	−	0.0939008i	$-0.0299336\pi$
$467$	9.00000	+	15.5885i	0.416470	+	0.721348i	−0.579111	+	0.815249i	$0.696600\pi$
$468$	1.00000	−	3.46410i	0.0462250	−	0.160128i
$469$	3.00000	−	3.46410i	0.138527	−	0.159957i
$470$		−	10.3923i		−	0.479361i
$471$	8.50000	+	14.7224i	0.391659	+	0.678374i
$472$	−7.50000	+	12.9904i	−0.345215	+	0.597931i
$473$	−36.0000	−	20.7846i	−1.65528	−	0.955677i
$474$	−6.00000	+	3.46410i	−0.275589	+	0.159111i
$475$			36.3731i			1.66891i
$476$	7.50000	−	2.59808i	0.343762	−	0.119083i
$477$	3.00000			0.137361
$478$	13.5000	+	23.3827i	0.617476	+	1.06950i
$479$	−1.50000	−	0.866025i	−0.0685367	−	0.0395697i	0.465340	−	0.885132i	$-0.345932\pi$
$479$	−1.50000	−	0.866025i	−0.0685367	−	0.0395697i	−0.533877	+	0.845562i	$0.679265\pi$
$480$	9.00000	−	15.5885i	0.410792	−	0.711512i
$481$	3.00000	+	12.1244i	0.136788	+	0.552823i
$482$	12.0000			0.546585
$483$	3.00000	−	15.5885i	0.136505	−	0.709299i
$484$	16.0000			0.727273
$485$	−30.0000	−	51.9615i	−1.36223	−	2.35945i
$486$	1.50000	+	0.866025i	0.0680414	+	0.0392837i
$487$	−22.5000	−	12.9904i	−1.01957	−	0.588650i	−0.105592	−	0.994410i	$-0.533674\pi$
$487$	−22.5000	−	12.9904i	−1.01957	−	0.588650i	−0.913980	+	0.405759i	$0.867007\pi$
$488$	1.50000	−	0.866025i	0.0679018	−	0.0392031i
$489$			12.1244i			0.548282i
$490$	−33.0000	+	25.9808i	−1.49079	+	1.17369i
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$	9.00000	−	5.19615i	0.405751	−	0.234261i
$493$	4.50000	−	7.79423i	0.202670	−	0.351034i
$494$	−22.5000	−	23.3827i	−1.01232	−	1.05204i
$495$	9.00000	+	15.5885i	0.404520	+	0.700649i
$496$		−	17.3205i		−	0.777714i
$497$	31.5000	+	6.06218i	1.41297	+	0.271926i
$498$	6.00000			0.268866
$499$	15.0000	−	8.66025i	0.671492	−	0.387686i	−0.125150	−	0.992138i	$-0.539941\pi$
$499$	15.0000	−	8.66025i	0.671492	−	0.387686i	0.796642	+	0.604452i	$0.206608\pi$
$500$	−6.00000	−	3.46410i	−0.268328	−	0.154919i
$501$	7.50000	+	4.33013i	0.335075	+	0.193456i
$502$	−18.0000	+	10.3923i	−0.803379	+	0.463831i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	1.50000	+	4.33013i	0.0668153	+	0.192879i
$505$		−	20.7846i		−	0.924903i
$506$	27.0000	+	46.7654i	1.20030	+	2.07897i
$507$	−11.5000	+	6.06218i	−0.510733	+	0.269231i
$508$	−1.00000	+	1.73205i	−0.0443678	+	0.0768473i
$509$	6.00000	−	3.46410i	0.265945	−	0.153544i	−0.361098	−	0.932528i	$-0.617598\pi$
$509$	6.00000	−	3.46410i	0.265945	−	0.153544i	0.627044	+	0.778984i	$0.284265\pi$
$510$	−18.0000			−0.797053
$511$	−18.0000	+	20.7846i	−0.796273	+	0.919457i
$512$			8.66025i			0.382733i
$513$	4.50000	−	2.59808i	0.198680	−	0.114708i
$514$	9.00000	+	5.19615i	0.396973	+	0.229192i
$515$	12.0000	+	6.92820i	0.528783	+	0.305293i
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$	−9.00000			−0.395820
$518$	12.0000	+	10.3923i	0.527250	+	0.456612i
$519$	−15.0000			−0.658427
$520$	−21.0000	+	5.19615i	−0.920911	+	0.227866i
$521$	15.0000	−	25.9808i	0.657162	−	1.13824i	−0.324185	−	0.945994i	$-0.605090\pi$
$521$	15.0000	−	25.9808i	0.657162	−	1.13824i	0.981347	−	0.192244i	$-0.0615766\pi$
$522$	−4.50000	−	2.59808i	−0.196960	−	0.113715i
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$	6.00000			0.262111
$525$	17.5000	−	6.06218i	0.763763	−	0.264575i
$526$			51.9615i			2.26563i
$527$	−9.00000	+	5.19615i	−0.392046	+	0.226348i
$528$	−22.5000	−	12.9904i	−0.979187	−	0.565334i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	9.00000	+	15.5885i	0.390935	+	0.677119i
$531$		−	8.66025i		−	0.375823i
$532$	−13.5000	−	2.59808i	−0.585299	−	0.112641i
$533$	−36.0000	−	10.3923i	−1.55933	−	0.450141i
$534$	3.00000	+	5.19615i	0.129823	+	0.224860i
$535$	−36.0000	−	20.7846i	−1.55642	−	0.898597i
$536$	1.50000	−	2.59808i	0.0647901	−	0.112220i
$537$	−6.00000	−	10.3923i	−0.258919	−	0.448461i
$538$			5.19615i			0.224022i
$539$	22.5000	+	28.5788i	0.969144	+	1.23098i
$540$			3.46410i			0.149071i
$541$	−27.0000	+	15.5885i	−1.16082	+	0.670200i	−0.951501	−	0.307647i	$-0.900458\pi$
$541$	−27.0000	+	15.5885i	−1.16082	+	0.670200i	−0.209320	+	0.977847i	$0.567125\pi$
$542$	16.5000	−	28.5788i	0.708736	−	1.22757i
$543$	2.50000	−	4.33013i	0.107285	−	0.185824i
$544$	13.5000	−	7.79423i	0.578808	−	0.334175i
$545$	−48.0000			−2.05609
$546$	−7.50000	+	14.7224i	−0.320970	+	0.630062i
$547$	14.0000			0.598597			0.299298	−	0.954160i	$-0.403247\pi$
$547$	14.0000			0.598597			0.299298	+	0.954160i	$0.403247\pi$
$548$	−9.00000	+	5.19615i	−0.384461	+	0.221969i
$549$	−0.500000	+	0.866025i	−0.0213395	+	0.0369611i
