LMFDB - Embedded newform 61.2.f.a.14.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(14,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("61.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.f (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:	$0.487087452330$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			14.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	61.14
Dual form			61.2.f.a.48.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{2} -2.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(3.00000 - 1.73205i) q^{6} +(-3.00000 + 1.73205i) q^{7} -1.73205i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{2} -2.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(3.00000 - 1.73205i) q^{6} +(-3.00000 + 1.73205i) q^{7} -1.73205i q^{8} +1.00000 q^{9} +(4.50000 + 2.59808i) q^{10} +3.46410i q^{11} +(-1.00000 + 1.73205i) q^{12} +(1.00000 + 1.73205i) q^{13} +(3.00000 - 5.19615i) q^{14} +(3.00000 + 5.19615i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-6.00000 - 3.46410i) q^{17} +(-1.50000 + 0.866025i) q^{18} +(1.00000 - 1.73205i) q^{19} -3.00000 q^{20} +(6.00000 - 3.46410i) q^{21} +(-3.00000 - 5.19615i) q^{22} +3.46410i q^{24} +(-2.00000 + 3.46410i) q^{25} +(-3.00000 - 1.73205i) q^{26} +4.00000 q^{27} +3.46410i q^{28} +(-1.50000 - 0.866025i) q^{29} +(-9.00000 - 5.19615i) q^{30} +(-9.00000 - 5.19615i) q^{31} +(-4.50000 - 2.59808i) q^{32} -6.92820i q^{33} +12.0000 q^{34} +(9.00000 + 5.19615i) q^{35} +(0.500000 - 0.866025i) q^{36} +1.73205i q^{37} +3.46410i q^{38} +(-2.00000 - 3.46410i) q^{39} +(-4.50000 + 2.59808i) q^{40} +3.00000 q^{41} +(-6.00000 + 10.3923i) q^{42} +(3.00000 - 1.73205i) q^{43} +(3.00000 + 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{45} +(-6.00000 + 10.3923i) q^{47} +(-5.00000 - 8.66025i) q^{48} +(2.50000 - 4.33013i) q^{49} -6.92820i q^{50} +(12.0000 + 6.92820i) q^{51} +2.00000 q^{52} +5.19615i q^{53} +(-6.00000 + 3.46410i) q^{54} +(9.00000 - 5.19615i) q^{55} +(3.00000 + 5.19615i) q^{56} +(-2.00000 + 3.46410i) q^{57} +3.00000 q^{58} +(-3.00000 + 1.73205i) q^{59} +6.00000 q^{60} +(-0.500000 - 7.79423i) q^{61} +18.0000 q^{62} +(-3.00000 + 1.73205i) q^{63} -1.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(6.00000 + 10.3923i) q^{66} +(-3.00000 + 1.73205i) q^{67} +(-6.00000 + 3.46410i) q^{68} -18.0000 q^{70} +(-9.00000 - 5.19615i) q^{71} -1.73205i q^{72} +(3.50000 - 6.06218i) q^{73} +(-1.50000 - 2.59808i) q^{74} +(4.00000 - 6.92820i) q^{75} +(-1.00000 - 1.73205i) q^{76} +(-6.00000 - 10.3923i) q^{77} +(6.00000 + 3.46410i) q^{78} +(-9.00000 + 5.19615i) q^{79} +(7.50000 - 12.9904i) q^{80} -11.0000 q^{81} +(-4.50000 + 2.59808i) q^{82} +(-3.00000 - 5.19615i) q^{83} -6.92820i q^{84} +20.7846i q^{85} +(-3.00000 + 5.19615i) q^{86} +(3.00000 + 1.73205i) q^{87} +6.00000 q^{88} +15.5885i q^{89} +(4.50000 + 2.59808i) q^{90} +(-6.00000 - 3.46410i) q^{91} +(18.0000 + 10.3923i) q^{93} -20.7846i q^{94} -6.00000 q^{95} +(9.00000 + 5.19615i) q^{96} +(-0.500000 + 0.866025i) q^{97} +8.66025i q^{98} +3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 4 q^{3} + q^{4} - 3 q^{5} + 6 q^{6} - 6 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 4 * q^3 + q^4 - 3 * q^5 + 6 * q^6 - 6 * q^7 + 2 * q^9	$ 2 q - 3 q^{2} - 4 q^{3} + q^{4} - 3 q^{5} + 6 q^{6} - 6 q^{7} + 2 q^{9} + 9 q^{10} - 2 q^{12} + 2 q^{13} + 6 q^{14} + 6 q^{15} + 5 q^{16} - 12 q^{17} - 3 q^{18} + 2 q^{19} - 6 q^{20} + 12 q^{21} - 6 q^{22} - 4 q^{25} - 6 q^{26} + 8 q^{27} - 3 q^{29} - 18 q^{30} - 18 q^{31} - 9 q^{32} + 24 q^{34} + 18 q^{35} + q^{36} - 4 q^{39} - 9 q^{40} + 6 q^{41} - 12 q^{42} + 6 q^{43} + 6 q^{44} - 3 q^{45} - 12 q^{47} - 10 q^{48} + 5 q^{49} + 24 q^{51} + 4 q^{52} - 12 q^{54} + 18 q^{55} + 6 q^{56} - 4 q^{57} + 6 q^{58} - 6 q^{59} + 12 q^{60} - q^{61} + 36 q^{62} - 6 q^{63} - 2 q^{64} + 6 q^{65} + 12 q^{66} - 6 q^{67} - 12 q^{68} - 36 q^{70} - 18 q^{71} + 7 q^{73} - 3 q^{74} + 8 q^{75} - 2 q^{76} - 12 q^{77} + 12 q^{78} - 18 q^{79} + 15 q^{80} - 22 q^{81} - 9 q^{82} - 6 q^{83} - 6 q^{86} + 6 q^{87} + 12 q^{88} + 9 q^{90} - 12 q^{91} + 36 q^{93} - 12 q^{95} + 18 q^{96} - q^{97}+O(q^{100}) $ 2 * q - 3 * q^2 - 4 * q^3 + q^4 - 3 * q^5 + 6 * q^6 - 6 * q^7 + 2 * q^9 + 9 * q^10 - 2 * q^12 + 2 * q^13 + 6 * q^14 + 6 * q^15 + 5 * q^16 - 12 * q^17 - 3 * q^18 + 2 * q^19 - 6 * q^20 + 12 * q^21 - 6 * q^22 - 4 * q^25 - 6 * q^26 + 8 * q^27 - 3 * q^29 - 18 * q^30 - 18 * q^31 - 9 * q^32 + 24 * q^34 + 18 * q^35 + q^36 - 4 * q^39 - 9 * q^40 + 6 * q^41 - 12 * q^42 + 6 * q^43 + 6 * q^44 - 3 * q^45 - 12 * q^47 - 10 * q^48 + 5 * q^49 + 24 * q^51 + 4 * q^52 - 12 * q^54 + 18 * q^55 + 6 * q^56 - 4 * q^57 + 6 * q^58 - 6 * q^59 + 12 * q^60 - q^61 + 36 * q^62 - 6 * q^63 - 2 * q^64 + 6 * q^65 + 12 * q^66 - 6 * q^67 - 12 * q^68 - 36 * q^70 - 18 * q^71 + 7 * q^73 - 3 * q^74 + 8 * q^75 - 2 * q^76 - 12 * q^77 + 12 * q^78 - 18 * q^79 + 15 * q^80 - 22 * q^81 - 9 * q^82 - 6 * q^83 - 6 * q^86 + 6 * q^87 + 12 * q^88 + 9 * q^90 - 12 * q^91 + 36 * q^93 - 12 * q^95 + 18 * q^96 - q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.135045	+	0.990839i	$0.543118\pi$
$3$	−2.00000			−1.15470			−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000			−1.15470			−0.577350	+	0.816497i	$0.695913\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$	3.00000	−	1.73205i	1.22474	−	0.707107i
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.188982	+	0.981981i	$0.560519\pi$
$8$		−	1.73205i		−	0.612372i
$9$	1.00000			0.333333
$10$	4.50000	+	2.59808i	1.42302	+	0.821584i
$11$			3.46410i			1.04447i	0.852803	+	0.522233i	$0.174901\pi$
$11$			3.46410i			1.04447i	−0.852803	+	0.522233i	$0.825099\pi$
$12$	−1.00000	+	1.73205i	−0.288675	+	0.500000i
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	3.00000	−	5.19615i	0.801784	−	1.38873i
$15$	3.00000	+	5.19615i	0.774597	+	1.34164i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	−6.00000	−	3.46410i	−1.45521	−	0.840168i	−0.456444	−	0.889752i	$-0.650877\pi$
$17$	−6.00000	−	3.46410i	−1.45521	−	0.840168i	−0.998770	+	0.0495842i	$0.984210\pi$
