LMFDB - Embedded newform 546.2.bi.a.257.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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([3, 1, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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:	$4.35983195036$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(3.00000 + 1.73205i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(3.00000 + 1.73205i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{10} +(3.00000 - 5.19615i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-2.50000 + 2.59808i) q^{13} +(0.500000 + 2.59808i) q^{14} +(-3.00000 - 5.19615i) q^{15} +1.00000 q^{16} +(-1.50000 - 2.59808i) q^{18} +(2.50000 + 4.33013i) q^{19} +(3.00000 + 1.73205i) q^{20} +(-1.50000 + 4.33013i) q^{21} +(-3.00000 + 5.19615i) q^{22} +3.46410i q^{23} +(1.50000 + 0.866025i) q^{24} +(3.50000 + 6.06218i) q^{25} +(2.50000 - 2.59808i) q^{26} -5.19615i q^{27} +(-0.500000 - 2.59808i) q^{28} +(6.00000 - 3.46410i) q^{29} +(3.00000 + 5.19615i) q^{30} +(-4.00000 - 6.92820i) q^{31} -1.00000 q^{32} +(-9.00000 + 5.19615i) q^{33} +(3.00000 - 8.66025i) q^{35} +(1.50000 + 2.59808i) q^{36} -8.66025i q^{37} +(-2.50000 - 4.33013i) q^{38} +(6.00000 - 1.73205i) q^{39} +(-3.00000 - 1.73205i) q^{40} +(9.00000 - 5.19615i) q^{41} +(1.50000 - 4.33013i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(3.00000 - 5.19615i) q^{44} +10.3923i q^{45} -3.46410i q^{46} +(6.00000 + 3.46410i) q^{47} +(-1.50000 - 0.866025i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(-3.50000 - 6.06218i) q^{50} +(-2.50000 + 2.59808i) q^{52} +(3.00000 - 1.73205i) q^{53} +5.19615i q^{54} +(18.0000 - 10.3923i) q^{55} +(0.500000 + 2.59808i) q^{56} -8.66025i q^{57} +(-6.00000 + 3.46410i) q^{58} +(-3.00000 - 5.19615i) q^{60} +(4.50000 - 2.59808i) q^{61} +(4.00000 + 6.92820i) q^{62} +(6.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(-12.0000 + 3.46410i) q^{65} +(9.00000 - 5.19615i) q^{66} +(-3.00000 - 1.73205i) q^{67} +(3.00000 - 5.19615i) q^{69} +(-3.00000 + 8.66025i) q^{70} +(-1.50000 - 2.59808i) q^{72} +(3.50000 + 6.06218i) q^{73} +8.66025i q^{74} -12.1244i q^{75} +(2.50000 + 4.33013i) q^{76} +(-15.0000 - 5.19615i) q^{77} +(-6.00000 + 1.73205i) q^{78} +(4.00000 - 6.92820i) q^{79} +(3.00000 + 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-9.00000 + 5.19615i) q^{82} +3.46410i q^{83} +(-1.50000 + 4.33013i) q^{84} +(0.500000 - 0.866025i) q^{86} -12.0000 q^{87} +(-3.00000 + 5.19615i) q^{88} +3.46410i q^{89} -10.3923i q^{90} +(8.00000 + 5.19615i) q^{91} +3.46410i q^{92} +13.8564i q^{93} +(-6.00000 - 3.46410i) q^{94} +17.3205i q^{95} +(1.50000 + 0.866025i) q^{96} +(-3.50000 + 6.06218i) q^{97} +(6.50000 - 2.59808i) q^{98} +18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + 6 q^{5} + 3 q^{6} - q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + 6 * q^5 + 3 * q^6 - q^7 - 2 * q^8 + 3 * q^9	$ 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + 6 q^{5} + 3 q^{6} - q^{7} - 2 q^{8} + 3 q^{9} - 6 q^{10} + 6 q^{11} - 3 q^{12} - 5 q^{13} + q^{14} - 6 q^{15} + 2 q^{16} - 3 q^{18} + 5 q^{19} + 6 q^{20} - 3 q^{21} - 6 q^{22} + 3 q^{24} + 7 q^{25} + 5 q^{26} - q^{28} + 12 q^{29} + 6 q^{30} - 8 q^{31} - 2 q^{32} - 18 q^{33} + 6 q^{35} + 3 q^{36} - 5 q^{38} + 12 q^{39} - 6 q^{40} + 18 q^{41} + 3 q^{42} - q^{43} + 6 q^{44} + 12 q^{47} - 3 q^{48} - 13 q^{49} - 7 q^{50} - 5 q^{52} + 6 q^{53} + 36 q^{55} + q^{56} - 12 q^{58} - 6 q^{60} + 9 q^{61} + 8 q^{62} + 12 q^{63} + 2 q^{64} - 24 q^{65} + 18 q^{66} - 6 q^{67} + 6 q^{69} - 6 q^{70} - 3 q^{72} + 7 q^{73} + 5 q^{76} - 30 q^{77} - 12 q^{78} + 8 q^{79} + 6 q^{80} - 9 q^{81} - 18 q^{82} - 3 q^{84} + q^{86} - 24 q^{87} - 6 q^{88} + 16 q^{91} - 12 q^{94} + 3 q^{96} - 7 q^{97} + 13 q^{98} + 36 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + 6 * q^5 + 3 * q^6 - q^7 - 2 * q^8 + 3 * q^9 - 6 * q^10 + 6 * q^11 - 3 * q^12 - 5 * q^13 + q^14 - 6 * q^15 + 2 * q^16 - 3 * q^18 + 5 * q^19 + 6 * q^20 - 3 * q^21 - 6 * q^22 + 3 * q^24 + 7 * q^25 + 5 * q^26 - q^28 + 12 * q^29 + 6 * q^30 - 8 * q^31 - 2 * q^32 - 18 * q^33 + 6 * q^35 + 3 * q^36 - 5 * q^38 + 12 * q^39 - 6 * q^40 + 18 * q^41 + 3 * q^42 - q^43 + 6 * q^44 + 12 * q^47 - 3 * q^48 - 13 * q^49 - 7 * q^50 - 5 * q^52 + 6 * q^53 + 36 * q^55 + q^56 - 12 * q^58 - 6 * q^60 + 9 * q^61 + 8 * q^62 + 12 * q^63 + 2 * q^64 - 24 * q^65 + 18 * q^66 - 6 * q^67 + 6 * q^69 - 6 * q^70 - 3 * q^72 + 7 * q^73 + 5 * q^76 - 30 * q^77 - 12 * q^78 + 8 * q^79 + 6 * q^80 - 9 * q^81 - 18 * q^82 - 3 * q^84 + q^86 - 24 * q^87 - 6 * q^88 + 16 * q^91 - 12 * q^94 + 3 * q^96 - 7 * q^97 + 13 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	1.00000			0.500000
$5$	3.00000	+	1.73205i	1.34164	+	0.774597i	0.987048	−	0.160424i	$-0.0512862\pi$
$5$	3.00000	+	1.73205i	1.34164	+	0.774597i	0.354593	+	0.935021i	$0.384620\pi$
$6$	1.50000	+	0.866025i	0.612372	+	0.353553i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−3.00000	−	1.73205i	−0.948683	−	0.547723i
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	0.500000	+	2.59808i	0.133631	+	0.694365i
$15$	−3.00000	−	5.19615i	−0.774597	−	1.34164i
$16$	1.00000			0.250000
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$	3.00000	+	1.73205i	0.670820	+	0.387298i
$21$	−1.50000	+	4.33013i	−0.327327	+	0.944911i
$22$	−3.00000	+	5.19615i	−0.639602	+	1.10782i
$23$			3.46410i			0.722315i	0.932505	+	0.361158i	$0.117618\pi$
$23$			3.46410i			0.722315i	−0.932505	+	0.361158i	$0.882382\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	3.50000	+	6.06218i	0.700000	+	1.21244i
$26$	2.50000	−	2.59808i	0.490290	−	0.509525i
$27$		−	5.19615i		−	1.00000i
$28$	−0.500000	−	2.59808i	−0.0944911	−	0.490990i
$29$	6.00000	−	3.46410i	1.11417	−	0.643268i	0.174265	−	0.984699i	$-0.444245\pi$
$29$	6.00000	−	3.46410i	1.11417	−	0.643268i	0.939907	+	0.341431i	$0.110912\pi$
$30$	3.00000	+	5.19615i	0.547723	+	0.948683i
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	−1.00000			−0.176777
$33$	−9.00000	+	5.19615i	−1.56670	+	0.904534i
$34$		0			0
$35$	3.00000	−	8.66025i	0.507093	−	1.46385i
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$		−	8.66025i		−	1.42374i	−0.702313	−	0.711868i	$-0.747849\pi$
$37$		−	8.66025i		−	1.42374i	0.702313	−	0.711868i	$-0.252151\pi$
$38$	−2.50000	−	4.33013i	−0.405554	−	0.702439i
$39$	6.00000	−	1.73205i	0.960769	−	0.277350i
$40$	−3.00000	−	1.73205i	−0.474342	−	0.273861i
$41$	9.00000	−	5.19615i	1.40556	−	0.811503i	0.410608	−	0.911812i	$-0.365317\pi$
$41$	9.00000	−	5.19615i	1.40556	−	0.811503i	0.994956	+	0.100309i	$0.0319833\pi$
$42$	1.50000	−	4.33013i	0.231455	−	0.668153i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$	3.00000	−	5.19615i	0.452267	−	0.783349i
$45$			10.3923i			1.54919i
$46$		−	3.46410i		−	0.510754i
$47$	6.00000	+	3.46410i	0.875190	+	0.505291i	0.869069	−	0.494690i	$-0.164718\pi$
$47$	6.00000	+	3.46410i	0.875190	+	0.505291i	0.00612051	+	0.999981i	$0.498052\pi$
$48$	−1.50000	−	0.866025i	−0.216506	−	0.125000i
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−3.50000	−	6.06218i	−0.494975	−	0.857321i
$51$		0			0
$52$	−2.50000	+	2.59808i	−0.346688	+	0.360288i
$53$	3.00000	−	1.73205i	0.412082	−	0.237915i	−0.279602	−	0.960116i	$-0.590203\pi$
$53$	3.00000	−	1.73205i	0.412082	−	0.237915i	0.691684	+	0.722200i	$0.256869\pi$
$54$			5.19615i			0.707107i
$55$	18.0000	−	10.3923i	2.42712	−	1.40130i
$56$	0.500000	+	2.59808i	0.0668153	+	0.347183i
$57$		−	8.66025i		−	1.14708i
$58$	−6.00000	+	3.46410i	−0.787839	+	0.454859i
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$	−3.00000	−	5.19615i	−0.387298	−	0.670820i
$61$	4.50000	−	2.59808i	0.576166	−	0.332650i	−0.183442	−	0.983030i	$-0.558724\pi$
$61$	4.50000	−	2.59808i	0.576166	−	0.332650i	0.759608	+	0.650381i	$0.225391\pi$
$62$	4.00000	+	6.92820i	0.508001	+	0.879883i
$63$	6.00000	−	5.19615i	0.755929	−	0.654654i
$64$	1.00000			0.125000
$65$	−12.0000	+	3.46410i	−1.48842	+	0.429669i
$66$	9.00000	−	5.19615i	1.10782	−	0.639602i
$67$	−3.00000	−	1.73205i	−0.366508	−	0.211604i	0.305424	−	0.952217i	$-0.401202\pi$
$67$	−3.00000	−	1.73205i	−0.366508	−	0.211604i	−0.671932	+	0.740613i	$0.734535\pi$
$68$		0			0
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$	−3.00000	+	8.66025i	−0.358569	+	1.03510i