$550$	−31.5000	+	54.5596i	−1.34316	+	2.32643i
$551$	−13.5000	+	7.79423i	−0.575119	+	0.332045i
$552$		−	10.3923i		−	0.442326i
$553$	10.0000	−	3.46410i	0.425243	−	0.147309i
$554$		−	32.9090i		−	1.39817i
$555$	−6.00000	−	10.3923i	−0.254686	−	0.441129i
$556$	7.00000	−	12.1244i	0.296866	−	0.514187i
$557$	−36.0000	−	20.7846i	−1.52537	−	0.880672i	−0.999548	−	0.0300772i	$-0.990425\pi$
$557$	−36.0000	−	20.7846i	−1.52537	−	0.880672i	−0.525821	−	0.850595i	$-0.676242\pi$
$558$	3.00000	+	5.19615i	0.127000	+	0.219971i
$559$	−8.00000	+	27.7128i	−0.338364	+	1.17213i
$560$	−30.0000	+	34.6410i	−1.26773	+	1.46385i
$561$			15.5885i			0.658145i
$562$	−6.00000	−	10.3923i	−0.253095	−	0.438373i
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$	−1.50000	−	0.866025i	−0.0631614	−	0.0364662i
$565$	27.0000	−	15.5885i	1.13590	−	0.655811i
$566$			38.1051i			1.60168i
$567$	−2.00000	−	1.73205i	−0.0839921	−	0.0727393i
$568$	21.0000			0.881140
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	0.979313	−	0.202350i	$-0.0648579\pi$
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	−0.664897	+	0.746935i	$0.731525\pi$
$570$	27.0000	+	15.5885i	1.13091	+	0.652929i
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	−0.770108	−	0.637913i	$-0.779798\pi$
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	0.937503	+	0.347977i	$0.113131\pi$
$572$	−4.50000	−	18.1865i	−0.188154	−	0.760417i
$573$	12.0000			0.501307
$574$	−45.0000	+	15.5885i	−1.87826	+	0.650650i
$575$	−42.0000			−1.75152
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−30.0000	−	17.3205i	−1.24892	−	0.721062i	−0.278023	−	0.960574i	$-0.589679\pi$
$577$	−30.0000	−	17.3205i	−1.24892	−	0.721062i	−0.970893	+	0.239512i	$0.923012\pi$
$578$	12.0000	+	6.92820i	0.499134	+	0.288175i
$579$	3.00000	−	1.73205i	0.124676	−	0.0719816i
$580$		−	10.3923i		−	0.431517i
$581$	−9.00000	−	1.73205i	−0.373383	−	0.0718576i
$582$	−30.0000			−1.24354
$583$	13.5000	−	7.79423i	0.559113	−	0.322804i
$584$	−9.00000	+	15.5885i	−0.372423	+	0.645055i
$585$	9.00000	−	8.66025i	0.372104	−	0.358057i
$586$	−9.00000	−	15.5885i	−0.371787	−	0.643953i
$587$		−	36.3731i		−	1.50128i	−0.660713	−	0.750639i	$-0.729746\pi$
$587$		−	36.3731i		−	1.50128i	0.660713	−	0.750639i	$-0.270254\pi$
$588$	1.00000	+	6.92820i	0.0412393	+	0.285714i
$589$	18.0000			0.741677
$590$	45.0000	−	25.9808i	1.85262	−	1.06961i
$591$	−21.0000	−	12.1244i	−0.863825	−	0.498729i
$592$	15.0000	+	8.66025i	0.616496	+	0.355934i
$593$	27.0000	−	15.5885i	1.10876	−	0.640141i	0.170250	−	0.985401i	$-0.445542\pi$
$593$	27.0000	−	15.5885i	1.10876	−	0.640141i	0.938507	+	0.345260i	$0.112209\pi$
$594$	9.00000			0.369274
$595$	27.0000	+	5.19615i	1.10689	+	0.213021i
$596$			3.46410i			0.141895i
$597$	−1.00000	−	1.73205i	−0.0409273	−	0.0708881i
$598$	27.0000	−	25.9808i	1.10411	−	1.06243i
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	−0.920783	−	0.390075i	$-0.872449\pi$
$599$	−3.00000	+	5.19615i	−0.122577	+	0.212309i	0.798206	+	0.602384i	$0.205782\pi$
$600$	10.5000	−	6.06218i	0.428661	−	0.247487i
$601$	−17.0000			−0.693444			−0.346722	−	0.937968i	$-0.612705\pi$
$601$	−17.0000			−0.693444			−0.346722	+	0.937968i	$0.612705\pi$
$602$	12.0000	+	34.6410i	0.489083	+	1.41186i
$603$			1.73205i			0.0705346i
$604$	7.50000	−	4.33013i	0.305171	−	0.176190i
$605$	48.0000	+	27.7128i	1.95148	+	1.12669i
$606$	−9.00000	−	5.19615i	−0.365600	−	0.211079i
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$	−27.0000			−1.09499
$609$	6.00000	+	5.19615i	0.243132	+	0.210559i
$610$	−6.00000			−0.242933
$611$	1.50000	+	6.06218i	0.0606835	+	0.245249i
$612$	−1.50000	+	2.59808i	−0.0606339	+	0.105021i
$613$	6.00000	+	3.46410i	0.242338	+	0.139914i	0.616251	−	0.787550i	$-0.288651\pi$
$613$	6.00000	+	3.46410i	0.242338	+	0.139914i	−0.373913	+	0.927464i	$0.621984\pi$
$614$	−10.5000	−	18.1865i	−0.423746	−	0.733949i
$615$	36.0000			1.45166
$616$	18.0000	+	15.5885i	0.725241	+	0.628077i
$617$			34.6410i			1.39459i	0.716782	+	0.697297i	$0.245614\pi$
$617$			34.6410i			1.39459i	−0.716782	+	0.697297i	$0.754386\pi$
$618$	6.00000	−	3.46410i	0.241355	−	0.139347i
$619$	−15.0000	−	8.66025i	−0.602901	−	0.348085i	0.167281	−	0.985909i	$-0.446501\pi$
$619$	−15.0000	−	8.66025i	−0.602901	−	0.348085i	−0.770182	+	0.637824i	$0.779835\pi$
$620$	−6.00000	+	10.3923i	−0.240966	+	0.417365i
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$			31.1769i			1.25008i
$623$	−3.00000	−	8.66025i	−0.120192	−	0.346966i