$18$	−1.50000	+	0.866025i	−0.353553	+	0.204124i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$	−3.00000			−0.670820
$21$	6.00000	−	3.46410i	1.30931	−	0.755929i
$22$	−3.00000	−	5.19615i	−0.639602	−	1.10782i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$			3.46410i			0.707107i
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	−3.00000	−	1.73205i	−0.588348	−	0.339683i
$27$	4.00000			0.769800
$28$			3.46410i			0.654654i
$29$	−1.50000	−	0.866025i	−0.278543	−	0.160817i	0.354221	−	0.935162i	$-0.384746\pi$
$29$	−1.50000	−	0.866025i	−0.278543	−	0.160817i	−0.632764	+	0.774345i	$0.718080\pi$
$30$	−9.00000	−	5.19615i	−1.64317	−	0.948683i
$31$	−9.00000	−	5.19615i	−1.61645	−	0.933257i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−9.00000	−	5.19615i	−1.61645	−	0.933257i	−0.628619	−	0.777714i	$-0.716379\pi$
$32$	−4.50000	−	2.59808i	−0.795495	−	0.459279i
$33$		−	6.92820i		−	1.20605i
$34$	12.0000			2.05798
$35$	9.00000	+	5.19615i	1.52128	+	0.878310i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$			1.73205i			0.284747i	0.989813	+	0.142374i	$0.0454735\pi$
$37$			1.73205i			0.284747i	−0.989813	+	0.142374i	$0.954527\pi$
$38$			3.46410i			0.561951i
$39$	−2.00000	−	3.46410i	−0.320256	−	0.554700i
$40$	−4.50000	+	2.59808i	−0.711512	+	0.410792i
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$	−6.00000	+	10.3923i	−0.925820	+	1.60357i
$43$	3.00000	−	1.73205i	0.457496	−	0.264135i	−0.253495	−	0.967337i	$-0.581580\pi$
$43$	3.00000	−	1.73205i	0.457496	−	0.264135i	0.710991	+	0.703201i	$0.248247\pi$
$44$	3.00000	+	1.73205i	0.452267	+	0.261116i
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$		0			0
$47$	−6.00000	+	10.3923i	−0.875190	+	1.51587i	−0.0186297	+	0.999826i	$0.505930\pi$
$47$	−6.00000	+	10.3923i	−0.875190	+	1.51587i	−0.856560	+	0.516047i	$0.827403\pi$
$48$	−5.00000	−	8.66025i	−0.721688	−	1.25000i
$49$	2.50000	−	4.33013i	0.357143	−	0.618590i
$50$		−	6.92820i		−	0.979796i
$51$	12.0000	+	6.92820i	1.68034	+	0.970143i
$52$	2.00000			0.277350
$53$			5.19615i			0.713746i	0.934153	+	0.356873i	$0.116157\pi$
$53$			5.19615i			0.713746i	−0.934153	+	0.356873i	$0.883843\pi$
$54$	−6.00000	+	3.46410i	−0.816497	+	0.471405i
$55$	9.00000	−	5.19615i	1.21356	−	0.700649i
$56$	3.00000	+	5.19615i	0.400892	+	0.694365i
$57$	−2.00000	+	3.46410i	−0.264906	+	0.458831i
$58$	3.00000			0.393919
$59$	−3.00000	+	1.73205i	−0.390567	+	0.225494i	−0.682406	−	0.730974i	$-0.739066\pi$
$59$	−3.00000	+	1.73205i	−0.390567	+	0.225494i	0.291839	+	0.956467i	$0.405733\pi$
$60$	6.00000			0.774597
$61$	−0.500000	−	7.79423i	−0.0640184	−	0.997949i
$61$	−0.500000	−	7.79423i	−0.0640184	−	0.997949i
$62$	18.0000			2.28600
$63$	−3.00000	+	1.73205i	−0.377964	+	0.218218i
$64$	−1.00000			−0.125000
$65$	3.00000	−	5.19615i	0.372104	−	0.644503i
$66$	6.00000	+	10.3923i	0.738549	+	1.27920i
$67$	−3.00000	+	1.73205i	−0.366508	+	0.211604i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	−3.00000	+	1.73205i	−0.366508	+	0.211604i	0.305424	+	0.952217i	$0.401202\pi$
$68$	−6.00000	+	3.46410i	−0.727607	+	0.420084i
$69$		0			0
$70$	−18.0000			−2.15141
$71$	−9.00000	−	5.19615i	−1.06810	−	0.616670i	−0.140441	−	0.990089i	$-0.544852\pi$
$71$	−9.00000	−	5.19615i	−1.06810	−	0.616670i	−0.927663	+	0.373419i	$0.878185\pi$
$72$		−	1.73205i		−	0.204124i
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$	−1.50000	−	2.59808i	−0.174371	−	0.302020i
$75$	4.00000	−	6.92820i	0.461880	−	0.800000i
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	−6.00000	−	10.3923i	−0.683763	−	1.18431i
$78$	6.00000	+	3.46410i	0.679366	+	0.392232i
$79$	−9.00000	+	5.19615i	−1.01258	+	0.584613i	−0.911946	−	0.410311i	$-0.865420\pi$
$79$	−9.00000	+	5.19615i	−1.01258	+	0.584613i	−0.100633	+	0.994924i	$0.532087\pi$
$80$	7.50000	−	12.9904i	0.838525	−	1.45237i
$81$	−11.0000			−1.22222
$82$	−4.50000	+	2.59808i	−0.496942	+	0.286910i
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	0.653079	−	0.757290i	$-0.273477\pi$
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	−0.982372	+	0.186938i	$0.940144\pi$
$84$		−	6.92820i		−	0.755929i
$85$			20.7846i			2.25441i
$86$	−3.00000	+	5.19615i	−0.323498	+	0.560316i
$87$	3.00000	+	1.73205i	0.321634	+	0.185695i
$88$	6.00000			0.639602
$89$			15.5885i			1.65237i	0.563397	+	0.826187i	$0.309494\pi$
$89$			15.5885i			1.65237i	−0.563397	+	0.826187i	$0.690506\pi$
$90$	4.50000	+	2.59808i	0.474342	+	0.273861i
$91$	−6.00000	−	3.46410i	−0.628971	−	0.363137i
$92$		0			0
$93$	18.0000	+	10.3923i	1.86651	+	1.07763i
$94$		−	20.7846i		−	2.14377i
$95$	−6.00000			−0.615587
$96$	9.00000	+	5.19615i	0.918559	+	0.530330i
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	−0.890292	−	0.455389i	$-0.849500\pi$
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	0.839525	+	0.543321i	$0.182833\pi$
$98$			8.66025i			0.874818i
$99$			3.46410i			0.348155i
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	13.5000	−	7.79423i	1.34330	−	0.775555i	0.356010	−	0.934482i	$-0.384137\pi$
$101$	13.5000	−	7.79423i	1.34330	−	0.775555i	0.987290	+	0.158927i	$0.0508036\pi$
$102$	−24.0000			−2.37635
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$	3.00000	−	1.73205i	0.294174	−	0.169842i
$105$	−18.0000	−	10.3923i	−1.75662	−	1.01419i
$106$	−4.50000	−	7.79423i	−0.437079	−	0.757042i
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	0.983531	−	0.180741i	$-0.0578495\pi$
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	−0.648292	+	0.761392i	$0.724516\pi$
$110$	−9.00000	+	15.5885i	−0.858116	+	1.48630i
$111$		−	3.46410i		−	0.328798i
$112$	−15.0000	−	8.66025i	−1.41737	−	0.818317i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		−	6.92820i		−	0.648886i
$115$		0			0
$116$	−1.50000	+	0.866025i	−0.139272	+	0.0804084i
$117$	1.00000	+	1.73205i	0.0924500	+	0.160128i
$118$	3.00000	−	5.19615i	0.276172	−	0.478345i
$119$	24.0000			2.20008
$120$	9.00000	−	5.19615i	0.821584	−	0.474342i
$121$	−1.00000			−0.0909091
$122$	7.50000	+	11.2583i	0.679018	+	1.01928i