$71$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$71$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	0.994850	−	0.101361i	$-0.0323196\pi$
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	−0.585206	+	0.810885i	$0.698986\pi$
$74$			8.66025i			1.00673i
$75$		−	12.1244i		−	1.40000i
$76$	2.50000	+	4.33013i	0.286770	+	0.496700i
$77$	−15.0000	−	5.19615i	−1.70941	−	0.592157i
$78$	−6.00000	+	1.73205i	−0.679366	+	0.196116i
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$	3.00000	+	1.73205i	0.335410	+	0.193649i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−9.00000	+	5.19615i	−0.993884	+	0.573819i
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$	−1.50000	+	4.33013i	−0.163663	+	0.472456i
$85$		0			0
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$	−12.0000			−1.28654
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$			3.46410i			0.367194i	0.983002	+	0.183597i	$0.0587741\pi$
$89$			3.46410i			0.367194i	−0.983002	+	0.183597i	$0.941226\pi$
$90$		−	10.3923i		−	1.09545i
$91$	8.00000	+	5.19615i	0.838628	+	0.544705i
$92$			3.46410i			0.361158i
$93$			13.8564i			1.43684i
$94$	−6.00000	−	3.46410i	−0.618853	−	0.357295i
$95$			17.3205i			1.77705i
$96$	1.50000	+	0.866025i	0.153093	+	0.0883883i
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	−0.987181	−	0.159602i	$-0.948979\pi$
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	0.631810	+	0.775123i	$0.282312\pi$
$98$	6.50000	−	2.59808i	0.656599	−	0.262445i
$99$	18.0000			1.80907
$100$	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	$0.0701767\pi$
$102$		0			0
$103$	4.50000	+	2.59808i	0.443398	+	0.255996i	0.705038	−	0.709170i	$-0.250930\pi$
$103$	4.50000	+	2.59808i	0.443398	+	0.255996i	−0.261640	+	0.965166i	$0.584263\pi$
$104$	2.50000	−	2.59808i	0.245145	−	0.254762i
$105$	−12.0000	+	10.3923i	−1.17108	+	1.01419i
$106$	−3.00000	+	1.73205i	−0.291386	+	0.168232i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		−	5.19615i		−	0.500000i
$109$	−10.5000	+	6.06218i	−1.00572	+	0.580651i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−10.5000	+	6.06218i	−1.00572	+	0.580651i	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−18.0000	+	10.3923i	−1.71623	+	0.990867i
$111$	−7.50000	+	12.9904i	−0.711868	+	1.23299i
$112$	−0.500000	−	2.59808i	−0.0472456	−	0.245495i
$113$	−6.00000	−	3.46410i	−0.564433	−	0.325875i	0.190490	−	0.981689i	$-0.438992\pi$
$113$	−6.00000	−	3.46410i	−0.564433	−	0.325875i	−0.754923	+	0.655814i	$0.772326\pi$
$114$			8.66025i			0.811107i
$115$	−6.00000	+	10.3923i	−0.559503	+	0.969087i
$116$	6.00000	−	3.46410i	0.557086	−	0.321634i
$117$	−10.5000	−	2.59808i	−0.970725	−	0.240192i
$118$		0			0
$119$		0			0
$120$	3.00000	+	5.19615i	0.273861	+	0.474342i
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	−4.50000	+	2.59808i	−0.407411	+	0.235219i
$123$	−18.0000			−1.62301
$124$	−4.00000	−	6.92820i	−0.359211	−	0.622171i
$125$			6.92820i			0.619677i
$126$	−6.00000	+	5.19615i	−0.534522	+	0.462910i
$127$	−0.500000	−	0.866025i	−0.0443678	−	0.0768473i	0.842989	−	0.537931i	$-0.180794\pi$
$127$	−0.500000	−	0.866025i	−0.0443678	−	0.0768473i	−0.887357	+	0.461084i	$0.847461\pi$
$128$	−1.00000			−0.0883883
$129$	1.50000	−	0.866025i	0.132068	−	0.0762493i
$130$	12.0000	−	3.46410i	1.05247	−	0.303822i
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	0.141865	+	0.989886i	$0.454690\pi$
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	−0.928199	+	0.372084i	$0.878643\pi$
$132$	−9.00000	+	5.19615i	−0.783349	+	0.452267i
$133$	10.0000	−	8.66025i	0.867110	−	0.750939i
$134$	3.00000	+	1.73205i	0.259161	+	0.149626i
$135$	9.00000	−	15.5885i	0.774597	−	1.34164i
$136$		0			0
$137$	6.00000			0.512615			0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000			0.512615			0.256307	+	0.966595i	$0.417494\pi$
$138$	−3.00000	+	5.19615i	−0.255377	+	0.442326i
$139$	−3.00000	−	1.73205i	−0.254457	−	0.146911i	0.367347	−	0.930084i	$-0.380266\pi$
$139$	−3.00000	−	1.73205i	−0.254457	−	0.146911i	−0.621803	+	0.783174i	$0.713600\pi$
$140$	3.00000	−	8.66025i	0.253546	−	0.731925i
$141$	−6.00000	−	10.3923i	−0.505291	−	0.875190i
$142$		0			0
$143$	6.00000	+	20.7846i	0.501745	+	1.73810i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	24.0000			1.99309
$146$	−3.50000	−	6.06218i	−0.289662	−	0.501709i
$147$	12.0000	+	1.73205i	0.989743	+	0.142857i
$148$		−	8.66025i		−	0.711868i
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$			12.1244i			0.989949i
$151$	3.00000	−	1.73205i	0.244137	−	0.140952i	−0.372940	−	0.927855i	$-0.621650\pi$
$151$	3.00000	−	1.73205i	0.244137	−	0.140952i	0.617076	+	0.786903i	$0.288317\pi$
$152$	−2.50000	−	4.33013i	−0.202777	−	0.351220i
$153$		0			0
$154$	15.0000	+	5.19615i	1.20873	+	0.418718i
$155$		−	27.7128i		−	2.22595i
$156$	6.00000	−	1.73205i	0.480384	−	0.138675i
$157$	−16.5000	+	9.52628i	−1.31684	+	0.760280i	−0.983220	−	0.182426i	$-0.941605\pi$
$157$	−16.5000	+	9.52628i	−1.31684	+	0.760280i	−0.333624	+	0.942706i	$0.608272\pi$
$158$	−4.00000	+	6.92820i	−0.318223	+	0.551178i
$159$	−6.00000			−0.475831
$160$	−3.00000	−	1.73205i	−0.237171	−	0.136931i
$161$	9.00000	−	1.73205i	0.709299	−	0.136505i
$162$	4.50000	−	7.79423i	0.353553	−	0.612372i
$163$	1.50000	−	0.866025i	0.117489	−	0.0678323i	−0.440104	−	0.897947i	$-0.645058\pi$
$163$	1.50000	−	0.866025i	0.117489	−	0.0678323i	0.557593	+	0.830115i	$0.311725\pi$
$164$	9.00000	−	5.19615i	0.702782	−	0.405751i
$165$	−36.0000			−2.80260
$166$		−	3.46410i		−	0.268866i
$167$	−3.00000	+	1.73205i	−0.232147	+	0.134030i	−0.611562	−	0.791196i	$-0.709459\pi$
$167$	−3.00000	+	1.73205i	−0.232147	+	0.134030i	0.379415	+	0.925227i	$0.376125\pi$
$168$	1.50000	−	4.33013i	0.115728	−	0.334077i
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	−7.50000	+	12.9904i	−0.573539	+	0.993399i
$172$	−0.500000	+	0.866025i	−0.0381246	+	0.0660338i
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	12.0000			0.909718
$175$	14.0000	−	12.1244i	1.05830	−	0.916515i
$176$	3.00000	−	5.19615i	0.226134	−	0.391675i
$177$		0			0
$178$		−	3.46410i		−	0.259645i
$179$	−21.0000	−	12.1244i	−1.56961	−	0.906217i	−0.996213	−	0.0869415i	$-0.972291\pi$
$179$	−21.0000	−	12.1244i	−1.56961	−	0.906217i	−0.573400	−	0.819275i	$-0.694376\pi$
$180$			10.3923i			0.774597i
$181$			15.5885i			1.15868i	0.815086	+	0.579340i	$0.196690\pi$
$181$			15.5885i			1.15868i	−0.815086	+	0.579340i	$0.803310\pi$
$182$	−8.00000	−	5.19615i	−0.592999	−	0.385164i
$183$	−9.00000			−0.665299
$184$		−	3.46410i		−	0.255377i
$185$	15.0000	−	25.9808i	1.10282	−	1.91014i
$186$		−	13.8564i		−	1.01600i
$187$		0			0
$188$	6.00000	+	3.46410i	0.437595	+	0.252646i
$189$	−13.5000	+	2.59808i	−0.981981	+	0.188982i
$190$		−	17.3205i		−	1.25656i
$191$	−18.0000	+	10.3923i	−1.30243	+	0.751961i	−0.980821	−	0.194910i	$-0.937558\pi$
$191$	−18.0000	+	10.3923i	−1.30243	+	0.751961i	−0.321613	+	0.946871i	$0.604225\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$	−4.50000	−	2.59808i	−0.323917	−	0.187014i	0.329220	−	0.944253i	$-0.393214\pi$
$193$	−4.50000	−	2.59808i	−0.323917	−	0.187014i	−0.653137	+	0.757240i	$0.726548\pi$
$194$	3.50000	−	6.06218i	0.251285	−	0.435239i
$195$	21.0000	+	5.19615i	1.50384	+	0.372104i
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	6.00000	+	10.3923i	0.427482	+	0.740421i	0.996649	−	0.0818013i	$-0.0260673\pi$
$197$	6.00000	+	10.3923i	0.427482	+	0.740421i	−0.569166	+	0.822222i	$0.692734\pi$
$198$	−18.0000			−1.27920
$199$			15.5885i			1.10504i	0.833501	+	0.552518i	$0.186333\pi$
$199$			15.5885i			1.10504i	−0.833501	+	0.552518i	$0.813667\pi$
$200$	−3.50000	−	6.06218i	−0.247487	−	0.428661i
$201$	3.00000	+	5.19615i	0.211604	+	0.366508i
$202$	−3.00000	+	5.19615i	−0.211079	+	0.365600i
$203$	−12.0000	−	13.8564i	−0.842235	−	0.972529i
$204$		0			0
$205$	36.0000			2.51435
$206$	−4.50000	−	2.59808i	−0.313530	−	0.181017i
$207$	−9.00000	+	5.19615i	−0.625543	+	0.361158i
$208$	−2.50000	+	2.59808i	−0.173344	+	0.180144i
$209$	30.0000			2.07514
$210$	12.0000	−	10.3923i	0.828079	−	0.717137i
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$	3.00000	−	1.73205i	0.206041	−	0.118958i
$213$		0			0
$214$		0			0
$215$	−3.00000	+	1.73205i	−0.204598	+	0.118125i