$624$	−5.00000	+	17.3205i	−0.200160	+	0.693375i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	3.00000	+	1.73205i	0.119904	+	0.0692267i
$627$	13.5000	−	23.3827i	0.539138	−	0.933815i
$628$	8.50000	+	14.7224i	0.339187	+	0.587489i
$629$		−	10.3923i		−	0.414368i
$630$	3.00000	−	15.5885i	0.119523	−	0.621059i
$631$		−	3.46410i		−	0.137904i	−0.997620	−	0.0689519i	$-0.978035\pi$
$631$		−	3.46410i		−	0.137904i	0.997620	−	0.0689519i	$-0.0219655\pi$
$632$	6.00000	−	3.46410i	0.238667	−	0.137795i
$633$	−7.00000	+	12.1244i	−0.278225	+	0.481900i
$634$		0			0
$635$	−6.00000	+	3.46410i	−0.238103	+	0.137469i
$636$	3.00000			0.118958
$637$	15.5000	−	19.9186i	0.614132	−	0.789203i
$638$	−27.0000			−1.06894
$639$	−10.5000	+	6.06218i	−0.415374	+	0.239816i
$640$	−21.0000	+	36.3731i	−0.830098	+	1.43777i
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$	−18.0000	+	10.3923i	−0.710403	+	0.410152i
$643$		−	19.0526i		−	0.751360i	−0.926750	−	0.375680i	$-0.877409\pi$
$643$		−	19.0526i		−	0.751360i	0.926750	−	0.375680i	$-0.122591\pi$
$644$	3.00000	−	15.5885i	0.118217	−	0.614271i
$645$		−	27.7128i		−	1.09119i
$646$	13.5000	+	23.3827i	0.531150	+	0.919979i
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	−1.50000	−	0.866025i	−0.0589256	−	0.0340207i
$649$	−22.5000	−	38.9711i	−0.883202	−	1.52975i
$650$	42.0000	+	12.1244i	1.64738	+	0.475556i
$651$	−3.00000	−	8.66025i	−0.117579	−	0.339422i
$652$			12.1244i			0.474826i
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	−0.904345	−	0.426801i	$-0.859640\pi$
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	0.0825519	−	0.996587i	$-0.473693\pi$
$654$	−12.0000	+	20.7846i	−0.469237	+	0.812743i
$655$	18.0000	+	10.3923i	0.703318	+	0.406061i
$656$	−45.0000	+	25.9808i	−1.75695	+	1.01438i
$657$		−	10.3923i		−	0.405442i
$658$	6.00000	+	5.19615i	0.233904	+	0.202567i
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$	9.00000	+	15.5885i	0.350325	+	0.606780i
$661$	9.00000	+	5.19615i	0.350059	+	0.202107i	0.664711	−	0.747100i	$-0.268554\pi$
$661$	9.00000	+	5.19615i	0.350059	+	0.202107i	−0.314652	+	0.949207i	$0.601888\pi$
$662$	27.0000	−	46.7654i	1.04938	−	1.81759i
$663$	10.5000	−	2.59808i	0.407786	−	0.100901i
$664$	−6.00000			−0.232845
$665$	−36.0000	−	31.1769i	−1.39602	−	1.20899i
$666$	−6.00000			−0.232495
$667$	−9.00000	−	15.5885i	−0.348481	−	0.603587i
$668$	7.50000	+	4.33013i	0.290184	+	0.167538i
$669$	22.5000	+	12.9904i	0.869900	+	0.502237i
$670$	−9.00000	+	5.19615i	−0.347700	+	0.200745i
$671$			5.19615i			0.200595i
$672$	4.50000	+	12.9904i	0.173591	+	0.501115i
$673$	−34.0000			−1.31060			−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000			−1.31060			−0.655302	+	0.755367i	$0.727459\pi$
$674$	−25.5000	+	14.7224i	−0.982223	+	0.567087i
$675$	−3.50000	+	6.06218i	−0.134715	+	0.233333i
$676$	−11.5000	+	6.06218i	−0.442308	+	0.233161i
$677$	−7.50000	−	12.9904i	−0.288248	−	0.499261i	0.685143	−	0.728408i	$-0.259740\pi$
$677$	−7.50000	−	12.9904i	−0.288248	−	0.499261i	−0.973392	+	0.229147i	$0.926406\pi$
$678$		−	15.5885i		−	0.598671i
$679$	45.0000	+	8.66025i	1.72694	+	0.332350i
$680$	18.0000			0.690268
$681$	−21.0000	+	12.1244i	−0.804722	+	0.464606i
$682$	27.0000	+	15.5885i	1.03388	+	0.596913i
$683$	15.0000	+	8.66025i	0.573959	+	0.331375i	0.758729	−	0.651406i	$-0.225821\pi$
$683$	15.0000	+	8.66025i	0.573959	+	0.331375i	−0.184770	+	0.982782i	$0.559154\pi$
$684$	4.50000	−	2.59808i	0.172062	−	0.0993399i
$685$	−36.0000			−1.37549
$686$	1.50000	−	32.0429i	0.0572703	−	1.22341i
$687$			6.92820i			0.264327i
$688$	20.0000	+	34.6410i	0.762493	+	1.32068i
$689$	−7.50000	−	7.79423i	−0.285727	−	0.296936i
$690$	−18.0000	+	31.1769i	−0.685248	+	1.18688i
$691$	−10.5000	+	6.06218i	−0.399439	+	0.230616i	−0.686242	−	0.727373i	$-0.740741\pi$
$691$	−10.5000	+	6.06218i	−0.399439	+	0.230616i	0.286803	+	0.957990i	$0.407407\pi$
$692$	−15.0000			−0.570214
$693$	−13.5000	−	2.59808i	−0.512823	−	0.0986928i
$694$		−	10.3923i		−	0.394486i
$695$	42.0000	−	24.2487i	1.59315	−	0.919806i
$696$	4.50000	+	2.59808i	0.170572	+	0.0984798i
$697$	27.0000	+	15.5885i	1.02270	+	0.590455i
$698$	21.0000	+	36.3731i	0.794862	+	1.37674i
$699$	27.0000			1.02123
$700$	17.5000	−	6.06218i	0.661438	−	0.229129i
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$	−1.50000	−	6.06218i	−0.0566139	−	0.228802i
$703$	−9.00000	+	15.5885i	−0.339441	+	0.587930i
$704$	4.50000	+	2.59808i	0.169600	+	0.0979187i
$705$	−3.00000	−	5.19615i	−0.112987	−	0.195698i
$706$	12.0000			0.451626
$707$	12.0000	+	10.3923i	0.451306	+	0.390843i