$123$	−6.00000			−0.541002
$124$	−9.00000	+	5.19615i	−0.808224	+	0.466628i
$125$	−3.00000			−0.268328
$126$	3.00000	−	5.19615i	0.267261	−	0.462910i
$127$	1.00000	+	1.73205i	0.0887357	+	0.153695i	0.906977	−	0.421180i	$-0.138384\pi$
$127$	1.00000	+	1.73205i	0.0887357	+	0.153695i	−0.818241	+	0.574875i	$0.805051\pi$
$128$	10.5000	−	6.06218i	0.928078	−	0.535826i
$129$	−6.00000	+	3.46410i	−0.528271	+	0.304997i
$130$			10.3923i			0.911465i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	−6.00000	−	3.46410i	−0.522233	−	0.301511i
$133$			6.92820i			0.600751i
$134$	3.00000	−	5.19615i	0.259161	−	0.448879i
$135$	−6.00000	−	10.3923i	−0.516398	−	0.894427i
$136$	−6.00000	+	10.3923i	−0.514496	+	0.891133i
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	6.00000	+	3.46410i	0.508913	+	0.293821i	0.732387	−	0.680889i	$-0.238406\pi$
$139$	6.00000	+	3.46410i	0.508913	+	0.293821i	−0.223474	+	0.974710i	$0.571740\pi$
$140$	9.00000	−	5.19615i	0.760639	−	0.439155i
$141$	12.0000	−	20.7846i	1.01058	−	1.75038i
$142$	18.0000			1.51053
$143$	−6.00000	+	3.46410i	−0.501745	+	0.289683i
$144$	2.50000	+	4.33013i	0.208333	+	0.360844i
$145$			5.19615i			0.431517i
$146$			12.1244i			1.00342i
$147$	−5.00000	+	8.66025i	−0.412393	+	0.714286i
$148$	1.50000	+	0.866025i	0.123299	+	0.0711868i
$149$	−15.0000			−1.22885			−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000			−1.22885			−0.614424	+	0.788976i	$0.710612\pi$
$150$			13.8564i			1.13137i
$151$	−3.00000	−	1.73205i	−0.244137	−	0.140952i	0.372940	−	0.927855i	$-0.378350\pi$
$151$	−3.00000	−	1.73205i	−0.244137	−	0.140952i	−0.617076	+	0.786903i	$0.711683\pi$
$152$	−3.00000	−	1.73205i	−0.243332	−	0.140488i
$153$	−6.00000	−	3.46410i	−0.485071	−	0.280056i
$154$	18.0000	+	10.3923i	1.45048	+	0.837436i
$155$			31.1769i			2.50419i
$156$	−4.00000			−0.320256
$157$	12.0000	+	6.92820i	0.957704	+	0.552931i	0.895466	−	0.445130i	$-0.146843\pi$
$157$	12.0000	+	6.92820i	0.957704	+	0.552931i	0.0622385	+	0.998061i	$0.480176\pi$
$158$	9.00000	−	15.5885i	0.716002	−	1.24015i
$159$		−	10.3923i		−	0.824163i
$160$			15.5885i			1.23238i
$161$		0			0
$162$	16.5000	−	9.52628i	1.29636	−	0.748455i
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$	−18.0000	+	10.3923i	−1.40130	+	0.809040i
$166$	9.00000	+	5.19615i	0.698535	+	0.403300i
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	−0.969693	−	0.244328i	$-0.921432\pi$
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	0.273252	−	0.961943i	$-0.411901\pi$
$168$	−6.00000	−	10.3923i	−0.462910	−	0.801784i
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	−18.0000	−	31.1769i	−1.38054	−	2.39116i
$171$	1.00000	−	1.73205i	0.0764719	−	0.132453i
$172$		−	3.46410i		−	0.264135i
$173$	−7.50000	−	4.33013i	−0.570214	−	0.329213i	0.187021	−	0.982356i	$-0.440117\pi$
$173$	−7.50000	−	4.33013i	−0.570214	−	0.329213i	−0.757235	+	0.653143i	$0.773450\pi$
$174$	−6.00000			−0.454859
$175$		−	13.8564i		−	1.04745i
$176$	−15.0000	+	8.66025i	−1.13067	+	0.652791i
$177$	6.00000	−	3.46410i	0.450988	−	0.260378i
$178$	−13.5000	−	23.3827i	−1.01187	−	1.75261i
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	−0.956088	−	0.293079i	$-0.905320\pi$
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	0.731858	+	0.681457i	$0.238654\pi$
$180$	−3.00000			−0.223607
$181$	−19.5000	+	11.2583i	−1.44942	+	0.836825i	−0.998447	−	0.0557107i	$-0.982258\pi$
$181$	−19.5000	+	11.2583i	−1.44942	+	0.836825i	−0.450977	+	0.892536i	$0.648924\pi$
$182$	12.0000			0.889499
$183$	1.00000	+	15.5885i	0.0739221	+	1.15233i
$184$		0			0
$185$	4.50000	−	2.59808i	0.330847	−	0.191014i
$186$	−36.0000			−2.63965
$187$	12.0000	−	20.7846i	0.877527	−	1.51992i
$188$	6.00000	+	10.3923i	0.437595	+	0.757937i
$189$	−12.0000	+	6.92820i	−0.872872	+	0.503953i
$190$	9.00000	−	5.19615i	0.652929	−	0.376969i
$191$		−	13.8564i		−	1.00261i	−0.865269	−	0.501307i	$-0.832853\pi$
$191$		−	13.8564i		−	1.00261i	0.865269	−	0.501307i	$-0.167147\pi$
$192$	2.00000			0.144338
$193$	−10.5000	−	6.06218i	−0.755807	−	0.436365i	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	−10.5000	−	6.06218i	−0.755807	−	0.436365i	−0.827788	+	0.561041i	$0.810401\pi$
$194$		−	1.73205i		−	0.124354i
$195$	−6.00000	+	10.3923i	−0.429669	+	0.744208i
$196$	−2.50000	−	4.33013i	−0.178571	−	0.309295i
$197$	−1.50000	+	2.59808i	−0.106871	+	0.185105i	−0.914501	−	0.404584i	$-0.867416\pi$
$197$	−1.50000	+	2.59808i	−0.106871	+	0.185105i	0.807630	+	0.589689i	$0.200750\pi$
$198$	−3.00000	−	5.19615i	−0.213201	−	0.369274i
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$	6.00000	+	3.46410i	0.424264	+	0.244949i
$201$	6.00000	−	3.46410i	0.423207	−	0.244339i
$202$	−13.5000	+	23.3827i	−0.949857	+	1.64520i
$203$	6.00000			0.421117
$204$	12.0000	−	6.92820i	0.840168	−	0.485071i
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$			13.8564i			0.965422i
$207$		0			0
$208$	−5.00000	+	8.66025i	−0.346688	+	0.600481i
$209$	6.00000	+	3.46410i	0.415029	+	0.239617i
$210$	36.0000			2.48424
$211$		−	3.46410i		−	0.238479i	−0.992866	−	0.119239i	$-0.961954\pi$
$211$		−	3.46410i		−	0.238479i	0.992866	−	0.119239i	$-0.0380456\pi$
$212$	4.50000	+	2.59808i	0.309061	+	0.178437i
$213$	18.0000	+	10.3923i	1.23334	+	0.712069i
$214$		0			0
$215$	−9.00000	−	5.19615i	−0.613795	−	0.354375i
$216$		−	6.92820i		−	0.471405i
$217$	36.0000			2.44384
$218$	−10.5000	−	6.06218i	−0.711150	−	0.410582i
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$		−	10.3923i		−	0.700649i
$221$		−	13.8564i		−	0.932083i
$222$	3.00000	+	5.19615i	0.201347	+	0.348743i
$223$	−12.0000	+	6.92820i	−0.803579	+	0.463947i	−0.844721	−	0.535207i	$-0.820234\pi$
$223$	−12.0000	+	6.92820i	−0.803579	+	0.463947i	0.0411418	+	0.999153i	$0.486900\pi$
$224$	18.0000			1.20268
$225$	−2.00000	+	3.46410i	−0.133333	+	0.230940i
$226$	−9.00000	+	5.19615i	−0.598671	+	0.345643i
$227$	6.00000	+	3.46410i	0.398234	+	0.229920i	0.685722	−	0.727864i	$-0.259487\pi$
$227$	6.00000	+	3.46410i	0.398234	+	0.229920i	−0.287488	+	0.957784i	$0.592820\pi$
$228$	2.00000	+	3.46410i	0.132453	+	0.229416i