$216$			5.19615i			0.353553i
$217$	−16.0000	+	13.8564i	−1.08615	+	0.940634i
$218$	10.5000	−	6.06218i	0.711150	−	0.410582i
$219$		−	12.1244i		−	0.819288i
$220$	18.0000	−	10.3923i	1.21356	−	0.700649i
$221$		0			0
$222$	7.50000	−	12.9904i	0.503367	−	0.871857i
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	−0.999128	−	0.0417488i	$-0.986707\pi$
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	0.463409	−	0.886145i	$-0.346626\pi$
$224$	0.500000	+	2.59808i	0.0334077	+	0.173591i
$225$	−10.5000	+	18.1865i	−0.700000	+	1.21244i
$226$	6.00000	+	3.46410i	0.399114	+	0.230429i
$227$			10.3923i			0.689761i	0.938647	+	0.344881i	$0.112081\pi$
$227$			10.3923i			0.689761i	−0.938647	+	0.344881i	$0.887919\pi$
$228$		−	8.66025i		−	0.573539i
$229$	−14.5000	+	25.1147i	−0.958187	+	1.65963i	−0.231287	+	0.972886i	$0.574293\pi$
$229$	−14.5000	+	25.1147i	−0.958187	+	1.65963i	−0.726900	+	0.686743i	$0.759040\pi$
$230$	6.00000	−	10.3923i	0.395628	−	0.685248i
$231$	18.0000	+	20.7846i	1.18431	+	1.36753i
$232$	−6.00000	+	3.46410i	−0.393919	+	0.227429i
$233$	−6.00000	−	3.46410i	−0.393073	−	0.226941i	0.290418	−	0.956900i	$-0.406206\pi$
$233$	−6.00000	−	3.46410i	−0.393073	−	0.226941i	−0.683491	+	0.729959i	$0.739539\pi$
$234$	10.5000	+	2.59808i	0.686406	+	0.169842i
$235$	12.0000	+	20.7846i	0.782794	+	1.35584i
$236$		0			0
$237$	−12.0000	+	6.92820i	−0.779484	+	0.450035i
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$	−3.00000	−	5.19615i	−0.193649	−	0.335410i
$241$	26.0000			1.67481			0.837404	−	0.546585i	$-0.184072\pi$
$241$	26.0000			1.67481			0.837404	+	0.546585i	$0.184072\pi$
$242$	12.5000	+	21.6506i	0.803530	+	1.39176i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	4.50000	−	2.59808i	0.288083	−	0.166325i
$245$	−24.0000	−	3.46410i	−1.53330	−	0.221313i
$246$	18.0000			1.14764
$247$	−17.5000	−	4.33013i	−1.11350	−	0.275519i
$248$	4.00000	+	6.92820i	0.254000	+	0.439941i
$249$	3.00000	−	5.19615i	0.190117	−	0.329293i
$250$		−	6.92820i		−	0.438178i
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$	6.00000	−	5.19615i	0.377964	−	0.327327i
$253$	18.0000	+	10.3923i	1.13165	+	0.653359i
$254$	0.500000	+	0.866025i	0.0313728	+	0.0543393i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−18.0000			−1.12281			−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000			−1.12281			−0.561405	+	0.827541i	$0.689739\pi$
$258$	−1.50000	+	0.866025i	−0.0933859	+	0.0539164i
$259$	−22.5000	+	4.33013i	−1.39808	+	0.269061i
$260$	−12.0000	+	3.46410i	−0.744208	+	0.214834i
$261$	18.0000	+	10.3923i	1.11417	+	0.643268i
$262$	9.00000	−	15.5885i	0.556022	−	0.963058i
$263$	12.0000	+	6.92820i	0.739952	+	0.427211i	0.822052	−	0.569413i	$-0.192829\pi$
$263$	12.0000	+	6.92820i	0.739952	+	0.427211i	−0.0821001	+	0.996624i	$0.526163\pi$
$264$	9.00000	−	5.19615i	0.553912	−	0.319801i
$265$	12.0000			0.737154
$266$	−10.0000	+	8.66025i	−0.613139	+	0.530994i
$267$	3.00000	−	5.19615i	0.183597	−	0.317999i
$268$	−3.00000	−	1.73205i	−0.183254	−	0.105802i
$269$	12.0000			0.731653			0.365826	−	0.930683i	$-0.380786\pi$
$269$	12.0000			0.731653			0.365826	+	0.930683i	$0.380786\pi$
$270$	−9.00000	+	15.5885i	−0.547723	+	0.948683i
$271$	1.00000			0.0607457			0.0303728	−	0.999539i	$-0.490331\pi$
$271$	1.00000			0.0607457			0.0303728	+	0.999539i	$0.490331\pi$
$272$		0			0
$273$	−7.50000	−	14.7224i	−0.453921	−	0.891042i
$274$	−6.00000			−0.362473
$275$	42.0000			2.53270
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	17.0000			1.02143			0.510716	−	0.859750i	$-0.329381\pi$
$277$	17.0000			1.02143			0.510716	+	0.859750i	$0.329381\pi$
$278$	3.00000	+	1.73205i	0.179928	+	0.103882i
$279$	12.0000	−	20.7846i	0.718421	−	1.24434i
$280$	−3.00000	+	8.66025i	−0.179284	+	0.517549i
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$	6.00000	+	10.3923i	0.357295	+	0.618853i
$283$	−1.50000	−	0.866025i	−0.0891657	−	0.0514799i	0.454754	−	0.890617i	$-0.349727\pi$
$283$	−1.50000	−	0.866025i	−0.0891657	−	0.0514799i	−0.543920	+	0.839137i	$0.683060\pi$
$284$		0			0
$285$	15.0000	−	25.9808i	0.888523	−	1.53897i
$286$	−6.00000	−	20.7846i	−0.354787	−	1.22902i
$287$	−18.0000	−	20.7846i	−1.06251	−	1.22688i
$288$	−1.50000	−	2.59808i	−0.0883883	−	0.153093i
$289$	−17.0000			−1.00000
$290$	−24.0000			−1.40933
$291$	10.5000	−	6.06218i	0.615521	−	0.355371i
$292$	3.50000	+	6.06218i	0.204822	+	0.354762i
$293$	6.00000	+	3.46410i	0.350524	+	0.202375i	0.664916	−	0.746918i	$-0.268467\pi$
$293$	6.00000	+	3.46410i	0.350524	+	0.202375i	−0.314392	+	0.949293i	$0.601801\pi$
$294$	−12.0000	−	1.73205i	−0.699854	−	0.101015i
$295$		0			0
$296$			8.66025i			0.503367i
$297$	−27.0000	−	15.5885i	−1.56670	−	0.904534i
$298$	−9.00000	−	15.5885i	−0.521356	−	0.903015i
$299$	−9.00000	−	8.66025i	−0.520483	−	0.500835i
$300$		−	12.1244i		−	0.700000i
$301$	2.50000	+	0.866025i	0.144098	+	0.0499169i
$302$	−3.00000	+	1.73205i	−0.172631	+	0.0996683i
$303$	−9.00000	+	5.19615i	−0.517036	+	0.298511i
$304$	2.50000	+	4.33013i	0.143385	+	0.248350i
$305$	18.0000			1.03068
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$	−15.0000	−	5.19615i	−0.854704	−	0.296078i
$309$	−4.50000	−	7.79423i	−0.255996	−	0.443398i
$310$			27.7128i			1.57398i
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	0.938460	−	0.345389i	$-0.112253\pi$
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	−0.768345	+	0.640036i	$0.778920\pi$
$312$	−6.00000	+	1.73205i	−0.339683	+	0.0980581i
$313$	−28.5000	−	16.4545i	−1.61092	−	0.930062i	−0.989158	−	0.146852i	$-0.953086\pi$
$313$	−28.5000	−	16.4545i	−1.61092	−	0.930062i	−0.621757	−	0.783210i	$-0.713581\pi$
$314$	16.5000	−	9.52628i	0.931149	−	0.537599i
$315$	27.0000	−	5.19615i	1.52128	−	0.292770i
$316$	4.00000	−	6.92820i	0.225018	−	0.389742i
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$	6.00000			0.336463
$319$		−	41.5692i		−	2.32743i
$320$	3.00000	+	1.73205i	0.167705	+	0.0968246i
$321$		0			0
$322$	−9.00000	+	1.73205i	−0.501550	+	0.0965234i
$323$		0			0
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−24.5000	−	6.06218i	−1.35902	−	0.336269i
$326$	−1.50000	+	0.866025i	−0.0830773	+	0.0479647i
$327$	21.0000			1.16130
$328$	−9.00000	+	5.19615i	−0.496942	+	0.286910i
$329$	6.00000	−	17.3205i	0.330791	−	0.954911i
$330$	36.0000			1.98173
$331$	−16.5000	+	9.52628i	−0.906922	+	0.523612i	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−16.5000	+	9.52628i	−0.906922	+	0.523612i	−0.0274825	+	0.999622i	$0.508749\pi$
$332$			3.46410i			0.190117i
$333$	22.5000	−	12.9904i	1.23299	−	0.711868i
$334$	3.00000	−	1.73205i	0.164153	−	0.0947736i
$335$	−6.00000	−	10.3923i	−0.327815	−	0.567792i
$336$	−1.50000	+	4.33013i	−0.0818317	+	0.236228i
$337$	5.00000			0.272367			0.136184	−	0.990684i	$-0.456516\pi$
$337$	5.00000			0.272367			0.136184	+	0.990684i	$0.456516\pi$
$338$	0.500000	+	12.9904i	0.0271964	+	0.706584i
$339$	6.00000	+	10.3923i	0.325875	+	0.564433i
$340$		0			0
$341$	−48.0000			−2.59935
$342$	7.50000	−	12.9904i	0.405554	−	0.702439i
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	0.500000	−	0.866025i	0.0269582	−	0.0466930i
$345$	18.0000	−	10.3923i	0.969087	−	0.559503i
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$		0			0		1.00000			$0$
$347$		0			0		−1.00000			$\pi$
$348$	−12.0000			−0.643268
$349$	−5.50000	−	9.52628i	−0.294408	−	0.509930i	0.680439	−	0.732805i	$-0.261789\pi$
$349$	−5.50000	−	9.52628i	−0.294408	−	0.509930i	−0.974847	+	0.222875i	$0.928456\pi$
$350$	−14.0000	+	12.1244i	−0.748331	+	0.648074i
$351$	13.5000	+	12.9904i	0.720577	+	0.693375i
$352$	−3.00000	+	5.19615i	−0.159901	+	0.276956i
$353$	9.00000	+	5.19615i	0.479022	+	0.276563i	0.720009	−	0.693965i	$-0.244138\pi$
$353$	9.00000	+	5.19615i	0.479022	+	0.276563i	−0.240987	+	0.970528i	$0.577471\pi$
$354$		0			0
$355$		0			0
$356$			3.46410i			0.183597i
$357$		0			0
$358$	21.0000	+	12.1244i	1.10988	+	0.640792i
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$		−	10.3923i		−	0.547723i
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$		−	15.5885i		−	0.819311i
$363$			43.3013i			2.27273i
$364$	8.00000	+	5.19615i	0.419314	+	0.272352i
$365$			24.2487i			1.26924i
$366$	9.00000			0.470438
$367$	1.50000	+	0.866025i	0.0782994	+	0.0452062i	0.538639	−	0.842537i	$-0.318939\pi$