$708$		−	8.66025i		−	0.325472i
$709$	−21.0000	+	12.1244i	−0.788672	+	0.455340i	−0.839495	−	0.543368i	$-0.817149\pi$
$709$	−21.0000	+	12.1244i	−0.788672	+	0.455340i	0.0508231	+	0.998708i	$0.483816\pi$
$710$	−63.0000	−	36.3731i	−2.36435	−	1.36506i
$711$	−2.00000	+	3.46410i	−0.0750059	+	0.129914i
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$			20.7846i			0.778390i
$714$	9.00000	−	10.3923i	0.336817	−	0.388922i
$715$	18.0000	−	62.3538i	0.673162	−	2.33190i
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	13.5000	+	7.79423i	0.504167	+	0.291081i
$718$	21.0000	−	36.3731i	0.783713	−	1.35743i
$719$	18.0000	+	31.1769i	0.671287	+	1.16270i	0.977539	+	0.210752i	$0.0675914\pi$
$719$	18.0000	+	31.1769i	0.671287	+	1.16270i	−0.306253	+	0.951950i	$0.599075\pi$
$720$		−	17.3205i		−	0.645497i
$721$	−10.0000	+	3.46410i	−0.372419	+	0.129010i
$722$		−	13.8564i		−	0.515682i
$723$	6.00000	−	3.46410i	0.223142	−	0.128831i
$724$	2.50000	−	4.33013i	0.0929118	−	0.160928i
$725$	10.5000	−	18.1865i	0.389960	−	0.675431i
$726$	24.0000	−	13.8564i	0.890724	−	0.514259i
$727$	4.00000			0.148352			0.0741759	−	0.997245i	$-0.476367\pi$
$727$	4.00000			0.148352			0.0741759	+	0.997245i	$0.476367\pi$
$728$	7.50000	−	14.7224i	0.277968	−	0.545650i
$729$	1.00000			0.0370370
$730$	54.0000	−	31.1769i	1.99863	−	1.15391i
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$	−0.500000	+	0.866025i	−0.0184805	+	0.0320092i
$733$	−39.0000	+	22.5167i	−1.44050	+	0.831672i	−0.997883	−	0.0650398i	$-0.979283\pi$
$733$	−39.0000	+	22.5167i	−1.44050	+	0.831672i	−0.442615	+	0.896712i	$0.645949\pi$
$734$			13.8564i			0.511449i
$735$	−9.00000	+	22.5167i	−0.331970	+	0.830540i
$736$		−	31.1769i		−	1.14920i
$737$	4.50000	+	7.79423i	0.165760	+	0.287104i
$738$	9.00000	−	15.5885i	0.331295	−	0.573819i
$739$	21.0000	+	12.1244i	0.772497	+	0.446002i	0.833765	−	0.552120i	$-0.186181\pi$
$739$	21.0000	+	12.1244i	0.772497	+	0.446002i	−0.0612673	+	0.998121i	$0.519514\pi$
$740$	−6.00000	−	10.3923i	−0.220564	−	0.382029i
$741$	−18.0000	−	5.19615i	−0.661247	−	0.190885i
$742$	−13.5000	−	2.59808i	−0.495601	−	0.0953784i
$743$		−	12.1244i		−	0.444799i	−0.974956	−	0.222400i	$-0.928611\pi$
$743$		−	12.1244i		−	0.444799i	0.974956	−	0.222400i	$-0.0713890\pi$
$744$	−3.00000	−	5.19615i	−0.109985	−	0.190500i
$745$	−6.00000	+	10.3923i	−0.219823	+	0.380745i
$746$	−1.50000	−	0.866025i	−0.0549189	−	0.0317074i
$747$	3.00000	−	1.73205i	0.109764	−	0.0633724i
$748$			15.5885i			0.569970i
$749$	30.0000	−	10.3923i	1.09618	−	0.379727i
$750$	−12.0000			−0.438178
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	7.50000	+	4.33013i	0.273497	+	0.157903i
$753$	−6.00000	+	10.3923i	−0.218652	+	0.378717i
$754$	4.50000	+	18.1865i	0.163880	+	0.662314i
$755$	30.0000			1.09181
$756$	−2.00000	−	1.73205i	−0.0727393	−	0.0629941i
$757$	1.00000			0.0363456			0.0181728	−	0.999835i	$-0.494215\pi$
$757$	1.00000			0.0363456			0.0181728	+	0.999835i	$0.494215\pi$
$758$	−15.0000	−	25.9808i	−0.544825	−	0.943664i
$759$	27.0000	+	15.5885i	0.980038	+	0.565825i
$760$	−27.0000	−	15.5885i	−0.979393	−	0.565453i
$761$	12.0000	−	6.92820i	0.435000	−	0.251147i	−0.266475	−	0.963842i	$-0.585859\pi$
$761$	12.0000	−	6.92820i	0.435000	−	0.251147i	0.701474	+	0.712695i	$0.252526\pi$
$762$			3.46410i			0.125491i
$763$	24.0000	−	27.7128i	0.868858	−	1.00327i
$764$	12.0000			0.434145
$765$	−9.00000	+	5.19615i	−0.325396	+	0.187867i
$766$	9.00000	−	15.5885i	0.325183	−	0.563234i
$767$	−22.5000	+	21.6506i	−0.812428	+	0.781759i
$768$	9.50000	+	16.4545i	0.342802	+	0.593750i
$769$		−	10.3923i		−	0.374756i	−0.982288	−	0.187378i	$-0.940001\pi$
$769$		−	10.3923i		−	0.374756i	0.982288	−	0.187378i	$-0.0599989\pi$
$770$	−27.0000	−	77.9423i	−0.973012	−	2.80885i
$771$	6.00000			0.216085
$772$	3.00000	−	1.73205i	0.107972	−	0.0623379i
$773$	−42.0000	−	24.2487i	−1.51064	−	0.872166i	−0.999923	−	0.0124137i	$-0.996048\pi$
$773$	−42.0000	−	24.2487i	−1.51064	−	0.872166i	−0.510712	−	0.859752i	$-0.670618\pi$
$774$	−12.0000	−	6.92820i	−0.431331	−	0.249029i
$775$	−21.0000	+	12.1244i	−0.754342	+	0.435520i
$776$	30.0000			1.07694
$777$	9.00000	+	1.73205i	0.322873	+	0.0621370i
$778$		−	36.3731i		−	1.30404i
$779$	−27.0000	−	46.7654i	−0.967375	−	1.67554i
$780$	9.00000	−	8.66025i	0.322252	−	0.310087i
$781$	−31.5000	+	54.5596i	−1.12716	+	1.95230i
$782$	−27.0000	+	15.5885i	−0.965518	+	0.557442i
$783$	−3.00000			−0.107211
$784$	−5.00000	−	34.6410i	−0.178571	−	1.23718i
$785$			58.8897i			2.10186i