$229$	−9.50000	−	16.4545i	−0.627778	−	1.08734i	−0.987997	−	0.154475i	$-0.950631\pi$
$229$	−9.50000	−	16.4545i	−0.627778	−	1.08734i	0.360219	−	0.932868i	$-0.382702\pi$
$230$		0			0
$231$	12.0000	+	20.7846i	0.789542	+	1.36753i
$232$	−1.50000	+	2.59808i	−0.0984798	+	0.170572i
$233$			12.1244i			0.794293i	0.917755	+	0.397146i	$0.130000\pi$
$233$			12.1244i			0.794293i	−0.917755	+	0.397146i	$0.870000\pi$
$234$	−3.00000	−	1.73205i	−0.196116	−	0.113228i
$235$	36.0000			2.34838
$236$			3.46410i			0.225494i
$237$	18.0000	−	10.3923i	1.16923	−	0.675053i
$238$	−36.0000	+	20.7846i	−2.33353	+	1.34727i
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	0.752536	−	0.658551i	$-0.228830\pi$
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	−0.946590	+	0.322440i	$0.895497\pi$
$240$	−15.0000	+	25.9808i	−0.968246	+	1.67705i
$241$	−11.0000			−0.708572			−0.354286	−	0.935137i	$-0.615276\pi$
$241$	−11.0000			−0.708572			−0.354286	+	0.935137i	$0.615276\pi$
$242$	1.50000	−	0.866025i	0.0964237	−	0.0556702i
$243$	10.0000			0.641500
$244$	−7.00000	−	3.46410i	−0.448129	−	0.221766i
$245$	−15.0000			−0.958315
$246$	9.00000	−	5.19615i	0.573819	−	0.331295i
$247$	4.00000			0.254514
$248$	−9.00000	+	15.5885i	−0.571501	+	0.989868i
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$	4.50000	−	2.59808i	0.284605	−	0.164317i
$251$	12.0000	−	6.92820i	0.757433	−	0.437304i	−0.0709402	−	0.997481i	$-0.522600\pi$
$251$	12.0000	−	6.92820i	0.757433	−	0.437304i	0.828373	+	0.560176i	$0.189267\pi$
$252$			3.46410i			0.218218i
$253$		0			0
$254$	−3.00000	−	1.73205i	−0.188237	−	0.108679i
$255$		−	41.5692i		−	2.60317i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	0.999325	−	0.0367485i	$-0.0117000\pi$
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	−0.531487	+	0.847066i	$0.678367\pi$
$258$	6.00000	−	10.3923i	0.373544	−	0.646997i
$259$	−3.00000	−	5.19615i	−0.186411	−	0.322873i
$260$	−3.00000	−	5.19615i	−0.186052	−	0.322252i
$261$	−1.50000	−	0.866025i	−0.0928477	−	0.0536056i
$262$		0			0
$263$	3.00000	−	5.19615i	0.184988	−	0.320408i	−0.758585	−	0.651575i	$-0.774109\pi$
$263$	3.00000	−	5.19615i	0.184988	−	0.320408i	0.943572	+	0.331166i	$0.107442\pi$
$264$	−12.0000			−0.738549
$265$	13.5000	−	7.79423i	0.829298	−	0.478796i
$266$	−6.00000	−	10.3923i	−0.367884	−	0.637193i
$267$		−	31.1769i		−	1.90800i
$268$			3.46410i			0.211604i
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	−0.969976	−	0.243201i	$-0.921803\pi$
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	0.695606	+	0.718423i	$0.255136\pi$
$270$	18.0000	+	10.3923i	1.09545	+	0.632456i
$271$	−10.0000			−0.607457			−0.303728	−	0.952759i	$-0.598232\pi$
$271$	−10.0000			−0.607457			−0.303728	+	0.952759i	$0.598232\pi$
$272$		−	34.6410i		−	2.10042i
$273$	12.0000	+	6.92820i	0.726273	+	0.419314i
$274$	−4.50000	−	2.59808i	−0.271855	−	0.156956i
$275$	−12.0000	−	6.92820i	−0.723627	−	0.417786i
$276$		0			0
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	−12.0000			−0.719712
$279$	−9.00000	−	5.19615i	−0.538816	−	0.311086i
$280$	9.00000	−	15.5885i	0.537853	−	0.931589i
$281$			19.0526i			1.13658i	0.822828	+	0.568290i	$0.192395\pi$
$281$			19.0526i			1.13658i	−0.822828	+	0.568290i	$0.807605\pi$
$282$			41.5692i			2.47541i
$283$	−13.0000	−	22.5167i	−0.772770	−	1.33848i	−0.936039	−	0.351895i	$-0.885537\pi$
$283$	−13.0000	−	22.5167i	−0.772770	−	1.33848i	0.163270	−	0.986581i	$-0.447796\pi$
$284$	−9.00000	+	5.19615i	−0.534052	+	0.308335i
$285$	12.0000			0.710819
$286$	6.00000	−	10.3923i	0.354787	−	0.614510i
$287$	−9.00000	+	5.19615i	−0.531253	+	0.306719i
$288$	−4.50000	−	2.59808i	−0.265165	−	0.153093i
$289$	15.5000	+	26.8468i	0.911765	+	1.57922i
$290$	−4.50000	−	7.79423i	−0.264249	−	0.457693i
$291$	1.00000	−	1.73205i	0.0586210	−	0.101535i
$292$	−3.50000	−	6.06218i	−0.204822	−	0.354762i
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	−0.940252	−	0.340480i	$-0.889411\pi$
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	0.764990	+	0.644042i	$0.222744\pi$
$294$		−	17.3205i		−	1.01015i
$295$	9.00000	+	5.19615i	0.524000	+	0.302532i
$296$	3.00000			0.174371
$297$			13.8564i			0.804030i
$298$	22.5000	−	12.9904i	1.30339	−	0.752513i
$299$		0			0
$300$	−4.00000	−	6.92820i	−0.230940	−	0.400000i
$301$	−6.00000	+	10.3923i	−0.345834	+	0.599002i
$302$	6.00000			0.345261
$303$	−27.0000	+	15.5885i	−1.55111	+	0.895533i
$304$	10.0000			0.573539
$305$	−19.5000	+	12.9904i	−1.11657	+	0.743827i
$306$	12.0000			0.685994
$307$	−3.00000	+	1.73205i	−0.171219	+	0.0988534i	−0.583161	−	0.812357i	$-0.698184\pi$
$307$	−3.00000	+	1.73205i	−0.171219	+	0.0988534i	0.411941	+	0.911210i	$0.364851\pi$
$308$	−12.0000			−0.683763
$309$	−8.00000	+	13.8564i	−0.455104	+	0.788263i
$310$	−27.0000	−	46.7654i	−1.53350	−	2.65609i
$311$	12.0000	−	6.92820i	0.680458	−	0.392862i	−0.119570	−	0.992826i	$-0.538152\pi$
$311$	12.0000	−	6.92820i	0.680458	−	0.392862i	0.800027	+	0.599963i	$0.204818\pi$
$312$	−6.00000	+	3.46410i	−0.339683	+	0.196116i
$313$			20.7846i			1.17482i	0.809291	+	0.587408i	$0.199852\pi$
$313$			20.7846i			1.17482i	−0.809291	+	0.587408i	$0.800148\pi$
$314$	−24.0000			−1.35440
$315$	9.00000	+	5.19615i	0.507093	+	0.292770i
$316$			10.3923i			0.584613i
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$	9.00000	+	15.5885i	0.504695	+	0.874157i
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$		0			0
$322$		0			0
$323$	−12.0000	+	6.92820i	−0.667698	+	0.385496i
$324$	−5.50000	+	9.52628i	−0.305556	+	0.529238i
$325$	−8.00000			−0.443760
$326$	−6.00000	+	3.46410i	−0.332309	+	0.191859i
$327$	−7.00000	−	12.1244i	−0.387101	−	0.670478i
$328$		−	5.19615i		−	0.286910i
$329$		−	41.5692i		−	2.29179i
$330$	18.0000	−	31.1769i	0.990867	−	1.71623i
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	−6.00000			−0.329293
$333$			1.73205i			0.0949158i
$334$	27.0000	+	15.5885i	1.47737	+	0.852962i
$335$	9.00000	+	5.19615i	0.491723	+	0.283896i
$336$	30.0000	+	17.3205i	1.63663	+	0.944911i
$337$	−24.0000	−	13.8564i	−1.30736	−	0.754807i	−0.325708	−	0.945470i	$-0.605603\pi$