$367$	1.50000	+	0.866025i	0.0782994	+	0.0452062i	−0.460339	+	0.887743i	$0.652272\pi$
$368$			3.46410i			0.180579i
$369$	27.0000	+	15.5885i	1.40556	+	0.811503i
$370$	−15.0000	+	25.9808i	−0.779813	+	1.35068i
$371$	−6.00000	−	6.92820i	−0.311504	−	0.359694i
$372$			13.8564i			0.718421i
$373$	1.00000	+	1.73205i	0.0517780	+	0.0896822i	0.890753	−	0.454488i	$-0.150178\pi$
$373$	1.00000	+	1.73205i	0.0517780	+	0.0896822i	−0.838975	+	0.544170i	$0.816844\pi$
$374$		0			0
$375$	6.00000	−	10.3923i	0.309839	−	0.536656i
$376$	−6.00000	−	3.46410i	−0.309426	−	0.178647i
$377$	−6.00000	+	24.2487i	−0.309016	+	1.24887i
$378$	13.5000	−	2.59808i	0.694365	−	0.133631i
$379$	−15.0000	+	8.66025i	−0.770498	+	0.444847i	−0.833052	−	0.553194i	$-0.813409\pi$
$379$	−15.0000	+	8.66025i	−0.770498	+	0.444847i	0.0625541	+	0.998042i	$0.480075\pi$
$380$			17.3205i			0.888523i
$381$			1.73205i			0.0887357i
$382$	18.0000	−	10.3923i	0.920960	−	0.531717i
$383$	18.0000	−	10.3923i	0.919757	−	0.531022i	0.0361995	−	0.999345i	$-0.488475\pi$
$383$	18.0000	−	10.3923i	0.919757	−	0.531022i	0.883558	+	0.468323i	$0.155141\pi$
$384$	1.50000	+	0.866025i	0.0765466	+	0.0441942i
$385$	−36.0000	−	41.5692i	−1.83473	−	2.11856i
$386$	4.50000	+	2.59808i	0.229044	+	0.132239i
$387$	−3.00000			−0.152499
$388$	−3.50000	+	6.06218i	−0.177686	+	0.307760i
$389$	−9.00000	+	5.19615i	−0.456318	+	0.263455i	−0.710495	−	0.703702i	$-0.751529\pi$
$389$	−9.00000	+	5.19615i	−0.456318	+	0.263455i	0.254177	+	0.967158i	$0.418196\pi$
$390$	−21.0000	−	5.19615i	−1.06338	−	0.263117i
$391$		0			0
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$	27.0000	−	15.5885i	1.36197	−	0.786334i
$394$	−6.00000	−	10.3923i	−0.302276	−	0.523557i
$395$	24.0000	−	13.8564i	1.20757	−	0.697191i
$396$	18.0000			0.904534
$397$	5.50000	+	9.52628i	0.276037	+	0.478110i	0.970396	−	0.241518i	$-0.0776454\pi$
$397$	5.50000	+	9.52628i	0.276037	+	0.478110i	−0.694359	+	0.719629i	$0.744312\pi$
$398$		−	15.5885i		−	0.781379i
$399$	−22.5000	+	4.33013i	−1.12641	+	0.216777i
$400$	3.50000	+	6.06218i	0.175000	+	0.303109i
$401$	6.00000			0.299626			0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000			0.299626			0.149813	+	0.988714i	$0.452133\pi$
$402$	−3.00000	−	5.19615i	−0.149626	−	0.259161i
$403$	28.0000	+	6.92820i	1.39478	+	0.345118i
$404$	3.00000	−	5.19615i	0.149256	−	0.258518i
$405$	−27.0000	+	15.5885i	−1.34164	+	0.774597i
$406$	12.0000	+	13.8564i	0.595550	+	0.687682i
$407$	−45.0000	−	25.9808i	−2.23057	−	1.28782i
$408$		0			0
$409$	19.0000			0.939490			0.469745	−	0.882802i	$-0.344346\pi$
$409$	19.0000			0.939490			0.469745	+	0.882802i	$0.344346\pi$
$410$	−36.0000			−1.77791
$411$	−9.00000	−	5.19615i	−0.443937	−	0.256307i
$412$	4.50000	+	2.59808i	0.221699	+	0.127998i
$413$		0			0
$414$	9.00000	−	5.19615i	0.442326	−	0.255377i
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$	2.50000	−	2.59808i	0.122573	−	0.127381i
$417$	3.00000	+	5.19615i	0.146911	+	0.254457i
$418$	−30.0000			−1.46735
$419$	15.0000	+	25.9808i	0.732798	+	1.26924i	0.955683	+	0.294398i	$0.0951193\pi$
$419$	15.0000	+	25.9808i	0.732798	+	1.26924i	−0.222885	+	0.974845i	$0.571547\pi$
$420$	−12.0000	+	10.3923i	−0.585540	+	0.507093i
$421$			27.7128i			1.35064i	0.737525	+	0.675320i	$0.235994\pi$
$421$			27.7128i			1.35064i	−0.737525	+	0.675320i	$0.764006\pi$
$422$	2.50000	+	4.33013i	0.121698	+	0.210787i
$423$			20.7846i			1.01058i
$424$	−3.00000	+	1.73205i	−0.145693	+	0.0841158i
$425$		0			0
$426$		0			0
$427$	−9.00000	−	10.3923i	−0.435541	−	0.502919i
$428$		0			0
$429$	9.00000	−	36.3731i	0.434524	−	1.75611i
$430$	3.00000	−	1.73205i	0.144673	−	0.0835269i
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	−0.997173	−	0.0751385i	$-0.976060\pi$
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	0.563658	+	0.826008i	$0.309393\pi$
$432$		−	5.19615i		−	0.250000i
$433$	18.0000	+	10.3923i	0.865025	+	0.499422i	0.865692	−	0.500577i	$-0.166879\pi$
$433$	18.0000	+	10.3923i	0.865025	+	0.499422i	−0.000666943		1.00000i	$0.500212\pi$
$434$	16.0000	−	13.8564i	0.768025	−	0.665129i
$435$	−36.0000	−	20.7846i	−1.72607	−	0.996546i
$436$	−10.5000	+	6.06218i	−0.502859	+	0.290326i
$437$	−15.0000	+	8.66025i	−0.717547	+	0.414276i
$438$			12.1244i			0.579324i
$439$			12.1244i			0.578664i	0.957229	+	0.289332i	$0.0934331\pi$
$439$			12.1244i			0.578664i	−0.957229	+	0.289332i	$0.906567\pi$
$440$	−18.0000	+	10.3923i	−0.858116	+	0.495434i
$441$	−16.5000	−	12.9904i	−0.785714	−	0.618590i
$442$		0			0
$443$	−33.0000	−	19.0526i	−1.56788	−	0.905214i	−0.996416	−	0.0845852i	$-0.973043\pi$
$443$	−33.0000	−	19.0526i	−1.56788	−	0.905214i	−0.571461	−	0.820629i	$-0.693623\pi$
$444$	−7.50000	+	12.9904i	−0.355934	+	0.616496i
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	8.00000	+	13.8564i	0.378811	+	0.656120i
$447$		−	31.1769i		−	1.47462i
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$	−15.0000	+	25.9808i	−0.707894	+	1.22611i	0.257743	+	0.966213i	$0.417021\pi$
$449$	−15.0000	+	25.9808i	−0.707894	+	1.22611i	−0.965637	+	0.259895i	$0.916312\pi$
$450$	10.5000	−	18.1865i	0.494975	−	0.857321i
$451$		−	62.3538i		−	2.93613i
$452$	−6.00000	−	3.46410i	−0.282216	−	0.162938i
$453$	−6.00000			−0.281905
$454$		−	10.3923i		−	0.487735i
$455$	15.0000	+	29.4449i	0.703211	+	1.38040i
$456$			8.66025i			0.405554i
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$	14.5000	−	25.1147i	0.677541	−	1.17353i
$459$		0			0
$460$	−6.00000	+	10.3923i	−0.279751	+	0.484544i
$461$	−18.0000	−	10.3923i	−0.838344	−	0.484018i	0.0183573	−	0.999831i	$-0.494156\pi$
$461$	−18.0000	−	10.3923i	−0.838344	−	0.484018i	−0.856701	+	0.515814i	$0.827490\pi$
$462$	−18.0000	−	20.7846i	−0.837436	−	0.966988i
$463$			19.0526i			0.885448i	0.896658	+	0.442724i	$0.145988\pi$
$463$			19.0526i			0.885448i	−0.896658	+	0.442724i	$0.854012\pi$
$464$	6.00000	−	3.46410i	0.278543	−	0.160817i
$465$	−24.0000	+	41.5692i	−1.11297	+	1.92773i
$466$	6.00000	+	3.46410i	0.277945	+	0.160471i
$467$	9.00000	−	15.5885i	0.416470	−	0.721348i	−0.579111	−	0.815249i	$-0.696600\pi$
$467$	9.00000	−	15.5885i	0.416470	−	0.721348i	0.995582	+	0.0939008i	$0.0299336\pi$
$468$	−10.5000	−	2.59808i	−0.485363	−	0.120096i
$469$	−3.00000	+	8.66025i	−0.138527	+	0.399893i
$470$	−12.0000	−	20.7846i	−0.553519	−	0.958723i
$471$	33.0000			1.52056
$472$		0			0
$473$	3.00000	+	5.19615i	0.137940	+	0.238919i
$474$	12.0000	−	6.92820i	0.551178	−	0.318223i
$475$	−17.5000	+	30.3109i	−0.802955	+	1.39076i
$476$		0			0
$477$	9.00000	+	5.19615i	0.412082	+	0.237915i
$478$	−6.00000			−0.274434
$479$	6.00000	+	3.46410i	0.274147	+	0.158279i	0.630771	−	0.775969i	$-0.282739\pi$
$479$	6.00000	+	3.46410i	0.274147	+	0.158279i	−0.356624	+	0.934248i	$0.616072\pi$
$480$	3.00000	+	5.19615i	0.136931	+	0.237171i
$481$	22.5000	+	21.6506i	1.02591	+	0.987184i
$482$	−26.0000			−1.18427
$483$	−15.0000	−	5.19615i	−0.682524	−	0.236433i
$484$	−12.5000	−	21.6506i	−0.568182	−	0.984120i
$485$	−21.0000	+	12.1244i	−0.953561	+	0.550539i
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$		−	15.5885i		−	0.706380i	−0.935552	−	0.353190i	$-0.885097\pi$
$487$		−	15.5885i		−	0.706380i	0.935552	−	0.353190i	$-0.114903\pi$
$488$	−4.50000	+	2.59808i	−0.203705	+	0.117609i
$489$	−3.00000			−0.135665
$490$	24.0000	+	3.46410i	1.08421	+	0.156492i
$491$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$491$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$492$	−18.0000			−0.811503
$493$		0			0
$494$	17.5000	+	4.33013i	0.787362	+	0.194822i
$495$	54.0000	+	31.1769i	2.42712	+	1.40130i
$496$	−4.00000	−	6.92820i	−0.179605	−	0.311086i
$497$		0			0
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$	−7.50000	−	4.33013i	−0.335746	−	0.193843i	0.322643	−	0.946521i	$-0.395429\pi$
$499$	−7.50000	−	4.33013i	−0.335746	−	0.193843i	−0.658389	+	0.752678i	$0.728762\pi$
$500$			6.92820i			0.309839i
$501$	6.00000			0.268060
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$	15.0000	−	25.9808i	0.668817	−	1.15842i	−0.309418	−	0.950926i	$-0.600134\pi$
$503$	15.0000	−	25.9808i	0.668817	−	1.15842i	0.978235	−	0.207499i	$-0.0665323\pi$
$504$	−6.00000	+	5.19615i	−0.267261	+	0.231455i
$505$	18.0000	−	10.3923i	0.800989	−	0.462451i
$506$	−18.0000	−	10.3923i	−0.800198	−	0.461994i