$786$	9.00000	−	5.19615i	0.321019	−	0.185341i
$787$	46.5000	+	26.8468i	1.65755	+	0.956985i	0.973842	+	0.227225i	$0.0729652\pi$
$787$	46.5000	+	26.8468i	1.65755	+	0.956985i	0.683704	+	0.729760i	$0.260368\pi$
$788$	−21.0000	−	12.1244i	−0.748094	−	0.431912i
$789$	15.0000	+	25.9808i	0.534014	+	0.924940i
$790$	−24.0000			−0.853882
$791$	−4.50000	+	23.3827i	−0.160002	+	0.831393i
$792$	−9.00000			−0.319801
$793$	3.50000	−	0.866025i	0.124289	−	0.0307535i
$794$	3.00000	−	5.19615i	0.106466	−	0.184405i
$795$	9.00000	+	5.19615i	0.319197	+	0.184289i
$796$	−1.00000	−	1.73205i	−0.0354441	−	0.0613909i
$797$	18.0000			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$	−22.5000	+	7.79423i	−0.796491	+	0.275913i
$799$		−	5.19615i		−	0.183827i
$800$	31.5000	−	18.1865i	1.11369	−	0.642991i
$801$	3.00000	+	1.73205i	0.106000	+	0.0611990i
$802$	−3.00000	+	5.19615i	−0.105934	+	0.183483i
$803$	−27.0000	−	46.7654i	−0.952809	−	1.65031i
$804$			1.73205i			0.0610847i
$805$	36.0000	−	41.5692i	1.26883	−	1.46512i
$806$	6.00000	−	20.7846i	0.211341	−	0.732107i
$807$	1.50000	+	2.59808i	0.0528025	+	0.0914566i
$808$	9.00000	+	5.19615i	0.316619	+	0.182800i
$809$	1.50000	−	2.59808i	0.0527372	−	0.0913435i	−0.838452	−	0.544976i	$-0.816539\pi$
$809$	1.50000	−	2.59808i	0.0527372	−	0.0913435i	0.891189	+	0.453632i	$0.149872\pi$
$810$	3.00000	+	5.19615i	0.105409	+	0.182574i
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$	6.00000	+	5.19615i	0.210559	+	0.182349i
$813$		−	19.0526i		−	0.668202i
$814$	−27.0000	+	15.5885i	−0.946350	+	0.546375i
$815$	−21.0000	+	36.3731i	−0.735598	+	1.27409i
$816$	7.50000	−	12.9904i	0.262553	−	0.454754i
$817$	−36.0000	+	20.7846i	−1.25948	+	0.727161i
$818$	−6.00000			−0.209785
$819$	0.500000	+	9.52628i	0.0174714	+	0.332875i
$820$	36.0000			1.25717
$821$	−27.0000	+	15.5885i	−0.942306	+	0.544041i	−0.890683	−	0.454626i	$-0.849773\pi$
$821$	−27.0000	+	15.5885i	−0.942306	+	0.544041i	−0.0516239	+	0.998667i	$0.516440\pi$
$822$	−9.00000	+	15.5885i	−0.313911	+	0.543710i
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$	−6.00000	+	3.46410i	−0.209020	+	0.120678i
$825$			36.3731i			1.26635i
$826$	−7.50000	+	38.9711i	−0.260958	+	1.35598i
$827$			25.9808i			0.903440i	0.892160	+	0.451720i	$0.149189\pi$
$827$			25.9808i			0.903440i	−0.892160	+	0.451720i	$0.850811\pi$
$828$	3.00000	+	5.19615i	0.104257	+	0.180579i
$829$	−6.50000	+	11.2583i	−0.225754	+	0.391018i	−0.956545	−	0.291583i	$-0.905818\pi$
$829$	−6.50000	+	11.2583i	−0.225754	+	0.391018i	0.730791	+	0.682601i	$0.239151\pi$
$830$	18.0000	+	10.3923i	0.624789	+	0.360722i
$831$	−9.50000	−	16.4545i	−0.329551	−	0.570800i
$832$	1.00000	−	3.46410i	0.0346688	−	0.120096i
$833$	−16.5000	+	12.9904i	−0.571691	+	0.450090i
$834$		−	24.2487i		−	0.839664i
$835$	15.0000	+	25.9808i	0.519096	+	0.899101i
$836$	13.5000	−	23.3827i	0.466907	−	0.808707i
$837$	3.00000	+	1.73205i	0.103695	+	0.0598684i
$838$	36.0000	−	20.7846i	1.24360	−	0.717992i
$839$			8.66025i			0.298985i	0.988763	+	0.149493i	$0.0477640\pi$
$839$			8.66025i			0.298985i	−0.988763	+	0.149493i	$0.952236\pi$
$840$	−3.00000	+	15.5885i	−0.103510	+	0.537853i
$841$	−20.0000			−0.689655
$842$	9.00000	+	15.5885i	0.310160	+	0.537214i
$843$	−6.00000	−	3.46410i	−0.206651	−	0.119310i
$844$	−7.00000	+	12.1244i	−0.240950	+	0.417338i
$845$	−45.0000	−	1.73205i	−1.54805	−	0.0595844i
$846$	−3.00000			−0.103142
$847$	−40.0000	+	13.8564i	−1.37442	+	0.476112i
$848$	−15.0000			−0.515102
$849$	11.0000	+	19.0526i	0.377519	+	0.653882i
$850$	−31.5000	−	18.1865i	−1.08044	−	0.623793i
$851$	−18.0000	−	10.3923i	−0.617032	−	0.356244i
$852$	−10.5000	+	6.06218i	−0.359724	+	0.207687i
$853$		−	51.9615i		−	1.77913i	−0.456810	−	0.889564i	$-0.651008\pi$
$853$		−	51.9615i		−	1.77913i	0.456810	−	0.889564i	$-0.348992\pi$
$854$	3.00000	−	3.46410i	0.102658	−	0.118539i
$855$	18.0000			0.615587
$856$	18.0000	−	10.3923i	0.615227	−	0.355202i
$857$	−10.5000	+	18.1865i	−0.358673	+	0.621240i	−0.987739	−	0.156112i	$-0.950104\pi$
$857$	−10.5000	+	18.1865i	−0.358673	+	0.621240i	0.629066	+	0.777352i	$0.283437\pi$
$858$	−22.5000	−	23.3827i	−0.768137	−	0.798272i
$859$	28.0000	+	48.4974i	0.955348	+	1.65471i	0.733571	+	0.679613i	$0.237852\pi$
$859$	28.0000	+	48.4974i	0.955348	+	1.65471i	0.221777	+	0.975097i	$0.428814\pi$
$860$		−	27.7128i		−	0.944999i
$861$	−18.0000	+	20.7846i	−0.613438	+	0.708338i
$862$	6.00000			0.204361
$863$	−33.0000	+	19.0526i	−1.12333	+	0.648557i	−0.942250	−	0.334911i	$-0.891294\pi$