$337$	−24.0000	−	13.8564i	−1.30736	−	0.754807i	−0.981655	+	0.190664i	$0.938936\pi$
$338$			15.5885i			0.847900i
$339$	−12.0000			−0.651751
$340$	18.0000	+	10.3923i	0.976187	+	0.563602i
$341$	18.0000	−	31.1769i	0.974755	−	1.68832i
$342$			3.46410i			0.187317i
$343$		−	6.92820i		−	0.374088i
$344$	−3.00000	−	5.19615i	−0.161749	−	0.280158i
$345$		0			0
$346$	15.0000			0.806405
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$	3.00000	−	1.73205i	0.160817	−	0.0928477i
$349$	4.50000	+	2.59808i	0.240879	+	0.139072i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	4.50000	+	2.59808i	0.240879	+	0.139072i	−0.374701	+	0.927146i	$0.622255\pi$
$350$	12.0000	+	20.7846i	0.641427	+	1.11098i
$351$	4.00000	+	6.92820i	0.213504	+	0.369800i
$352$	9.00000	−	15.5885i	0.479702	−	0.830868i
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	0.934751	−	0.355303i	$-0.115622\pi$
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	−0.775077	+	0.631867i	$0.782289\pi$
$354$	−6.00000	+	10.3923i	−0.318896	+	0.552345i
$355$			31.1769i			1.65470i
$356$	13.5000	+	7.79423i	0.715499	+	0.413093i
$357$	−48.0000			−2.54043
$358$		−	10.3923i		−	0.549250i
$359$	−15.0000	+	8.66025i	−0.791670	+	0.457071i	−0.840550	−	0.541734i	$-0.817768\pi$
$359$	−15.0000	+	8.66025i	−0.791670	+	0.457071i	0.0488803	+	0.998805i	$0.484435\pi$
$360$	−4.50000	+	2.59808i	−0.237171	+	0.136931i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	19.5000	−	33.7750i	1.02490	−	1.77517i
$363$	2.00000			0.104973
$364$	−6.00000	+	3.46410i	−0.314485	+	0.181568i
$365$	−21.0000			−1.09919
$366$	−15.0000	−	22.5167i	−0.784063	−	1.17696i
$367$	−8.00000			−0.417597			−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000			−0.417597			−0.208798	+	0.977959i	$0.566955\pi$
$368$		0			0
$369$	3.00000			0.156174
$370$	−4.50000	+	7.79423i	−0.233944	+	0.405203i
$371$	−9.00000	−	15.5885i	−0.467257	−	0.809312i
$372$	18.0000	−	10.3923i	0.933257	−	0.538816i
$373$	25.5000	−	14.7224i	1.32034	−	0.762299i	0.336557	−	0.941663i	$-0.390737\pi$
$373$	25.5000	−	14.7224i	1.32034	−	0.762299i	0.983783	+	0.179364i	$0.0574041\pi$
$374$			41.5692i			2.14949i
$375$	6.00000			0.309839
$376$	18.0000	+	10.3923i	0.928279	+	0.535942i
$377$		−	3.46410i		−	0.178410i
$378$	12.0000	−	20.7846i	0.617213	−	1.06904i
$379$	8.00000	+	13.8564i	0.410932	+	0.711756i	0.994992	−	0.0999550i	$-0.0318699\pi$
$379$	8.00000	+	13.8564i	0.410932	+	0.711756i	−0.584060	+	0.811711i	$0.698537\pi$
$380$	−3.00000	+	5.19615i	−0.153897	+	0.266557i
$381$	−2.00000	−	3.46410i	−0.102463	−	0.177471i
$382$	12.0000	+	20.7846i	0.613973	+	1.06343i
$383$	18.0000	+	10.3923i	0.919757	+	0.531022i	0.883558	−	0.468323i	$-0.155141\pi$
$383$	18.0000	+	10.3923i	0.919757	+	0.531022i	0.0361995	+	0.999345i	$0.488475\pi$
$384$	−21.0000	+	12.1244i	−1.07165	+	0.618718i
$385$	−18.0000	+	31.1769i	−0.917365	+	1.58892i
$386$	21.0000			1.06887
$387$	3.00000	−	1.73205i	0.152499	−	0.0880451i
$388$	0.500000	+	0.866025i	0.0253837	+	0.0439658i
$389$		−	29.4449i		−	1.49291i	−0.665434	−	0.746457i	$-0.731753\pi$
$389$		−	29.4449i		−	1.49291i	0.665434	−	0.746457i	$-0.268247\pi$
$390$		−	20.7846i		−	1.05247i
$391$		0			0
$392$	−7.50000	−	4.33013i	−0.378807	−	0.218704i
$393$		0			0
$394$		−	5.19615i		−	0.261778i
$395$	27.0000	+	15.5885i	1.35852	+	0.784340i
$396$	3.00000	+	1.73205i	0.150756	+	0.0870388i
$397$	−28.5000	−	16.4545i	−1.43037	−	0.825827i	−0.433225	−	0.901286i	$-0.642624\pi$
$397$	−28.5000	−	16.4545i	−1.43037	−	0.825827i	−0.997149	+	0.0754589i	$0.975958\pi$
$398$	−6.00000	−	3.46410i	−0.300753	−	0.173640i
$399$		−	13.8564i		−	0.693688i
$400$	−20.0000			−1.00000
$401$	−1.50000	−	0.866025i	−0.0749064	−	0.0432472i	0.462079	−	0.886839i	$-0.347104\pi$
$401$	−1.50000	−	0.866025i	−0.0749064	−	0.0432472i	−0.536985	+	0.843592i	$0.680437\pi$
$402$	−6.00000	+	10.3923i	−0.299253	+	0.518321i
$403$		−	20.7846i		−	1.03536i
$404$		−	15.5885i		−	0.775555i
$405$	16.5000	+	28.5788i	0.819892	+	1.42009i
$406$	−9.00000	+	5.19615i	−0.446663	+	0.257881i
$407$	−6.00000			−0.297409
$408$	12.0000	−	20.7846i	0.594089	−	1.02899i
$409$	31.5000	−	18.1865i	1.55757	−	0.899266i	0.560087	−	0.828434i	$-0.310768\pi$
$409$	31.5000	−	18.1865i	1.55757	−	0.899266i	0.997488	−	0.0708321i	$-0.0225654\pi$
$410$	13.5000	+	7.79423i	0.666717	+	0.384930i
$411$	−3.00000	−	5.19615i	−0.147979	−	0.256307i
$412$	−4.00000	−	6.92820i	−0.197066	−	0.341328i
$413$	6.00000	−	10.3923i	0.295241	−	0.511372i
$414$		0			0
$415$	−9.00000	+	15.5885i	−0.441793	+	0.765207i
$416$		−	10.3923i		−	0.509525i
$417$	−12.0000	−	6.92820i	−0.587643	−	0.339276i
$418$	−12.0000			−0.586939
$419$			27.7128i			1.35386i	0.736048	+	0.676930i	$0.236690\pi$
$419$			27.7128i			1.35386i	−0.736048	+	0.676930i	$0.763310\pi$
$420$	−18.0000	+	10.3923i	−0.878310	+	0.507093i
$421$	−18.0000	+	10.3923i	−0.877266	+	0.506490i	−0.869756	−	0.493482i	$-0.835724\pi$
$421$	−18.0000	+	10.3923i	−0.877266	+	0.506490i	−0.00751023	+	0.999972i	$0.502391\pi$
$422$	3.00000	+	5.19615i	0.146038	+	0.252945i
$423$	−6.00000	+	10.3923i	−0.291730	+	0.505291i
$424$	9.00000			0.437079
$425$	24.0000	−	13.8564i	1.16417	−	0.672134i
$426$	−36.0000			−1.74421
$427$	15.0000	+	22.5167i	0.725901	+	1.08966i
$428$		0			0
$429$	12.0000	−	6.92820i	0.579365	−	0.334497i
$430$	18.0000			0.868037
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$	10.0000	+	17.3205i	0.481125	+	0.833333i
$433$	−34.5000	+	19.9186i	−1.65796	+	0.957226i	−0.684312	+	0.729190i	$0.739897\pi$
$433$	−34.5000	+	19.9186i	−1.65796	+	0.957226i	−0.973653	+	0.228036i	$0.926769\pi$
$434$	−54.0000	+	31.1769i	−2.59208	+	1.49654i
$435$		−	10.3923i		−	0.498273i
$436$	7.00000			0.335239
$437$		0			0
$438$		−	24.2487i		−	1.15865i
$439$	−10.0000	+	17.3205i	−0.477274	+	0.826663i	−0.999661	−	0.0260459i	$-0.991708\pi$
$439$	−10.0000	+	17.3205i	−0.477274	+	0.826663i	0.522387	+	0.852709i	$0.325042\pi$
$440$	−9.00000	−	15.5885i	−0.429058	−	0.743151i
$441$	2.50000	−	4.33013i	0.119048	−	0.206197i
$442$	12.0000	+	20.7846i	0.570782	+	0.988623i