$507$	−10.5000	+	19.9186i	−0.466321	+	0.884615i
$508$	−0.500000	−	0.866025i	−0.0221839	−	0.0384237i
$509$			24.2487i			1.07481i	0.843326	+	0.537403i	$0.180594\pi$
$509$			24.2487i			1.07481i	−0.843326	+	0.537403i	$0.819406\pi$
$510$		0			0
$511$	14.0000	−	12.1244i	0.619324	−	0.536350i
$512$	−1.00000			−0.0441942
$513$	22.5000	−	12.9904i	0.993399	−	0.573539i
$514$	18.0000			0.793946
$515$	9.00000	+	15.5885i	0.396587	+	0.686909i
$516$	1.50000	−	0.866025i	0.0660338	−	0.0381246i
$517$	36.0000	−	20.7846i	1.58328	−	0.914106i
$518$	22.5000	−	4.33013i	0.988593	−	0.190255i
$519$			10.3923i			0.456172i
$520$	12.0000	−	3.46410i	0.526235	−	0.151911i
$521$	−6.00000	−	10.3923i	−0.262865	−	0.455295i	0.704137	−	0.710064i	$-0.251334\pi$
$521$	−6.00000	−	10.3923i	−0.262865	−	0.455295i	−0.967002	+	0.254769i	$0.918001\pi$
$522$	−18.0000	−	10.3923i	−0.787839	−	0.454859i
$523$			8.66025i			0.378686i	0.981911	+	0.189343i	$0.0606359\pi$
$523$			8.66025i			0.378686i	−0.981911	+	0.189343i	$0.939364\pi$
$524$	−9.00000	+	15.5885i	−0.393167	+	0.680985i
$525$	−31.5000	+	6.06218i	−1.37477	+	0.264575i
$526$	−12.0000	−	6.92820i	−0.523225	−	0.302084i
$527$		0			0
$528$	−9.00000	+	5.19615i	−0.391675	+	0.226134i
$529$	11.0000			0.478261
$530$	−12.0000			−0.521247
$531$		0			0
$532$	10.0000	−	8.66025i	0.433555	−	0.375470i
$533$	−9.00000	+	36.3731i	−0.389833	+	1.57549i
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$		0			0
$536$	3.00000	+	1.73205i	0.129580	+	0.0748132i
$537$	21.0000	+	36.3731i	0.906217	+	1.56961i
$538$	−12.0000			−0.517357
$539$	−6.00000	+	41.5692i	−0.258438	+	1.79051i
$540$	9.00000	−	15.5885i	0.387298	−	0.670820i
$541$	1.50000	+	0.866025i	0.0644900	+	0.0372333i	0.531898	−	0.846808i	$-0.321479\pi$
$541$	1.50000	+	0.866025i	0.0644900	+	0.0372333i	−0.467408	+	0.884042i	$0.654812\pi$
$542$	−1.00000			−0.0429537
$543$	13.5000	−	23.3827i	0.579340	−	1.00345i
$544$		0			0
$545$	−42.0000			−1.79908
$546$	7.50000	+	14.7224i	0.320970	+	0.630062i
$547$	−25.0000			−1.06892			−0.534461	−	0.845193i	$-0.679486\pi$
$547$	−25.0000			−1.06892			−0.534461	+	0.845193i	$0.679486\pi$
$548$	6.00000			0.256307
$549$	13.5000	+	7.79423i	0.576166	+	0.332650i
$550$	−42.0000			−1.79089
$551$	30.0000	+	17.3205i	1.27804	+	0.737878i
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	−20.0000	−	6.92820i	−0.850487	−	0.294617i
$554$	−17.0000			−0.722261
$555$	−45.0000	+	25.9808i	−1.91014	+	1.10282i
$556$	−3.00000	−	1.73205i	−0.127228	−	0.0734553i
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	−0.991254	−	0.131965i	$-0.957871\pi$
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	0.609912	+	0.792469i	$0.291205\pi$
$558$	−12.0000	+	20.7846i	−0.508001	+	0.879883i
$559$	−1.00000	−	3.46410i	−0.0422955	−	0.146516i
$560$	3.00000	−	8.66025i	0.126773	−	0.365963i
$561$		0			0
$562$	12.0000			0.506189
$563$	−18.0000			−0.758610			−0.379305	−	0.925272i	$-0.623837\pi$
$563$	−18.0000			−0.758610			−0.379305	+	0.925272i	$0.623837\pi$
$564$	−6.00000	−	10.3923i	−0.252646	−	0.437595i
$565$	−12.0000	−	20.7846i	−0.504844	−	0.874415i
$566$	1.50000	+	0.866025i	0.0630497	+	0.0364018i
$567$	22.5000	+	7.79423i	0.944911	+	0.327327i
$568$		0			0
$569$			27.7128i			1.16178i	0.813982	+	0.580891i	$0.197296\pi$
$569$			27.7128i			1.16178i	−0.813982	+	0.580891i	$0.802704\pi$
$570$	−15.0000	+	25.9808i	−0.628281	+	1.08821i
$571$	−9.50000	−	16.4545i	−0.397563	−	0.688599i	0.595862	−	0.803087i	$-0.296811\pi$
$571$	−9.50000	−	16.4545i	−0.397563	−	0.688599i	−0.993425	+	0.114488i	$0.963477\pi$
$572$	6.00000	+	20.7846i	0.250873	+	0.869048i
$573$	36.0000			1.50392
$574$	18.0000	+	20.7846i	0.751305	+	0.867533i
$575$	−21.0000	+	12.1244i	−0.875761	+	0.505621i
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−18.5000	−	32.0429i	−0.770165	−	1.33397i	−0.937472	−	0.348060i	$-0.886840\pi$
$577$	−18.5000	−	32.0429i	−0.770165	−	1.33397i	0.167307	−	0.985905i	$-0.446493\pi$
$578$	17.0000			0.707107
$579$	4.50000	+	7.79423i	0.187014	+	0.323917i
$580$	24.0000			0.996546
$581$	9.00000	−	1.73205i	0.373383	−	0.0718576i
$582$	−10.5000	+	6.06218i	−0.435239	+	0.251285i
$583$		−	20.7846i		−	0.860811i
$584$	−3.50000	−	6.06218i	−0.144831	−	0.250855i
$585$	−27.0000	−	25.9808i	−1.11631	−	1.07417i
$586$	−6.00000	−	3.46410i	−0.247858	−	0.143101i
$587$	−39.0000	+	22.5167i	−1.60970	+	0.929362i	−0.620266	+	0.784391i	$0.712975\pi$
$587$	−39.0000	+	22.5167i	−1.60970	+	0.929362i	−0.989436	+	0.144971i	$0.953691\pi$
$588$	12.0000	+	1.73205i	0.494872	+	0.0714286i
$589$	20.0000	−	34.6410i	0.824086	−	1.42736i
$590$		0			0
$591$		−	20.7846i		−	0.854965i
$592$		−	8.66025i		−	0.355934i
$593$	6.00000	+	3.46410i	0.246390	+	0.142254i	0.618110	−	0.786091i	$-0.287898\pi$
$593$	6.00000	+	3.46410i	0.246390	+	0.142254i	−0.371720	+	0.928345i	$0.621232\pi$
$594$	27.0000	+	15.5885i	1.10782	+	0.639602i
$595$		0			0
$596$	9.00000	+	15.5885i	0.368654	+	0.638528i
$597$	13.5000	−	23.3827i	0.552518	−	0.956990i
$598$	9.00000	+	8.66025i	0.368037	+	0.354144i
$599$	24.0000	−	13.8564i	0.980613	−	0.566157i	0.0781581	−	0.996941i	$-0.475096\pi$
$599$	24.0000	−	13.8564i	0.980613	−	0.566157i	0.902455	+	0.430784i	$0.141763\pi$
$600$			12.1244i			0.494975i
$601$	1.50000	−	0.866025i	0.0611863	−	0.0353259i	−0.469095	−	0.883148i	$-0.655420\pi$
$601$	1.50000	−	0.866025i	0.0611863	−	0.0353259i	0.530281	+	0.847822i	$0.322086\pi$
$602$	−2.50000	−	0.866025i	−0.101892	−	0.0352966i
$603$		−	10.3923i		−	0.423207i
$604$	3.00000	−	1.73205i	0.122068	−	0.0704761i
$605$		−	86.6025i		−	3.52089i
$606$	9.00000	−	5.19615i	0.365600	−	0.211079i
$607$	−13.5000	+	7.79423i	−0.547948	+	0.316358i	−0.748294	−	0.663367i	$-0.769127\pi$
$607$	−13.5000	+	7.79423i	−0.547948	+	0.316358i	0.200346	+	0.979725i	$0.435793\pi$
$608$	−2.50000	−	4.33013i	−0.101388	−	0.175610i
$609$	6.00000	+	31.1769i	0.243132	+	1.26335i
$610$	−18.0000			−0.728799
$611$	−24.0000	+	6.92820i	−0.970936	+	0.280285i
$612$		0			0
$613$	22.5000	+	12.9904i	0.908766	+	0.524677i	0.880034	−	0.474911i	$-0.157520\pi$
$613$	22.5000	+	12.9904i	0.908766	+	0.524677i	0.0287324	+	0.999587i	$0.490853\pi$
$614$	4.00000			0.161427
$615$	−54.0000	−	31.1769i	−2.17749	−	1.25717i
$616$	15.0000	+	5.19615i	0.604367	+	0.209359i
$617$	18.0000	−	31.1769i	0.724653	−	1.25514i	−0.234464	−	0.972125i	$-0.575334\pi$
$617$	18.0000	−	31.1769i	0.724653	−	1.25514i	0.959117	−	0.283011i	$-0.0913331\pi$
$618$	4.50000	+	7.79423i	0.181017	+	0.313530i
$619$	8.50000	+	14.7224i	0.341644	+	0.591744i	0.984738	−	0.174042i	$-0.0556830\pi$
$619$	8.50000	+	14.7224i	0.341644	+	0.591744i	−0.643094	+	0.765787i	$0.722350\pi$
$620$		−	27.7128i		−	1.11297i
$621$	18.0000			0.722315
$622$	−3.00000	−	5.19615i	−0.120289	−	0.208347i
$623$	9.00000	−	1.73205i	0.360577	−	0.0693932i
$624$	6.00000	−	1.73205i	0.240192	−	0.0693375i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	28.5000	+	16.4545i	1.13909	+	0.657653i
$627$	−45.0000	−	25.9808i	−1.79713	−	1.03757i
$628$	−16.5000	+	9.52628i	−0.658422	+	0.380140i
$629$		0			0
$630$	−27.0000	+	5.19615i	−1.07571	+	0.207020i
$631$	22.5000	+	12.9904i	0.895711	+	0.517139i	0.875806	−	0.482663i	$-0.160330\pi$
$631$	22.5000	+	12.9904i	0.895711	+	0.517139i	0.0199047	+	0.999802i	$0.493664\pi$
$632$	−4.00000	+	6.92820i	−0.159111	+	0.275589i
$633$			8.66025i			0.344214i
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$		−	3.46410i		−	0.137469i
$636$	−6.00000			−0.237915
$637$	9.50000	−	23.3827i	0.376404	−	0.926456i
$638$			41.5692i			1.64574i
$639$		0			0
$640$	−3.00000	−	1.73205i	−0.118585	−	0.0684653i
$641$		−	38.1051i		−	1.50506i	−0.658557	−	0.752531i	$-0.728833\pi$
$641$		−	38.1051i		−	1.50506i	0.658557	−	0.752531i	$-0.271167\pi$
$642$		0			0
$643$	−5.50000	+	9.52628i	−0.216899	+	0.375680i	−0.953858	−	0.300257i	$-0.902928\pi$
$643$	−5.50000	+	9.52628i	−0.216899	+	0.375680i	0.736959	+	0.675937i	$0.236261\pi$
$644$	9.00000	−	1.73205i	0.354650	−	0.0682524i
$645$	6.00000			0.236250
$646$		0			0
$647$	18.0000	−	31.1769i	0.707653	−	1.22569i	−0.258073	−	0.966126i	$-0.583087\pi$
$647$	18.0000	−	31.1769i	0.707653	−	1.22569i	0.965726	−	0.259565i	$-0.0835793\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$		0			0
$650$	24.5000	+	6.06218i	0.960969	+	0.237778i