$863$	−33.0000	+	19.0526i	−1.12333	+	0.648557i	−0.181083	+	0.983468i	$0.557960\pi$
$864$	−4.50000	−	2.59808i	−0.153093	−	0.0883883i
$865$	−45.0000	−	25.9808i	−1.53005	−	0.883372i
$866$	28.5000	−	16.4545i	0.968469	−	0.559146i
$867$	8.00000			0.271694
$868$	−3.00000	−	8.66025i	−0.101827	−	0.293948i
$869$			20.7846i			0.705070i
$870$	−9.00000	−	15.5885i	−0.305129	−	0.528498i
$871$	4.50000	−	4.33013i	0.152477	−	0.146721i
$872$	12.0000	−	20.7846i	0.406371	−	0.703856i
$873$	−15.0000	+	8.66025i	−0.507673	+	0.293105i
$874$	54.0000			1.82658
$875$	18.0000	+	3.46410i	0.608511	+	0.117108i
$876$		−	10.3923i		−	0.351123i
$877$	−39.0000	+	22.5167i	−1.31694	+	0.760334i	−0.983235	−	0.182345i	$-0.941631\pi$
$877$	−39.0000	+	22.5167i	−1.31694	+	0.760334i	−0.333702	+	0.942679i	$0.608298\pi$
$878$	−3.00000	−	1.73205i	−0.101245	−	0.0584539i
$879$	−9.00000	−	5.19615i	−0.303562	−	0.175262i
$880$	−45.0000	−	77.9423i	−1.51695	−	2.62743i
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$	7.50000	+	9.52628i	0.252538	+	0.320767i
$883$	34.0000			1.14419			0.572096	−	0.820187i	$-0.306131\pi$
$883$	34.0000			1.14419			0.572096	+	0.820187i	$0.306131\pi$
$884$	10.5000	−	2.59808i	0.353153	−	0.0873828i
$885$	15.0000	−	25.9808i	0.504219	−	0.873334i
$886$	−9.00000	−	5.19615i	−0.302361	−	0.174568i
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	0.747539	−	0.664218i	$-0.231235\pi$
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	−0.948999	+	0.315279i	$0.897902\pi$
$888$	6.00000			0.201347
$889$	1.00000	−	5.19615i	0.0335389	−	0.174273i
$890$			20.7846i			0.696702i
$891$	4.50000	−	2.59808i	0.150756	−	0.0870388i
$892$	22.5000	+	12.9904i	0.753356	+	0.434950i
$893$	−4.50000	+	7.79423i	−0.150587	+	0.260824i
$894$	3.00000	+	5.19615i	0.100335	+	0.173785i
$895$		−	41.5692i		−	1.38951i
$896$	−10.5000	−	30.3109i	−0.350780	−	1.01262i
$897$	6.00000	−	20.7846i	0.200334	−	0.693978i
$898$	−6.00000	−	10.3923i	−0.200223	−	0.346796i
$899$	−9.00000	−	5.19615i	−0.300167	−	0.173301i
$900$	−3.50000	+	6.06218i	−0.116667	+	0.202073i
$901$	4.50000	+	7.79423i	0.149917	+	0.259663i
$902$		−	93.5307i		−	3.11423i
$903$	16.0000	+	13.8564i	0.532447	+	0.461112i
$904$			15.5885i			0.518464i
$905$	15.0000	−	8.66025i	0.498617	−	0.287877i
$906$	7.50000	−	12.9904i	0.249171	−	0.431577i
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	−0.937018	−	0.349281i	$-0.886426\pi$
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	0.770996	+	0.636841i	$0.219759\pi$
$908$	−21.0000	+	12.1244i	−0.696909	+	0.402361i
$909$	−6.00000			−0.199007
$910$	−48.0000	+	31.1769i	−1.59118	+	1.03350i
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$	−22.5000	+	12.9904i	−0.745049	+	0.430155i
$913$	9.00000	−	15.5885i	0.297857	−	0.515903i
$914$	−15.0000	+	25.9808i	−0.496156	+	0.859367i
$915$	−3.00000	+	1.73205i	−0.0991769	+	0.0572598i
$916$			6.92820i			0.228914i
$917$	−15.0000	+	5.19615i	−0.495344	+	0.171592i
$918$			5.19615i			0.171499i
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	0.703378	−	0.710816i	$-0.251674\pi$
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	−0.967274	+	0.253735i	$0.918341\pi$
$920$	18.0000	−	31.1769i	0.593442	−	1.02787i
$921$	−10.5000	−	6.06218i	−0.345987	−	0.199756i
$922$	6.00000	+	10.3923i	0.197599	+	0.342252i
$923$	42.0000	+	12.1244i	1.38245	+	0.399078i
$924$	−13.5000	−	2.59808i	−0.444117	−	0.0854704i
$925$		−	24.2487i		−	0.797293i
$926$	27.0000	+	46.7654i	0.887275	+	1.53681i
$927$	2.00000	−	3.46410i	0.0656886	−	0.113776i
$928$	13.5000	+	7.79423i	0.443159	+	0.255858i
$929$	18.0000	−	10.3923i	0.590561	−	0.340960i	−0.174758	−	0.984611i	$-0.555914\pi$
$929$	18.0000	−	10.3923i	0.590561	−	0.340960i	0.765319	+	0.643651i	$0.222581\pi$
$930$			20.7846i			0.681554i
$931$	36.0000	−	5.19615i	1.17985	−	0.170297i
$932$	27.0000			0.884414
$933$	9.00000	+	15.5885i	0.294647	+	0.510343i
$934$	27.0000	+	15.5885i	0.883467	+	0.510070i
$935$	−27.0000	+	46.7654i	−0.882994	+	1.52939i
$936$	1.50000	+	6.06218i	0.0490290	+	0.198148i
$937$	43.0000			1.40475			0.702374	−	0.711808i	$-0.252123\pi$
$937$	43.0000			1.40475			0.702374	+	0.711808i	$0.252123\pi$
$938$	1.50000	−	7.79423i	0.0489767	−	0.254491i
$939$	2.00000			0.0652675
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	18.0000	+	10.3923i	0.586783	+	0.338779i	0.763825	−	0.645424i	$-0.223319\pi$
$941$	18.0000	+	10.3923i	0.586783	+	0.338779i	−0.177041	+	0.984203i	$0.556653\pi$
$942$	25.5000	+	14.7224i	0.830835	+	0.479683i
$943$	54.0000	−	31.1769i	1.75848	−	1.01526i