$443$	3.00000	+	5.19615i	0.142534	+	0.246877i	0.928450	−	0.371457i	$-0.121142\pi$
$443$	3.00000	+	5.19615i	0.142534	+	0.246877i	−0.785916	+	0.618333i	$0.787808\pi$
$444$	−3.00000	−	1.73205i	−0.142374	−	0.0821995i
$445$	40.5000	−	23.3827i	1.91988	−	1.10845i
$446$	12.0000	−	20.7846i	0.568216	−	0.984180i
$447$	30.0000			1.41895
$448$	3.00000	−	1.73205i	0.141737	−	0.0818317i
$449$	−15.0000	−	25.9808i	−0.707894	−	1.22611i	−0.965637	−	0.259895i	$-0.916312\pi$
$449$	−15.0000	−	25.9808i	−0.707894	−	1.22611i	0.257743	−	0.966213i	$-0.417021\pi$
$450$		−	6.92820i		−	0.326599i
$451$			10.3923i			0.489355i
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$	6.00000	+	3.46410i	0.281905	+	0.162758i
$454$	−12.0000			−0.563188
$455$			20.7846i			0.974398i
$456$	6.00000	+	3.46410i	0.280976	+	0.162221i
$457$	−19.5000	−	11.2583i	−0.912172	−	0.526642i	−0.0310423	−	0.999518i	$-0.509883\pi$
$457$	−19.5000	−	11.2583i	−0.912172	−	0.526642i	−0.881129	+	0.472876i	$0.843216\pi$
$458$	28.5000	+	16.4545i	1.33172	+	0.768867i
$459$	−24.0000	−	13.8564i	−1.12022	−	0.646762i
$460$		0			0
$461$	27.0000			1.25752			0.628758	−	0.777601i	$-0.283564\pi$
$461$	27.0000			1.25752			0.628758	+	0.777601i	$0.283564\pi$
$462$	−36.0000	−	20.7846i	−1.67487	−	0.966988i
$463$	−20.0000	+	34.6410i	−0.929479	+	1.60990i	−0.145284	+	0.989390i	$0.546410\pi$
$463$	−20.0000	+	34.6410i	−0.929479	+	1.60990i	−0.784195	+	0.620515i	$0.786924\pi$
$464$		−	8.66025i		−	0.402042i
$465$		−	62.3538i		−	2.89159i
$466$	−10.5000	−	18.1865i	−0.486403	−	0.842475i
$467$	18.0000	−	10.3923i	0.832941	−	0.480899i	−0.0219178	−	0.999760i	$-0.506977\pi$
$467$	18.0000	−	10.3923i	0.832941	−	0.480899i	0.854858	+	0.518861i	$0.173644\pi$
$468$	2.00000			0.0924500
$469$	6.00000	−	10.3923i	0.277054	−	0.479872i
$470$	−54.0000	+	31.1769i	−2.49083	+	1.43808i
$471$	−24.0000	−	13.8564i	−1.10586	−	0.638470i
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	6.00000	+	10.3923i	0.275880	+	0.477839i
$474$	−18.0000	+	31.1769i	−0.826767	+	1.43200i
$475$	4.00000	+	6.92820i	0.183533	+	0.317888i
$476$	12.0000	−	20.7846i	0.550019	−	0.952661i
$477$			5.19615i			0.237915i
$478$	9.00000	+	5.19615i	0.411650	+	0.237666i
$479$	−6.00000			−0.274147			−0.137073	−	0.990561i	$-0.543770\pi$
$479$	−6.00000			−0.274147			−0.137073	+	0.990561i	$0.543770\pi$
$480$		−	31.1769i		−	1.42302i
$481$	−3.00000	+	1.73205i	−0.136788	+	0.0789747i
$482$	16.5000	−	9.52628i	0.751554	−	0.433910i
$483$		0			0
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$	3.00000			0.136223
$486$	−15.0000	+	8.66025i	−0.680414	+	0.392837i
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	−13.5000	+	0.866025i	−0.611116	+	0.0392031i
$489$	−8.00000			−0.361773
$490$	22.5000	−	12.9904i	1.01645	−	0.586846i
$491$	30.0000			1.35388			0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000			1.35388			0.676941	+	0.736038i	$0.263305\pi$
$492$	−3.00000	+	5.19615i	−0.135250	+	0.234261i
$493$	6.00000	+	10.3923i	0.270226	+	0.468046i
$494$	−6.00000	+	3.46410i	−0.269953	+	0.155857i
$495$	9.00000	−	5.19615i	0.404520	−	0.233550i
$496$		−	51.9615i		−	2.33314i
$497$	36.0000			1.61482
$498$	−18.0000	−	10.3923i	−0.806599	−	0.465690i
$499$		−	34.6410i		−	1.55074i	−0.631504	−	0.775372i	$-0.717562\pi$
$499$		−	34.6410i		−	1.55074i	0.631504	−	0.775372i	$-0.282438\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$	18.0000	+	31.1769i	0.804181	+	1.39288i
$502$	−12.0000	+	20.7846i	−0.535586	+	0.927663i
$503$	−18.0000	−	31.1769i	−0.802580	−	1.39011i	−0.917912	−	0.396783i	$-0.870127\pi$
$503$	−18.0000	−	31.1769i	−0.802580	−	1.39011i	0.115332	−	0.993327i	$-0.463207\pi$
$504$	3.00000	+	5.19615i	0.133631	+	0.231455i
$505$	−40.5000	−	23.3827i	−1.80223	−	1.04052i
$506$		0			0
$507$	−9.00000	+	15.5885i	−0.399704	+	0.692308i
$508$	2.00000			0.0887357
$509$	−13.5000	+	7.79423i	−0.598377	+	0.345473i	−0.768403	−	0.639966i	$-0.778948\pi$
$509$	−13.5000	+	7.79423i	−0.598377	+	0.345473i	0.170026	+	0.985440i	$0.445615\pi$
$510$	36.0000	+	62.3538i	1.59411	+	2.76107i
$511$			24.2487i			1.07270i
$512$		−	8.66025i		−	0.382733i
$513$	4.00000	−	6.92820i	0.176604	−	0.305888i
$514$	−22.5000	−	12.9904i	−0.992432	−	0.572981i
$515$	−24.0000			−1.05757
$516$			6.92820i			0.304997i
$517$	−36.0000	−	20.7846i	−1.58328	−	0.914106i
$518$	9.00000	+	5.19615i	0.395437	+	0.228306i
$519$	15.0000	+	8.66025i	0.658427	+	0.380143i
$520$	−9.00000	−	5.19615i	−0.394676	−	0.227866i
$521$		−	25.9808i		−	1.13824i	−0.822255	−	0.569119i	$-0.807284\pi$
$521$		−	25.9808i		−	1.13824i	0.822255	−	0.569119i	$-0.192716\pi$
$522$	3.00000			0.131306
$523$	−18.0000	−	10.3923i	−0.787085	−	0.454424i	0.0518503	−	0.998655i	$-0.483488\pi$
$523$	−18.0000	−	10.3923i	−0.787085	−	0.454424i	−0.838935	+	0.544231i	$0.816821\pi$
$524$		0			0
$525$			27.7128i			1.20949i
$526$			10.3923i			0.453126i
$527$	36.0000	+	62.3538i	1.56818	+	2.71618i
$528$	30.0000	−	17.3205i	1.30558	−	0.753778i
$529$	23.0000			1.00000
$530$	−13.5000	+	23.3827i	−0.586403	+	1.01568i
$531$	−3.00000	+	1.73205i	−0.130189	+	0.0751646i
$532$	6.00000	+	3.46410i	0.260133	+	0.150188i
$533$	3.00000	+	5.19615i	0.129944	+	0.225070i
$534$	27.0000	+	46.7654i	1.16840	+	2.02374i
$535$		0			0
$536$	3.00000	+	5.19615i	0.129580	+	0.224440i
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$		−	15.5885i		−	0.672066i
$539$	15.0000	+	8.66025i	0.646096	+	0.373024i
$540$	−12.0000			−0.516398
$541$			13.8564i			0.595733i	0.954607	+	0.297867i	$0.0962751\pi$
$541$			13.8564i			0.595733i	−0.954607	+	0.297867i	$0.903725\pi$
$542$	15.0000	−	8.66025i	0.644305	−	0.371990i
$543$	39.0000	−	22.5167i	1.67365	−	0.966282i
$544$	18.0000	+	31.1769i	0.771744	+	1.33670i
$545$	10.5000	−	18.1865i	0.449771	−	0.779026i
$546$	−24.0000			−1.02711
$547$	33.0000	−	19.0526i	1.41098	−	0.814629i	0.415498	−	0.909594i	$-0.363607\pi$
$547$	33.0000	−	19.0526i	1.41098	−	0.814629i	0.995481	+	0.0949657i	$0.0302741\pi$
$548$	3.00000			0.128154
$549$	−0.500000	−	7.79423i	−0.0213395	−	0.332650i
$550$	24.0000			1.02336
$551$	−3.00000	+	1.73205i	−0.127804	+	0.0737878i