$651$	36.0000	−	6.92820i	1.41095	−	0.271538i
$652$	1.50000	−	0.866025i	0.0587445	−	0.0339162i
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$	−21.0000			−0.821165
$655$	−54.0000	+	31.1769i	−2.10995	+	1.21818i
$656$	9.00000	−	5.19615i	0.351391	−	0.202876i
$657$	−10.5000	+	18.1865i	−0.409644	+	0.709524i
$658$	−6.00000	+	17.3205i	−0.233904	+	0.675224i
$659$	24.0000	+	13.8564i	0.934907	+	0.539769i	0.888360	−	0.459147i	$-0.151845\pi$
$659$	24.0000	+	13.8564i	0.934907	+	0.539769i	0.0465470	+	0.998916i	$0.485178\pi$
$660$	−36.0000			−1.40130
$661$	−25.0000	+	43.3013i	−0.972387	+	1.68422i	−0.284087	+	0.958799i	$0.591690\pi$
$661$	−25.0000	+	43.3013i	−0.972387	+	1.68422i	−0.688301	+	0.725426i	$0.741643\pi$
$662$	16.5000	−	9.52628i	0.641291	−	0.370249i
$663$		0			0
$664$		−	3.46410i		−	0.134433i
$665$	45.0000	−	8.66025i	1.74503	−	0.335830i
$666$	−22.5000	+	12.9904i	−0.871857	+	0.503367i
$667$	12.0000	+	20.7846i	0.464642	+	0.804783i
$668$	−3.00000	+	1.73205i	−0.116073	+	0.0670151i
$669$			27.7128i			1.07144i
$670$	6.00000	+	10.3923i	0.231800	+	0.401490i
$671$		−	31.1769i		−	1.20357i
$672$	1.50000	−	4.33013i	0.0578638	−	0.167038i
$673$	−0.500000	−	0.866025i	−0.0192736	−	0.0333828i	0.856228	−	0.516599i	$-0.172802\pi$
$673$	−0.500000	−	0.866025i	−0.0192736	−	0.0333828i	−0.875501	+	0.483216i	$0.839469\pi$
$674$	−5.00000			−0.192593
$675$	31.5000	−	18.1865i	1.21244	−	0.700000i
$676$	−0.500000	−	12.9904i	−0.0192308	−	0.499630i
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	−0.639618	−	0.768693i	$-0.720908\pi$
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	0.985517	+	0.169580i	$0.0542410\pi$
$678$	−6.00000	−	10.3923i	−0.230429	−	0.399114i
$679$	17.5000	+	6.06218i	0.671588	+	0.232645i
$680$		0			0
$681$	9.00000	−	15.5885i	0.344881	−	0.597351i
$682$	48.0000			1.83801
$683$	18.0000			0.688751			0.344375	−	0.938832i	$-0.388091\pi$
$683$	18.0000			0.688751			0.344375	+	0.938832i	$0.388091\pi$
$684$	−7.50000	+	12.9904i	−0.286770	+	0.496700i
$685$	18.0000	+	10.3923i	0.687745	+	0.397070i
$686$	−10.0000	−	15.5885i	−0.381802	−	0.595170i
$687$	43.5000	−	25.1147i	1.65963	−	0.958187i
$688$	−0.500000	+	0.866025i	−0.0190623	+	0.0330169i
$689$	−3.00000	+	12.1244i	−0.114291	+	0.461901i
$690$	−18.0000	+	10.3923i	−0.685248	+	0.395628i
$691$	−17.0000			−0.646710			−0.323355	−	0.946278i	$-0.604811\pi$
$691$	−17.0000			−0.646710			−0.323355	+	0.946278i	$0.604811\pi$
$692$	−3.00000	−	5.19615i	−0.114043	−	0.197528i
$693$	−9.00000	−	46.7654i	−0.341882	−	1.77647i
$694$		0			0
$695$	−6.00000	−	10.3923i	−0.227593	−	0.394203i
$696$	12.0000			0.454859
$697$		0			0
$698$	5.50000	+	9.52628i	0.208178	+	0.360575i
$699$	6.00000	+	10.3923i	0.226941	+	0.393073i
$700$	14.0000	−	12.1244i	0.529150	−	0.458258i
$701$		−	13.8564i		−	0.523349i	−0.965156	−	0.261675i	$-0.915725\pi$
$701$		−	13.8564i		−	0.523349i	0.965156	−	0.261675i	$-0.0842747\pi$
$702$	−13.5000	−	12.9904i	−0.509525	−	0.490290i
$703$	37.5000	−	21.6506i	1.41434	−	0.816569i
$704$	3.00000	−	5.19615i	0.113067	−	0.195837i
$705$		−	41.5692i		−	1.56559i
$706$	−9.00000	−	5.19615i	−0.338719	−	0.195560i
$707$	−15.0000	−	5.19615i	−0.564133	−	0.195421i
$708$		0			0
$709$	−34.5000	+	19.9186i	−1.29567	+	0.748058i	−0.979654	−	0.200694i	$-0.935680\pi$
$709$	−34.5000	+	19.9186i	−1.29567	+	0.748058i	−0.316021	+	0.948752i	$0.602347\pi$
$710$		0			0
$711$	24.0000			0.900070
$712$		−	3.46410i		−	0.129823i
$713$	24.0000	−	13.8564i	0.898807	−	0.518927i
$714$		0			0
$715$	−18.0000	+	72.7461i	−0.673162	+	2.72055i
$716$	−21.0000	−	12.1244i	−0.784807	−	0.453108i
$717$	−9.00000	−	5.19615i	−0.336111	−	0.194054i
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$	−15.0000	−	25.9808i	−0.559406	−	0.968919i	−0.997546	−	0.0700124i	$-0.977696\pi$
$719$	−15.0000	−	25.9808i	−0.559406	−	0.968919i	0.438141	−	0.898906i	$-0.355637\pi$
$720$			10.3923i			0.387298i
$721$	4.50000	−	12.9904i	0.167589	−	0.483787i
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$	−39.0000	−	22.5167i	−1.45043	−	0.837404i
$724$			15.5885i			0.579340i
$725$	42.0000	+	24.2487i	1.55984	+	0.900575i
$726$		−	43.3013i		−	1.60706i
$727$		−	10.3923i		−	0.385429i	−0.981255	−	0.192715i	$-0.938271\pi$
$727$		−	10.3923i		−	0.385429i	0.981255	−	0.192715i	$-0.0617292\pi$
$728$	−8.00000	−	5.19615i	−0.296500	−	0.192582i
$729$	−27.0000			−1.00000
$730$		−	24.2487i		−	0.897485i
$731$		0			0
$732$	−9.00000			−0.332650
$733$	23.0000	−	39.8372i	0.849524	−	1.47142i	−0.0321090	−	0.999484i	$-0.510222\pi$
$733$	23.0000	−	39.8372i	0.849524	−	1.47142i	0.881633	−	0.471935i	$-0.156444\pi$
$734$	−1.50000	−	0.866025i	−0.0553660	−	0.0319656i
$735$	33.0000	+	25.9808i	1.21722	+	0.958315i
$736$		−	3.46410i		−	0.127688i
$737$	−18.0000	+	10.3923i	−0.663039	+	0.382805i
$738$	−27.0000	−	15.5885i	−0.993884	−	0.573819i
$739$	−28.5000	−	16.4545i	−1.04839	−	0.605288i	−0.126191	−	0.992006i	$-0.540275\pi$
$739$	−28.5000	−	16.4545i	−1.04839	−	0.605288i	−0.922198	+	0.386718i	$0.873609\pi$
$740$	15.0000	−	25.9808i	0.551411	−	0.955072i
$741$	22.5000	+	21.6506i	0.826558	+	0.795356i
$742$	6.00000	+	6.92820i	0.220267	+	0.254342i
$743$	15.0000	+	25.9808i	0.550297	+	0.953142i	0.998253	+	0.0590862i	$0.0188187\pi$
$743$	15.0000	+	25.9808i	0.550297	+	0.953142i	−0.447956	+	0.894055i	$0.647848\pi$
$744$		−	13.8564i		−	0.508001i
$745$			62.3538i			2.28447i
$746$	−1.00000	−	1.73205i	−0.0366126	−	0.0634149i
$747$	−9.00000	+	5.19615i	−0.329293	+	0.190117i
$748$		0			0
$749$		0			0
$750$	−6.00000	+	10.3923i	−0.219089	+	0.379473i
$751$	−17.0000			−0.620339			−0.310169	−	0.950681i	$-0.600386\pi$
$751$	−17.0000			−0.620339			−0.310169	+	0.950681i	$0.600386\pi$
$752$	6.00000	+	3.46410i	0.218797	+	0.126323i
$753$	18.0000	−	10.3923i	0.655956	−	0.378717i
$754$	6.00000	−	24.2487i	0.218507	−	0.883086i
$755$	12.0000			0.436725
$756$	−13.5000	+	2.59808i	−0.490990	+	0.0944911i
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	−0.971652	−	0.236414i	$-0.924028\pi$
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	0.281086	−	0.959683i	$-0.409305\pi$
$758$	15.0000	−	8.66025i	0.544825	−	0.314555i
$759$	−18.0000	−	31.1769i	−0.653359	−	1.13165i
$760$		−	17.3205i		−	0.628281i
$761$	−3.00000	+	1.73205i	−0.108750	+	0.0627868i	−0.553388	−	0.832923i	$-0.686665\pi$
$761$	−3.00000	+	1.73205i	−0.108750	+	0.0627868i	0.444639	+	0.895710i	$0.353332\pi$
$762$		−	1.73205i		−	0.0627456i
$763$	21.0000	+	24.2487i	0.760251	+	0.877862i
$764$	−18.0000	+	10.3923i	−0.651217	+	0.375980i
$765$		0			0
$766$	−18.0000	+	10.3923i	−0.650366	+	0.375489i
$767$		0			0
$768$	−1.50000	−	0.866025i	−0.0541266	−	0.0312500i
$769$	0.500000	+	0.866025i	0.0180305	+	0.0312297i	0.874900	−	0.484304i	$-0.160927\pi$
$769$	0.500000	+	0.866025i	0.0180305	+	0.0312297i	−0.856869	+	0.515534i	$0.827594\pi$
$770$	36.0000	+	41.5692i	1.29735	+	1.49805i
$771$	27.0000	+	15.5885i	0.972381	+	0.561405i
$772$	−4.50000	−	2.59808i	−0.161959	−	0.0935068i
$773$			41.5692i			1.49514i	0.664183	+	0.747570i	$0.268780\pi$
$773$			41.5692i			1.49514i	−0.664183	+	0.747570i	$0.731220\pi$
$774$	3.00000			0.107833
$775$	28.0000	−	48.4974i	1.00579	−	1.74208i
$776$	3.50000	−	6.06218i	0.125643	−	0.217620i
$777$	37.5000	+	12.9904i	1.34531	+	0.466027i
$778$	9.00000	−	5.19615i	0.322666	−	0.186291i
$779$	45.0000	+	25.9808i	1.61229	+	0.930857i
$780$	21.0000	+	5.19615i	0.751921	+	0.186052i
$781$		0			0
$782$		0			0
$783$	−18.0000	−	31.1769i	−0.643268	−	1.11417i
$784$	−6.50000	+	2.59808i	−0.232143	+	0.0927884i
$785$	−66.0000			−2.35564
$786$	−27.0000	+	15.5885i	−0.963058	+	0.556022i
$787$	−53.0000			−1.88925			−0.944623	−	0.328158i	$-0.893572\pi$
$787$	−53.0000			−1.88925			−0.944623	+	0.328158i	$0.893572\pi$
$788$	6.00000	+	10.3923i	0.213741	+	0.370211i
$789$	−12.0000	−	20.7846i	−0.427211	−	0.739952i
$790$	−24.0000	+	13.8564i	−0.853882	+	0.492989i
$791$	−6.00000	+	17.3205i	−0.213335	+	0.615846i
$792$	−18.0000			−0.639602
$793$	−4.50000	+	18.1865i	−0.159800	+	0.645823i
$794$	−5.50000	−	9.52628i	−0.195188	−	0.338075i
$795$	−18.0000	−	10.3923i	−0.638394	−	0.368577i
$796$			15.5885i			0.552518i
$797$	−9.00000	+	15.5885i	−0.318796	+	0.552171i	−0.980237	−	0.197826i	$-0.936612\pi$