$944$			43.3013i			1.40934i
$945$	−3.00000	−	8.66025i	−0.0975900	−	0.281718i
$946$	−72.0000			−2.34092
$947$	46.5000	−	26.8468i	1.51105	−	0.872403i	0.511130	−	0.859503i	$-0.329227\pi$
$947$	46.5000	−	26.8468i	1.51105	−	0.872403i	0.999917	−	0.0129001i	$-0.00410633\pi$
$948$	−2.00000	+	3.46410i	−0.0649570	+	0.112509i
$949$	−27.0000	+	25.9808i	−0.876457	+	0.843371i
$950$	31.5000	+	54.5596i	1.02199	+	1.77015i
$951$		0			0
$952$	−9.00000	+	10.3923i	−0.291692	+	0.336817i
$953$	9.00000			0.291539			0.145769	−	0.989319i	$-0.453434\pi$
$953$	9.00000			0.291539			0.145769	+	0.989319i	$0.453434\pi$
$954$	4.50000	−	2.59808i	0.145693	−	0.0841158i
$955$	36.0000	+	20.7846i	1.16493	+	0.672574i
$956$	13.5000	+	7.79423i	0.436621	+	0.252083i
$957$	−13.5000	+	7.79423i	−0.436393	+	0.251952i
$958$	−3.00000			−0.0969256
$959$	18.0000	−	20.7846i	0.581250	−	0.671170i
$960$			3.46410i			0.111803i
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$	15.0000	+	15.5885i	0.483619	+	0.502592i
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$	6.00000	−	3.46410i	0.193247	−	0.111571i
$965$	12.0000			0.386294
$966$	−9.00000	−	25.9808i	−0.289570	−	0.835917i
$967$		−	1.73205i		−	0.0556990i	−0.999612	−	0.0278495i	$-0.991134\pi$
$967$		−	1.73205i		−	0.0556990i	0.999612	−	0.0278495i	$-0.00886592\pi$
$968$	−24.0000	+	13.8564i	−0.771389	+	0.445362i
$969$	13.5000	+	7.79423i	0.433682	+	0.250387i
$970$	−90.0000	−	51.9615i	−2.88973	−	1.66838i
$971$	−9.00000	−	15.5885i	−0.288824	−	0.500257i	0.684706	−	0.728820i	$-0.259931\pi$
$971$	−9.00000	−	15.5885i	−0.288824	−	0.500257i	−0.973529	+	0.228562i	$0.926597\pi$
$972$	1.00000			0.0320750
$973$	−7.00000	+	36.3731i	−0.224410	+	1.16607i
$974$	−45.0000			−1.44189
$975$	24.5000	−	6.06218i	0.784628	−	0.194145i
$976$	2.50000	−	4.33013i	0.0800230	−	0.138604i
$977$	6.00000	+	3.46410i	0.191957	+	0.110826i	0.592898	−	0.805277i	$-0.297984\pi$
$977$	6.00000	+	3.46410i	0.191957	+	0.110826i	−0.400941	+	0.916104i	$0.631317\pi$
$978$	10.5000	+	18.1865i	0.335753	+	0.581541i
$979$	18.0000			0.575282
$980$	−9.00000	+	22.5167i	−0.287494	+	0.719268i
$981$			13.8564i			0.442401i
$982$	36.0000	−	20.7846i	1.14881	−	0.663264i
$983$	4.50000	+	2.59808i	0.143528	+	0.0828658i	0.570044	−	0.821614i	$-0.306926\pi$
$983$	4.50000	+	2.59808i	0.143528	+	0.0828658i	−0.426517	+	0.904480i	$0.640259\pi$
$984$	−9.00000	+	15.5885i	−0.286910	+	0.496942i
$985$	−42.0000	−	72.7461i	−1.33823	−	2.31788i
$986$		−	15.5885i		−	0.496438i
$987$	4.50000	+	0.866025i	0.143237	+	0.0275659i
$988$	−18.0000	−	5.19615i	−0.572656	−	0.165312i
$989$	−24.0000	−	41.5692i	−0.763156	−	1.32182i
$990$	27.0000	+	15.5885i	0.858116	+	0.495434i
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$	−9.00000	−	15.5885i	−0.285750	−	0.494934i
$993$		−	31.1769i		−	0.989369i
$994$	52.5000	−	18.1865i	1.66520	−	0.576842i
$995$		−	6.92820i		−	0.219639i
$996$	3.00000	−	1.73205i	0.0950586	−	0.0548821i
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	0.0512480	+	0.998686i	$0.483680\pi$
$997$	−26.5000	+	45.8993i	−0.839263	+	1.45365i	−0.890511	+	0.454961i	$0.849653\pi$
$998$	15.0000	−	25.9808i	0.474817	−	0.822407i
$999$	−3.00000	+	1.73205i	−0.0949158	+	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bj.b.25.1	yes	2
3.2	odd	2		819.2.dl.a.298.1		2
7.2	even	3		273.2.bj.a.142.1	yes	2
7.3	odd	6		1911.2.c.e.883.2		2
7.4	even	3		1911.2.c.b.883.2		2
13.12	even	2		273.2.bj.a.25.1	✓	2
21.2	odd	6		819.2.dl.d.415.1		2
39.38	odd	2		819.2.dl.d.298.1		2
91.25	even	6		1911.2.c.b.883.1		2
91.38	odd	6		1911.2.c.e.883.1		2
91.51	even	6	inner	273.2.bj.b.142.1	yes	2
273.233	odd	6		819.2.dl.a.415.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bj.a.25.1	✓	2	13.12	even	2
273.2.bj.a.142.1	yes	2	7.2	even	3
273.2.bj.b.25.1	yes	2	1.1	even	1	trivial
273.2.bj.b.142.1	yes	2	91.51	even	6	inner
819.2.dl.a.298.1		2	3.2	odd	2
819.2.dl.a.415.1		2	273.233	odd	6
819.2.dl.d.298.1		2	39.38	odd	2
819.2.dl.d.415.1		2	21.2	odd	6
1911.2.c.b.883.1		2	91.25	even	6
1911.2.c.b.883.2		2	7.4	even	3
1911.2.c.e.883.1		2	91.38	odd	6