$552$		0			0
$553$	18.0000	−	31.1769i	0.765438	−	1.32578i
$554$		0			0
$555$	−9.00000	+	5.19615i	−0.382029	+	0.220564i
$556$	6.00000	−	3.46410i	0.254457	−	0.146911i
$557$		−	1.73205i		−	0.0733893i	−0.999327	−	0.0366947i	$-0.988317\pi$
$557$		−	1.73205i		−	0.0733893i	0.999327	−	0.0366947i	$-0.0116829\pi$
$558$	18.0000			0.762001
$559$	6.00000	+	3.46410i	0.253773	+	0.146516i
$560$			51.9615i			2.19578i
$561$	−24.0000	+	41.5692i	−1.01328	+	1.75505i
$562$	−16.5000	−	28.5788i	−0.696010	−	1.20553i
$563$	−21.0000	+	36.3731i	−0.885044	+	1.53294i	−0.0393818	+	0.999224i	$0.512539\pi$
$563$	−21.0000	+	36.3731i	−0.885044	+	1.53294i	−0.845663	+	0.533718i	$0.820794\pi$
$564$	−12.0000	−	20.7846i	−0.505291	−	0.875190i
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$	39.0000	+	22.5167i	1.63929	+	0.946446i
$567$	33.0000	−	19.0526i	1.38587	−	0.800132i
$568$	−9.00000	+	15.5885i	−0.377632	+	0.654077i
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$	−18.0000	+	10.3923i	−0.753937	+	0.435286i
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	0.995788	−	0.0916910i	$-0.0292272\pi$
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	−0.577301	+	0.816532i	$0.695894\pi$
$572$			6.92820i			0.289683i
$573$			27.7128i			1.15772i
$574$	9.00000	−	15.5885i	0.375653	−	0.650650i
$575$		0			0
$576$	−1.00000			−0.0416667
$577$		−	22.5167i		−	0.937381i	−0.883362	−	0.468690i	$-0.844726\pi$
$577$		−	22.5167i		−	0.937381i	0.883362	−	0.468690i	$-0.155274\pi$
$578$	−46.5000	−	26.8468i	−1.93415	−	1.11668i
$579$	21.0000	+	12.1244i	0.872730	+	0.503871i
$580$	4.50000	+	2.59808i	0.186852	+	0.107879i
$581$	18.0000	+	10.3923i	0.746766	+	0.431145i
$582$			3.46410i			0.143592i
$583$	−18.0000			−0.745484
$584$	−10.5000	−	6.06218i	−0.434493	−	0.250855i
$585$	3.00000	−	5.19615i	0.124035	−	0.214834i
$586$		−	10.3923i		−	0.429302i
$587$			6.92820i			0.285958i	0.989726	+	0.142979i	$0.0456681\pi$
$587$			6.92820i			0.285958i	−0.989726	+	0.142979i	$0.954332\pi$
$588$	5.00000	+	8.66025i	0.206197	+	0.357143i
$589$	−18.0000	+	10.3923i	−0.741677	+	0.428207i
$590$	−18.0000			−0.741048
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$	−7.50000	+	4.33013i	−0.308248	+	0.177967i
$593$	−1.50000	−	0.866025i	−0.0615976	−	0.0355634i	0.468885	−	0.883259i	$-0.344656\pi$
$593$	−1.50000	−	0.866025i	−0.0615976	−	0.0355634i	−0.530483	+	0.847696i	$0.677989\pi$
$594$	−12.0000	−	20.7846i	−0.492366	−	0.852803i
$595$	−36.0000	−	62.3538i	−1.47586	−	2.55626i
$596$	−7.50000	+	12.9904i	−0.307212	+	0.532107i
$597$	−4.00000	−	6.92820i	−0.163709	−	0.283552i
$598$		0			0
$599$		−	17.3205i		−	0.707697i	−0.935303	−	0.353848i	$-0.884873\pi$
$599$		−	17.3205i		−	0.707697i	0.935303	−	0.353848i	$-0.115127\pi$
$600$	−12.0000	−	6.92820i	−0.489898	−	0.282843i
$601$	−5.00000			−0.203954			−0.101977	−	0.994787i	$-0.532517\pi$
$601$	−5.00000			−0.203954			−0.101977	+	0.994787i	$0.532517\pi$
$602$		−	20.7846i		−	0.847117i
$603$	−3.00000	+	1.73205i	−0.122169	+	0.0705346i
$604$	−3.00000	+	1.73205i	−0.122068	+	0.0704761i
$605$	1.50000	+	2.59808i	0.0609837	+	0.105627i
$606$	27.0000	−	46.7654i	1.09680	−	1.89971i
$607$	−22.0000			−0.892952			−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000			−0.892952			−0.446476	+	0.894795i	$0.647321\pi$
$608$	−9.00000	+	5.19615i	−0.364998	+	0.210732i
$609$	−12.0000			−0.486265
$610$	18.0000	−	36.3731i	0.728799	−	1.47270i
$611$	−24.0000			−0.970936
$612$	−6.00000	+	3.46410i	−0.242536	+	0.140028i
$613$	−5.00000			−0.201948			−0.100974	−	0.994889i	$-0.532196\pi$
$613$	−5.00000			−0.201948			−0.100974	+	0.994889i	$0.532196\pi$
$614$	3.00000	−	5.19615i	0.121070	−	0.209700i
$615$	9.00000	+	15.5885i	0.362915	+	0.628587i
$616$	−18.0000	+	10.3923i	−0.725241	+	0.418718i
$617$	−18.0000	+	10.3923i	−0.724653	+	0.418378i	−0.816463	−	0.577398i	$-0.804068\pi$
$617$	−18.0000	+	10.3923i	−0.724653	+	0.418378i	0.0918100	+	0.995777i	$0.470735\pi$
$618$		−	27.7128i		−	1.11477i
$619$	−32.0000			−1.28619			−0.643094	−	0.765787i	$-0.722350\pi$
$619$	−32.0000			−1.28619			−0.643094	+	0.765787i	$0.722350\pi$
$620$	27.0000	+	15.5885i	1.08435	+	0.626048i
$621$		0			0
$622$	−12.0000	+	20.7846i	−0.481156	+	0.833387i
$623$	−27.0000	−	46.7654i	−1.08173	−	1.87362i
$624$	10.0000	−	17.3205i	0.400320	−	0.693375i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−18.0000	−	31.1769i	−0.719425	−	1.24608i
$627$	−12.0000	−	6.92820i	−0.479234	−	0.276686i
$628$	12.0000	−	6.92820i	0.478852	−	0.276465i
$629$	6.00000	−	10.3923i	0.239236	−	0.414368i
$630$	−18.0000			−0.717137
$631$	15.0000	−	8.66025i	0.597141	−	0.344759i	−0.170775	−	0.985310i	$-0.554627\pi$
$631$	15.0000	−	8.66025i	0.597141	−	0.344759i	0.767916	+	0.640551i	$0.221294\pi$
$632$	9.00000	+	15.5885i	0.358001	+	0.620076i
$633$			6.92820i			0.275371i
$634$			10.3923i			0.412731i
$635$	3.00000	−	5.19615i	0.119051	−	0.206203i
$636$	−9.00000	−	5.19615i	−0.356873	−	0.206041i
$637$	10.0000			0.396214
$638$			10.3923i			0.411435i
$639$	−9.00000	−	5.19615i	−0.356034	−	0.205557i
$640$	−31.5000	−	18.1865i	−1.24515	−	0.718886i
$641$	28.5000	+	16.4545i	1.12568	+	0.649913i	0.942845	−	0.333230i	$-0.108139\pi$
$641$	28.5000	+	16.4545i	1.12568	+	0.649913i	0.182837	+	0.983143i	$0.441472\pi$
$642$		0			0
$643$			24.2487i			0.956276i	0.878285	+	0.478138i	$0.158688\pi$
$643$			24.2487i			0.956276i	−0.878285	+	0.478138i	$0.841312\pi$
$644$		0			0
$645$	18.0000	+	10.3923i	0.708749	+	0.409197i
$646$	12.0000	−	20.7846i	0.472134	−	0.817760i
$647$			13.8564i			0.544752i	0.962191	+	0.272376i	$0.0878094\pi$
$647$			13.8564i			0.544752i	−0.962191	+	0.272376i	$0.912191\pi$
$648$			19.0526i			0.748455i
$649$	−6.00000	−	10.3923i	−0.235521	−	0.407934i
$650$	12.0000	−	6.92820i	0.470679	−	0.271746i
$651$	−72.0000			−2.82190
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	31.5000	−	18.1865i	1.23269	−	0.711694i	0.265100	−	0.964221i	$-0.414595\pi$
$653$	31.5000	−	18.1865i	1.23269	−	0.711694i	0.967590	+	0.252527i	$0.0812616\pi$
$654$	21.0000	+	12.1244i	0.821165	+	0.474100i