$797$	−9.00000	+	15.5885i	−0.318796	+	0.552171i	0.661441	+	0.749997i	$0.269945\pi$
$798$	22.5000	−	4.33013i	0.796491	−	0.153285i
$799$		0			0
$800$	−3.50000	−	6.06218i	−0.123744	−	0.214330i
$801$	−9.00000	+	5.19615i	−0.317999	+	0.183597i
$802$	−6.00000			−0.211867
$803$	42.0000			1.48215
$804$	3.00000	+	5.19615i	0.105802	+	0.183254i
$805$	30.0000	+	10.3923i	1.05736	+	0.366281i
$806$	−28.0000	−	6.92820i	−0.986258	−	0.244036i
$807$	−18.0000	−	10.3923i	−0.633630	−	0.365826i
$808$	−3.00000	+	5.19615i	−0.105540	+	0.182800i
$809$	6.00000	+	3.46410i	0.210949	+	0.121791i	0.601752	−	0.798683i	$-0.294469\pi$
$809$	6.00000	+	3.46410i	0.210949	+	0.121791i	−0.390803	+	0.920474i	$0.627803\pi$
$810$	27.0000	−	15.5885i	0.948683	−	0.547723i
$811$	−1.00000			−0.0351147			−0.0175574	−	0.999846i	$-0.505589\pi$
$811$	−1.00000			−0.0351147			−0.0175574	+	0.999846i	$0.505589\pi$
$812$	−12.0000	−	13.8564i	−0.421117	−	0.486265i
$813$	−1.50000	−	0.866025i	−0.0526073	−	0.0303728i
$814$	45.0000	+	25.9808i	1.57725	+	0.910625i
$815$	6.00000			0.210171
$816$		0			0
$817$	−5.00000			−0.174928
$818$	−19.0000			−0.664319
$819$	−1.50000	+	28.5788i	−0.0524142	+	0.998625i
$820$	36.0000			1.25717
$821$	54.0000			1.88461			0.942306	−	0.334751i	$-0.108652\pi$
$821$	54.0000			1.88461			0.942306	+	0.334751i	$0.108652\pi$
$822$	9.00000	+	5.19615i	0.313911	+	0.181237i
$823$	56.0000			1.95204			0.976019	−	0.217687i	$-0.0698512\pi$
$823$	56.0000			1.95204			0.976019	+	0.217687i	$0.0698512\pi$
$824$	−4.50000	−	2.59808i	−0.156765	−	0.0905083i
$825$	−63.0000	−	36.3731i	−2.19338	−	1.26635i
$826$		0			0
$827$	48.0000			1.66912			0.834562	−	0.550914i	$-0.185721\pi$
$827$	48.0000			1.66912			0.834562	+	0.550914i	$0.185721\pi$
$828$	−9.00000	+	5.19615i	−0.312772	+	0.180579i
$829$	−1.50000	−	0.866025i	−0.0520972	−	0.0300783i	0.473725	−	0.880673i	$-0.342909\pi$
$829$	−1.50000	−	0.866025i	−0.0520972	−	0.0300783i	−0.525822	+	0.850594i	$0.676242\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$	−25.5000	−	14.7224i	−0.884585	−	0.510716i
$832$	−2.50000	+	2.59808i	−0.0866719	+	0.0900721i
$833$		0			0
$834$	−3.00000	−	5.19615i	−0.103882	−	0.179928i
$835$	−12.0000			−0.415277
$836$	30.0000			1.03757
$837$	−36.0000	+	20.7846i	−1.24434	+	0.718421i
$838$	−15.0000	−	25.9808i	−0.518166	−	0.897491i
$839$	−18.0000	−	10.3923i	−0.621429	−	0.358782i	0.155996	−	0.987758i	$-0.450141\pi$
$839$	−18.0000	−	10.3923i	−0.621429	−	0.358782i	−0.777425	+	0.628975i	$0.783475\pi$
$840$	12.0000	−	10.3923i	0.414039	−	0.358569i
$841$	9.50000	−	16.4545i	0.327586	−	0.567396i
$842$		−	27.7128i		−	0.955047i
$843$	18.0000	+	10.3923i	0.619953	+	0.357930i
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$	21.0000	−	39.8372i	0.722422	−	1.37044i
$846$		−	20.7846i		−	0.714590i
$847$	−50.0000	+	43.3013i	−1.71802	+	1.48785i
$848$	3.00000	−	1.73205i	0.103020	−	0.0594789i
$849$	1.50000	+	2.59808i	0.0514799	+	0.0891657i
$850$		0			0
$851$	30.0000			1.02839
$852$		0			0
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$	9.00000	+	10.3923i	0.307974	+	0.355617i
$855$	−45.0000	+	25.9808i	−1.53897	+	0.888523i
$856$		0			0
$857$	−12.0000	−	20.7846i	−0.409912	−	0.709989i	0.584967	−	0.811057i	$-0.301107\pi$
$857$	−12.0000	−	20.7846i	−0.409912	−	0.709989i	−0.994880	+	0.101068i	$0.967774\pi$
$858$	−9.00000	+	36.3731i	−0.307255	+	1.24176i
$859$	−1.50000	−	0.866025i	−0.0511793	−	0.0295484i	0.474192	−	0.880421i	$-0.342740\pi$
$859$	−1.50000	−	0.866025i	−0.0511793	−	0.0295484i	−0.525371	+	0.850873i	$0.676074\pi$
$860$	−3.00000	+	1.73205i	−0.102299	+	0.0590624i
$861$	9.00000	+	46.7654i	0.306719	+	1.59376i
$862$	9.00000	−	15.5885i	0.306541	−	0.530945i
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	−0.912558	−	0.408946i	$-0.865896\pi$
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	0.810437	+	0.585826i	$0.199230\pi$
$864$			5.19615i			0.176777i
$865$		−	20.7846i		−	0.706698i
$866$	−18.0000	−	10.3923i	−0.611665	−	0.353145i
$867$	25.5000	+	14.7224i	0.866025	+	0.500000i
$868$	−16.0000	+	13.8564i	−0.543075	+	0.470317i
$869$	−24.0000	−	41.5692i	−0.814144	−	1.41014i
$870$	36.0000	+	20.7846i	1.22051	+	0.704664i
$871$	12.0000	−	3.46410i	0.406604	−	0.117377i
$872$	10.5000	−	6.06218i	0.355575	−	0.205291i
$873$	−21.0000			−0.710742
$874$	15.0000	−	8.66025i	0.507383	−	0.292937i
$875$	18.0000	−	3.46410i	0.608511	−	0.117108i
$876$		−	12.1244i		−	0.409644i
$877$	24.0000	−	13.8564i	0.810422	−	0.467898i	−0.0366801	−	0.999327i	$-0.511678\pi$
$877$	24.0000	−	13.8564i	0.810422	−	0.467898i	0.847103	+	0.531429i	$0.178345\pi$
$878$		−	12.1244i		−	0.409177i
$879$	−6.00000	−	10.3923i	−0.202375	−	0.350524i
$880$	18.0000	−	10.3923i	0.606780	−	0.350325i
$881$	−18.0000	−	31.1769i	−0.606435	−	1.05038i	−0.991823	−	0.127622i	$-0.959266\pi$
$881$	−18.0000	−	31.1769i	−0.606435	−	1.05038i	0.385387	−	0.922755i	$-0.374068\pi$
$882$	16.5000	+	12.9904i	0.555584	+	0.437409i
$883$	−19.0000			−0.639401			−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000			−0.639401			−0.319700	+	0.947519i	$0.603582\pi$
$884$		0			0
$885$		0			0
$886$	33.0000	+	19.0526i	1.10866	+	0.640083i
$887$	−6.00000			−0.201460			−0.100730	−	0.994914i	$-0.532118\pi$
$887$	−6.00000			−0.201460			−0.100730	+	0.994914i	$0.532118\pi$
$888$	7.50000	−	12.9904i	0.251684	−	0.435929i
$889$	−2.00000	+	1.73205i	−0.0670778	+	0.0580911i
$890$	6.00000	−	10.3923i	0.201120	−	0.348351i
$891$	27.0000	+	46.7654i	0.904534	+	1.56670i
$892$	−8.00000	−	13.8564i	−0.267860	−	0.463947i
$893$			34.6410i			1.15922i
$894$			31.1769i			1.04271i
$895$	−42.0000	−	72.7461i	−1.40391	−	2.43164i
$896$	0.500000	+	2.59808i	0.0167038	+	0.0867956i
$897$	6.00000	+	20.7846i	0.200334	+	0.693978i
$898$	15.0000	−	25.9808i	0.500556	−	0.866989i
$899$	−48.0000	−	27.7128i	−1.60089	−	0.924274i
$900$	−10.5000	+	18.1865i	−0.350000	+	0.606218i
$901$		0			0
$902$			62.3538i			2.07616i
$903$	−3.00000	−	3.46410i	−0.0998337	−	0.115278i
$904$	6.00000	+	3.46410i	0.199557	+	0.115214i
$905$	−27.0000	+	46.7654i	−0.897510	+	1.55453i
$906$	6.00000			0.199337
$907$	0.500000	−	0.866025i	0.0166022	−	0.0287559i	−0.857605	−	0.514309i	$-0.828048\pi$
$907$	0.500000	−	0.866025i	0.0166022	−	0.0287559i	0.874207	+	0.485553i	$0.161382\pi$
$908$			10.3923i			0.344881i
$909$	18.0000			0.597022
$910$	−15.0000	−	29.4449i	−0.497245	−	0.976088i
$911$		−	13.8564i		−	0.459083i	−0.973299	−	0.229542i	$-0.926277\pi$
$911$		−	13.8564i		−	0.459083i	0.973299	−	0.229542i	$-0.0737227\pi$
$912$		−	8.66025i		−	0.286770i
$913$	18.0000	+	10.3923i	0.595713	+	0.343935i
$914$		0			0
$915$	−27.0000	−	15.5885i	−0.892592	−	0.515339i
$916$	−14.5000	+	25.1147i	−0.479093	+	0.829814i
$917$	45.0000	+	15.5885i	1.48603	+	0.514776i
$918$		0			0
$919$	−17.5000	−	30.3109i	−0.577272	−	0.999864i	−0.995791	−	0.0916559i	$-0.970784\pi$
$919$	−17.5000	−	30.3109i	−0.577272	−	0.999864i	0.418519	−	0.908208i	$-0.362549\pi$
$920$	6.00000	−	10.3923i	0.197814	−	0.342624i
$921$	6.00000	+	3.46410i	0.197707	+	0.114146i
$922$	18.0000	+	10.3923i	0.592798	+	0.342252i
$923$		0			0
$924$	18.0000	+	20.7846i	0.592157	+	0.683763i
$925$	52.5000	−	30.3109i	1.72619	−	0.996616i
$926$		−	19.0526i		−	0.626106i
$927$			15.5885i			0.511992i
$928$	−6.00000	+	3.46410i	−0.196960	+	0.113715i
$929$	24.0000	−	13.8564i	0.787414	−	0.454614i	−0.0516371	−	0.998666i	$-0.516444\pi$
$929$	24.0000	−	13.8564i	0.787414	−	0.454614i	0.839052	+	0.544052i	$0.183111\pi$
$930$	24.0000	−	41.5692i	0.786991	−	1.36311i
$931$	−27.5000	−	21.6506i	−0.901276	−	0.709571i
$932$	−6.00000	−	3.46410i	−0.196537	−	0.113470i
$933$		−	10.3923i		−	0.340229i
$934$	−9.00000	+	15.5885i	−0.294489	+	0.510070i
$935$		0			0
$936$	10.5000	+	2.59808i	0.343203	+	0.0849208i
$937$			8.66025i			0.282918i	0.989944	+	0.141459i	$0.0451794\pi$
$937$			8.66025i			0.282918i	−0.989944	+	0.141459i	$0.954821\pi$
$938$	3.00000	−	8.66025i	0.0979535	−	0.282767i
$939$	28.5000	+	49.3634i	0.930062	+	1.61092i
$940$	12.0000	+	20.7846i	0.391397	+	0.677919i
$941$	12.0000	−	6.92820i	0.391189	−	0.225853i	−0.291486	−	0.956575i	$-0.594150\pi$
$941$	12.0000	−	6.92820i	0.391189	−	0.225853i	0.682675	+	0.730722i	$0.260816\pi$
$942$	−33.0000			−1.07520
$943$	18.0000	+	31.1769i	0.586161	+	1.01526i
$944$		0			0