1911.2.c.e.883.2		2	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.00000 - 1.73205i) q^{5} -1.73205i q^{6} +(-0.500000 + 2.59808i) q^{7} +1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.00000 - 1.73205i) q^{5} -1.73205i q^{6} +(-0.500000 + 2.59808i) q^{7} +1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.00000 - 5.19615i) q^{10} +(-4.50000 - 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.00000 + 3.46410i) q^{13} +(1.50000 + 4.33013i) q^{14} -3.46410i q^{15} +(2.50000 + 4.33013i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.50000 - 0.866025i) q^{18} +(-4.50000 + 2.59808i) q^{19} -3.46410i q^{20} +(2.00000 + 1.73205i) q^{21} -9.00000 q^{22} +(-3.00000 - 5.19615i) q^{23} +(1.50000 + 0.866025i) q^{24} +(3.50000 - 6.06218i) q^{25} +(1.50000 + 6.06218i) q^{26} -1.00000 q^{27} +(2.00000 + 1.73205i) q^{28} +3.00000 q^{29} +(-3.00000 - 5.19615i) q^{30} +(-3.00000 - 1.73205i) q^{31} +(4.50000 + 2.59808i) q^{32} +(-4.50000 + 2.59808i) q^{33} -5.19615i q^{34} +(3.00000 + 8.66025i) q^{35} -1.00000 q^{36} +(3.00000 - 1.73205i) q^{37} +(-4.50000 + 7.79423i) q^{38} +(2.50000 + 2.59808i) q^{39} +(3.00000 + 5.19615i) q^{40} +10.3923i q^{41} +(4.50000 + 0.866025i) q^{42} +8.00000 q^{43} +(-4.50000 + 2.59808i) q^{44} +(-3.00000 - 1.73205i) q^{45} +(-9.00000 - 5.19615i) q^{46} +(1.50000 - 0.866025i) q^{47} +5.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} -12.1244i q^{50} +(-1.50000 - 2.59808i) q^{51} +(2.50000 + 2.59808i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(-1.50000 + 0.866025i) q^{54} -18.0000 q^{55} +(-4.50000 - 0.866025i) q^{56} +5.19615i q^{57} +(4.50000 - 2.59808i) q^{58} +(7.50000 + 4.33013i) q^{59} +(-3.00000 - 1.73205i) q^{60} +(-0.500000 - 0.866025i) q^{61} -6.00000 q^{62} +(2.50000 - 0.866025i) q^{63} -1.00000 q^{64} +(3.00000 + 12.1244i) q^{65} +(-4.50000 + 7.79423i) q^{66} +(-1.50000 - 0.866025i) q^{67} +(-1.50000 - 2.59808i) q^{68} -6.00000 q^{69} +(12.0000 + 10.3923i) q^{70} -12.1244i q^{71} +(1.50000 - 0.866025i) q^{72} +(9.00000 + 5.19615i) q^{73} +(3.00000 - 5.19615i) q^{74} +(-3.50000 - 6.06218i) q^{75} +5.19615i q^{76} +(9.00000 - 10.3923i) q^{77} +(6.00000 + 1.73205i) q^{78} +(-2.00000 - 3.46410i) q^{79} +(15.0000 + 8.66025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(9.00000 + 15.5885i) q^{82} +3.46410i q^{83} +(2.50000 - 0.866025i) q^{84} -10.3923i q^{85} +(12.0000 - 6.92820i) q^{86} +(1.50000 - 2.59808i) q^{87} +(4.50000 - 7.79423i) q^{88} +(-3.00000 + 1.73205i) q^{89} -6.00000 q^{90} +(-8.50000 - 4.33013i) q^{91} -6.00000 q^{92} +(-3.00000 + 1.73205i) q^{93} +(1.50000 - 2.59808i) q^{94} +(-9.00000 + 15.5885i) q^{95} +(4.50000 - 2.59808i) q^{96} -17.3205i q^{97} +(-12.0000 + 1.73205i) q^{98} +5.19615i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + q^{3} + q^{4} + 6 q^{5} - q^{7} - q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + q^3 + q^4 + 6 * q^5 - q^7 - q^9	\( 2 q + 3 q^{2} + q^{3} + q^{4} + 6 q^{5} - q^{7} - q^{9} + 6 q^{10} - 9 q^{11} - q^{12} - 2 q^{13} + 3 q^{14} + 5 q^{16} + 3 q^{17} - 3 q^{18} - 9 q^{19} + 4 q^{21} - 18 q^{22} - 6 q^{23} + 3 q^{24} + 7 q^{25} + 3 q^{26} - 2 q^{27} + 4 q^{28} + 6 q^{29} - 6 q^{30} - 6 q^{31} + 9 q^{32} - 9 q^{33} + 6 q^{35} - 2 q^{36} + 6 q^{37} - 9 q^{38} + 5 q^{39} + 6 q^{40} + 9 q^{42} + 16 q^{43} - 9 q^{44} - 6 q^{45} - 18 q^{46} + 3 q^{47} + 10 q^{48} - 13 q^{49} - 3 q^{51} + 5 q^{52} - 3 q^{53} - 3 q^{54} - 36 q^{55} - 9 q^{56} + 9 q^{58} + 15 q^{59} - 6 q^{60} - q^{61} - 12 q^{62} + 5 q^{63} - 2 q^{64} + 6 q^{65} - 9 q^{66} - 3 q^{67} - 3 q^{68} - 12 q^{69} + 24 q^{70} + 3 q^{72} + 18 q^{73} + 6 q^{74} - 7 q^{75} + 18 q^{77} + 12 q^{78} - 4 q^{79} + 30 q^{80} - q^{81} + 18 q^{82} + 5 q^{84} + 24 q^{86} + 3 q^{87} + 9 q^{88} - 6 q^{89} - 12 q^{90} - 17 q^{91} - 12 q^{92} - 6 q^{93} + 3 q^{94} - 18 q^{95} + 9 q^{96} - 24 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 + q^3 + q^4 + 6 * q^5 - q^7 - q^9 + 6 * q^10 - 9 * q^11 - q^12 - 2 * q^13 + 3 * q^14 + 5 * q^16 + 3 * q^17 - 3 * q^18 - 9 * q^19 + 4 * q^21 - 18 * q^22 - 6 * q^23 + 3 * q^24 + 7 * q^25 + 3 * q^26 - 2 * q^27 + 4 * q^28 + 6 * q^29 - 6 * q^30 - 6 * q^31 + 9 * q^32 - 9 * q^33 + 6 * q^35 - 2 * q^36 + 6 * q^37 - 9 * q^38 + 5 * q^39 + 6 * q^40 + 9 * q^42 + 16 * q^43 - 9 * q^44 - 6 * q^45 - 18 * q^46 + 3 * q^47 + 10 * q^48 - 13 * q^49 - 3 * q^51 + 5 * q^52 - 3 * q^53 - 3 * q^54 - 36 * q^55 - 9 * q^56 + 9 * q^58 + 15 * q^59 - 6 * q^60 - q^61 - 12 * q^62 + 5 * q^63 - 2 * q^64 + 6 * q^65 - 9 * q^66 - 3 * q^67 - 3 * q^68 - 12 * q^69 + 24 * q^70 + 3 * q^72 + 18 * q^73 + 6 * q^74 - 7 * q^75 + 18 * q^77 + 12 * q^78 - 4 * q^79 + 30 * q^80 - q^81 + 18 * q^82 + 5 * q^84 + 24 * q^86 + 3 * q^87 + 9 * q^88 - 6 * q^89 - 12 * q^90 - 17 * q^91 - 12 * q^92 - 6 * q^93 + 3 * q^94 - 18 * q^95 + 9 * q^96 - 24 * q^98

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