$945$	−45.0000	−	15.5885i	−1.46385	−	0.507093i
$946$	−3.00000	−	5.19615i	−0.0975384	−	0.168941i
$947$	−48.0000			−1.55979			−0.779895	−	0.625910i	$-0.784728\pi$
$947$	−48.0000			−1.55979			−0.779895	+	0.625910i	$0.784728\pi$
$948$	−12.0000	+	6.92820i	−0.389742	+	0.225018i
$949$	−24.5000	−	6.06218i	−0.795304	−	0.196787i
$950$	17.5000	−	30.3109i	0.567775	−	0.983415i
$951$	−27.0000	+	15.5885i	−0.875535	+	0.505490i
$952$		0			0
$953$	33.0000	+	19.0526i	1.06897	+	0.617173i	0.927901	−	0.372826i	$-0.121611\pi$
$953$	33.0000	+	19.0526i	1.06897	+	0.617173i	0.141074	+	0.989999i	$0.454945\pi$
$954$	−9.00000	−	5.19615i	−0.291386	−	0.168232i
$955$	−72.0000			−2.32987
$956$	6.00000			0.194054
$957$	−36.0000	+	62.3538i	−1.16371	+	2.01561i
$958$	−6.00000	−	3.46410i	−0.193851	−	0.111920i
$959$	−3.00000	−	15.5885i	−0.0968751	−	0.503378i
$960$	−3.00000	−	5.19615i	−0.0968246	−	0.167705i
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	−22.5000	−	21.6506i	−0.725429	−	0.698044i
$963$		0			0
$964$	26.0000			0.837404
$965$	−9.00000	−	15.5885i	−0.289720	−	0.501810i
$966$	15.0000	+	5.19615i	0.482617	+	0.167183i
$967$			8.66025i			0.278495i	0.990258	+	0.139247i	$0.0444684\pi$
$967$			8.66025i			0.278495i	−0.990258	+	0.139247i	$0.955532\pi$
$968$	12.5000	+	21.6506i	0.401765	+	0.695878i
$969$		0			0
$970$	21.0000	−	12.1244i	0.674269	−	0.389290i
$971$	−3.00000	−	5.19615i	−0.0962746	−	0.166752i	0.813865	−	0.581054i	$-0.197359\pi$
$971$	−3.00000	−	5.19615i	−0.0962746	−	0.166752i	−0.910140	+	0.414301i	$0.864026\pi$
$972$	13.5000	−	7.79423i	0.433013	−	0.250000i
$973$	−3.00000	+	8.66025i	−0.0961756	+	0.277635i
$974$			15.5885i			0.499486i
$975$	31.5000	+	30.3109i	1.00881	+	0.970725i
$976$	4.50000	−	2.59808i	0.144041	−	0.0831624i
$977$	18.0000	−	31.1769i	0.575871	−	0.997438i	−0.420075	−	0.907489i	$-0.637996\pi$
$977$	18.0000	−	31.1769i	0.575871	−	0.997438i	0.995946	−	0.0899487i	$-0.0286703\pi$
$978$	3.00000			0.0959294
$979$	18.0000	+	10.3923i	0.575282	+	0.332140i
$980$	−24.0000	−	3.46410i	−0.766652	−	0.110657i
$981$	−31.5000	−	18.1865i	−1.00572	−	0.580651i
$982$		0			0
$983$	−30.0000	+	17.3205i	−0.956851	+	0.552438i	−0.895203	−	0.445659i	$-0.852969\pi$
$983$	−30.0000	+	17.3205i	−0.956851	+	0.552438i	−0.0616488	+	0.998098i	$0.519636\pi$
$984$	18.0000			0.573819
$985$			41.5692i			1.32451i
$986$		0			0
$987$	−24.0000	+	20.7846i	−0.763928	+	0.661581i
$988$	−17.5000	−	4.33013i	−0.556749	−	0.137760i
$989$	−3.00000	−	1.73205i	−0.0953945	−	0.0550760i
$990$	−54.0000	−	31.1769i	−1.71623	−	0.990867i
$991$	−27.5000	+	47.6314i	−0.873566	+	1.51306i	−0.0152841	+	0.999883i	$0.504865\pi$
$991$	−27.5000	+	47.6314i	−0.873566	+	1.51306i	−0.858282	+	0.513178i	$0.828468\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$	33.0000			1.04722
$994$		0			0
$995$	−27.0000	+	46.7654i	−0.855958	+	1.48256i
$996$	3.00000	−	5.19615i	0.0950586	−	0.164646i
$997$		−	43.3013i		−	1.37136i	−0.727901	−	0.685682i	$-0.759504\pi$
$997$		−	43.3013i		−	1.37136i	0.727901	−	0.685682i	$-0.240496\pi$
$998$	7.50000	+	4.33013i	0.237408	+	0.137068i
$999$	−45.0000			−1.42374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.a.257.1	yes	2
3.2	odd	2		546.2.bi.c.257.1	yes	2
7.3	odd	6		546.2.bn.c.101.1	yes	2
13.4	even	6		546.2.bn.b.173.1	yes	2
21.17	even	6		546.2.bn.b.101.1	yes	2
39.17	odd	6		546.2.bn.c.173.1	yes	2
91.17	odd	6		546.2.bi.c.17.1	yes	2
273.17	even	6	inner	546.2.bi.a.17.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.a.17.1	✓	2	273.17	even	6	inner
546.2.bi.a.257.1	yes	2	1.1	even	1	trivial
546.2.bi.c.17.1	yes	2	91.17	odd	6
546.2.bi.c.257.1	yes	2	3.2	odd	2
546.2.bn.b.101.1	yes	2	21.17	even	6
546.2.bn.b.173.1	yes	2	13.4	even	6
546.2.bn.c.101.1	yes	2	7.3	odd	6
546.2.bn.c.173.1	yes	2	39.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(3.00000 + 1.73205i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(3.00000 + 1.73205i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-0.500000 - 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{10} +(3.00000 - 5.19615i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-2.50000 + 2.59808i) q^{13} +(0.500000 + 2.59808i) q^{14} +(-3.00000 - 5.19615i) q^{15} +1.00000 q^{16} +(-1.50000 - 2.59808i) q^{18} +(2.50000 + 4.33013i) q^{19} +(3.00000 + 1.73205i) q^{20} +(-1.50000 + 4.33013i) q^{21} +(-3.00000 + 5.19615i) q^{22} +3.46410i q^{23} +(1.50000 + 0.866025i) q^{24} +(3.50000 + 6.06218i) q^{25} +(2.50000 - 2.59808i) q^{26} -5.19615i q^{27} +(-0.500000 - 2.59808i) q^{28} +(6.00000 - 3.46410i) q^{29} +(3.00000 + 5.19615i) q^{30} +(-4.00000 - 6.92820i) q^{31} -1.00000 q^{32} +(-9.00000 + 5.19615i) q^{33} +(3.00000 - 8.66025i) q^{35} +(1.50000 + 2.59808i) q^{36} -8.66025i q^{37} +(-2.50000 - 4.33013i) q^{38} +(6.00000 - 1.73205i) q^{39} +(-3.00000 - 1.73205i) q^{40} +(9.00000 - 5.19615i) q^{41} +(1.50000 - 4.33013i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(3.00000 - 5.19615i) q^{44} +10.3923i q^{45} -3.46410i q^{46} +(6.00000 + 3.46410i) q^{47} +(-1.50000 - 0.866025i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(-3.50000 - 6.06218i) q^{50} +(-2.50000 + 2.59808i) q^{52} +(3.00000 - 1.73205i) q^{53} +5.19615i q^{54} +(18.0000 - 10.3923i) q^{55} +(0.500000 + 2.59808i) q^{56} -8.66025i q^{57} +(-6.00000 + 3.46410i) q^{58} +(-3.00000 - 5.19615i) q^{60} +(4.50000 - 2.59808i) q^{61} +(4.00000 + 6.92820i) q^{62} +(6.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(-12.0000 + 3.46410i) q^{65} +(9.00000 - 5.19615i) q^{66} +(-3.00000 - 1.73205i) q^{67} +(3.00000 - 5.19615i) q^{69} +(-3.00000 + 8.66025i) q^{70} +(-1.50000 - 2.59808i) q^{72} +(3.50000 + 6.06218i) q^{73} +8.66025i q^{74} -12.1244i q^{75} +(2.50000 + 4.33013i) q^{76} +(-15.0000 - 5.19615i) q^{77} +(-6.00000 + 1.73205i) q^{78} +(4.00000 - 6.92820i) q^{79} +(3.00000 + 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-9.00000 + 5.19615i) q^{82} +3.46410i q^{83} +(-1.50000 + 4.33013i) q^{84} +(0.500000 - 0.866025i) q^{86} -12.0000 q^{87} +(-3.00000 + 5.19615i) q^{88} +3.46410i q^{89} -10.3923i q^{90} +(8.00000 + 5.19615i) q^{91} +3.46410i q^{92} +13.8564i q^{93} +(-6.00000 - 3.46410i) q^{94} +17.3205i q^{95} +(1.50000 + 0.866025i) q^{96} +(-3.50000 + 6.06218i) q^{97} +(6.50000 - 2.59808i) q^{98} +18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + 6 q^{5} + 3 q^{6} - q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + 6 * q^5 + 3 * q^6 - q^7 - 2 * q^8 + 3 * q^9	\( 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + 6 q^{5} + 3 q^{6} - q^{7} - 2 q^{8} + 3 q^{9} - 6 q^{10} + 6 q^{11} - 3 q^{12} - 5 q^{13} + q^{14} - 6 q^{15} + 2 q^{16} - 3 q^{18} + 5 q^{19} + 6 q^{20} - 3 q^{21} - 6 q^{22} + 3 q^{24} + 7 q^{25} + 5 q^{26} - q^{28} + 12 q^{29} + 6 q^{30} - 8 q^{31} - 2 q^{32} - 18 q^{33} + 6 q^{35} + 3 q^{36} - 5 q^{38} + 12 q^{39} - 6 q^{40} + 18 q^{41} + 3 q^{42} - q^{43} + 6 q^{44} + 12 q^{47} - 3 q^{48} - 13 q^{49} - 7 q^{50} - 5 q^{52} + 6 q^{53} + 36 q^{55} + q^{56} - 12 q^{58} - 6 q^{60} + 9 q^{61} + 8 q^{62} + 12 q^{63} + 2 q^{64} - 24 q^{65} + 18 q^{66} - 6 q^{67} + 6 q^{69} - 6 q^{70} - 3 q^{72} + 7 q^{73} + 5 q^{76} - 30 q^{77} - 12 q^{78} + 8 q^{79} + 6 q^{80} - 9 q^{81} - 18 q^{82} - 3 q^{84} + q^{86} - 24 q^{87} - 6 q^{88} + 16 q^{91} - 12 q^{94} + 3 q^{96} - 7 q^{97} + 13 q^{98} + 36 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + 6 * q^5 + 3 * q^6 - q^7 - 2 * q^8 + 3 * q^9 - 6 * q^10 + 6 * q^11 - 3 * q^12 - 5 * q^13 + q^14 - 6 * q^15 + 2 * q^16 - 3 * q^18 + 5 * q^19 + 6 * q^20 - 3 * q^21 - 6 * q^22 + 3 * q^24 + 7 * q^25 + 5 * q^26 - q^28 + 12 * q^29 + 6 * q^30 - 8 * q^31 - 2 * q^32 - 18 * q^33 + 6 * q^35 + 3 * q^36 - 5 * q^38 + 12 * q^39 - 6 * q^40 + 18 * q^41 + 3 * q^42 - q^43 + 6 * q^44 + 12 * q^47 - 3 * q^48 - 13 * q^49 - 7 * q^50 - 5 * q^52 + 6 * q^53 + 36 * q^55 + q^56 - 12 * q^58 - 6 * q^60 + 9 * q^61 + 8 * q^62 + 12 * q^63 + 2 * q^64 - 24 * q^65 + 18 * q^66 - 6 * q^67 + 6 * q^69 - 6 * q^70 - 3 * q^72 + 7 * q^73 + 5 * q^76 - 30 * q^77 - 12 * q^78 + 8 * q^79 + 6 * q^80 - 9 * q^81 - 18 * q^82 - 3 * q^84 + q^86 - 24 * q^87 - 6 * q^88 + 16 * q^91 - 12 * q^94 + 3 * q^96 - 7 * q^97 + 13 * q^98 + 36 * q^99

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