$655$		0			0
$656$	7.50000	+	12.9904i	0.292826	+	0.507189i
$657$	3.50000	−	6.06218i	0.136548	−	0.236508i
$658$	36.0000	+	62.3538i	1.40343	+	2.43081i
$659$	9.00000	−	15.5885i	0.350590	−	0.607240i	−0.635763	−	0.771885i	$-0.719314\pi$
$659$	9.00000	−	15.5885i	0.350590	−	0.607240i	0.986353	+	0.164644i	$0.0526477\pi$
$660$			20.7846i			0.809040i
$661$	−1.50000	−	0.866025i	−0.0583432	−	0.0336845i	0.470545	−	0.882376i	$-0.344057\pi$
$661$	−1.50000	−	0.866025i	−0.0583432	−	0.0336845i	−0.528888	+	0.848692i	$0.677391\pi$
$662$		0			0
$663$			27.7128i			1.07628i
$664$	−9.00000	+	5.19615i	−0.349268	+	0.201650i
$665$	18.0000	−	10.3923i	0.698010	−	0.402996i
$666$	−1.50000	−	2.59808i	−0.0581238	−	0.100673i
$667$		0			0
$668$	−18.0000			−0.696441
$669$	24.0000	−	13.8564i	0.927894	−	0.535720i
$670$	−18.0000			−0.695401
$671$	27.0000	−	1.73205i	1.04232	−	0.0668651i
$672$	−36.0000			−1.38873
$673$	−25.5000	+	14.7224i	−0.982953	+	0.567508i	−0.903160	−	0.429303i	$-0.858759\pi$
$673$	−25.5000	+	14.7224i	−0.982953	+	0.567508i	−0.0797925	+	0.996811i	$0.525426\pi$
$674$	48.0000			1.84889
$675$	−8.00000	+	13.8564i	−0.307920	+	0.533333i
$676$	−4.50000	−	7.79423i	−0.173077	−	0.299778i
$677$	−13.5000	+	7.79423i	−0.518847	+	0.299557i	−0.736463	−	0.676478i	$-0.763505\pi$
$677$	−13.5000	+	7.79423i	−0.518847	+	0.299557i	0.217616	+	0.976035i	$0.430172\pi$
$678$	18.0000	−	10.3923i	0.691286	−	0.399114i
$679$		−	3.46410i		−	0.132940i
$680$	36.0000			1.38054
$681$	−12.0000	−	6.92820i	−0.459841	−	0.265489i
$682$			62.3538i			2.38765i
$683$	18.0000	−	31.1769i	0.688751	−	1.19295i	−0.283491	−	0.958975i	$-0.591493\pi$
$683$	18.0000	−	31.1769i	0.688751	−	1.19295i	0.972242	−	0.233977i	$-0.0751739\pi$
$684$	−1.00000	−	1.73205i	−0.0382360	−	0.0662266i
$685$	4.50000	−	7.79423i	0.171936	−	0.297802i
$686$	6.00000	+	10.3923i	0.229081	+	0.396780i
$687$	19.0000	+	32.9090i	0.724895	+	1.25556i
$688$	15.0000	+	8.66025i	0.571870	+	0.330169i
$689$	−9.00000	+	5.19615i	−0.342873	+	0.197958i
$690$		0			0
$691$	−8.00000			−0.304334			−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000			−0.304334			−0.152167	+	0.988355i	$0.548625\pi$
$692$	−7.50000	+	4.33013i	−0.285107	+	0.164607i
$693$	−6.00000	−	10.3923i	−0.227921	−	0.394771i
$694$		0			0
$695$		−	20.7846i		−	0.788405i
$696$	3.00000	−	5.19615i	0.113715	−	0.196960i
$697$	−18.0000	−	10.3923i	−0.681799	−	0.393637i
$698$	−9.00000			−0.340655
$699$		−	24.2487i		−	0.917170i
$700$	−12.0000	−	6.92820i	−0.453557	−	0.261861i
$701$	−10.5000	−	6.06218i	−0.396580	−	0.228965i	0.288428	−	0.957502i	$-0.406868\pi$
$701$	−10.5000	−	6.06218i	−0.396580	−	0.228965i	−0.685007	+	0.728536i	$0.740201\pi$
$702$	−12.0000	−	6.92820i	−0.452911	−	0.261488i
$703$	3.00000	+	1.73205i	0.113147	+	0.0653255i
$704$		−	3.46410i		−	0.130558i
$705$	−72.0000			−2.71168
$706$	−9.00000	−	5.19615i	−0.338719	−	0.195560i
$707$	−27.0000	+	46.7654i	−1.01544	+	1.75879i
$708$		−	6.92820i		−	0.260378i
$709$			39.8372i			1.49612i	0.663633	+	0.748058i	$0.269014\pi$
$709$			39.8372i			1.49612i	−0.663633	+	0.748058i	$0.730986\pi$
$710$	−27.0000	−	46.7654i	−1.01329	−	1.75507i
$711$	−9.00000	+	5.19615i	−0.337526	+	0.194871i
$712$	27.0000			1.01187
$713$		0			0
$714$	72.0000	−	41.5692i	2.69453	−	1.55569i
$715$	18.0000	+	10.3923i	0.673162	+	0.388650i
$716$	3.00000	+	5.19615i	0.112115	+	0.194189i
$717$	6.00000	+	10.3923i	0.224074	+	0.388108i
$718$	15.0000	−	25.9808i	0.559795	−	0.969593i
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	0.997546	+	0.0700124i	$0.0223039\pi$
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	−0.438141	+	0.898906i	$0.644363\pi$
$720$	7.50000	−	12.9904i	0.279508	−	0.484123i
$721$			27.7128i			1.03208i
$722$	−22.5000	−	12.9904i	−0.837363	−	0.483452i
$723$	22.0000			0.818189
$724$			22.5167i			0.836825i
$725$	6.00000	−	3.46410i	0.222834	−	0.128654i
$726$	−3.00000	+	1.73205i	−0.111340	+	0.0642824i
$727$	−5.00000	−	8.66025i	−0.185440	−	0.321191i	0.758285	−	0.651923i	$-0.226038\pi$
$727$	−5.00000	−	8.66025i	−0.185440	−	0.321191i	−0.943725	+	0.330732i	$0.892704\pi$
$728$	−6.00000	+	10.3923i	−0.222375	+	0.385164i
$729$	13.0000			0.481481
$730$	31.5000	−	18.1865i	1.16587	−	0.673114i
$731$	−24.0000			−0.887672
$732$	14.0000	+	6.92820i	0.517455	+	0.256074i
$733$	41.0000			1.51437			0.757185	−	0.653201i	$-0.226574\pi$
$733$	41.0000			1.51437			0.757185	+	0.653201i	$0.226574\pi$
$734$	12.0000	−	6.92820i	0.442928	−	0.255725i
$735$	30.0000			1.10657
$736$		0			0
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$	−4.50000	+	2.59808i	−0.165647	+	0.0956365i
$739$	45.0000	−	25.9808i	1.65535	−	0.955718i	0.680534	−	0.732717i	$-0.261748\pi$
$739$	45.0000	−	25.9808i	1.65535	−	0.955718i	0.974818	−	0.223001i	$-0.0715853\pi$
$740$		−	5.19615i		−	0.191014i
$741$	−8.00000			−0.293887
$742$	27.0000	+	15.5885i	0.991201	+	0.572270i
$743$			27.7128i			1.01668i	0.861155	+	0.508342i	$0.169742\pi$
$743$			27.7128i			1.01668i	−0.861155	+	0.508342i	$0.830258\pi$
$744$	18.0000	−	31.1769i	0.659912	−	1.14300i
$745$	22.5000	+	38.9711i	0.824336	+	1.42779i
$746$	−25.5000	+	44.1673i	−0.933621	+	1.61708i
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$	−12.0000	−	20.7846i	−0.438763	−	0.759961i
$749$		0			0
$750$	−9.00000	+	5.19615i	−0.328634	+	0.189737i
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	−60.0000			−2.18797
$753$	−24.0000	+	13.8564i	−0.874609	+	0.504956i
$754$	3.00000	+	5.19615i	0.109254	+	0.189233i
$755$			10.3923i			0.378215i
$756$			13.8564i			0.503953i
$757$	−11.5000	+	19.9186i	−0.417975	+	0.723953i	−0.995736	−	0.0922527i	$-0.970593\pi$
$757$	−11.5000	+	19.9186i	−0.417975	+	0.723953i	0.577761	+	0.816206i	$0.303927\pi$
$758$	−24.0000	−	13.8564i	−0.871719	−	0.503287i
$759$		0			0
$760$			10.3923i			0.376969i
$761$	−30.0000	−	17.3205i	−1.08750	−	0.627868i	−0.154590	−	0.987979i	$-0.549406\pi$
$761$	−30.0000	−	17.3205i	−1.08750	−	0.627868i	−0.932910	+	0.360111i	$0.882739\pi$
$762$	6.00000	+	3.46410i	0.217357	+	0.125491i
$763$	−21.0000	−	12.1244i	−0.760251	−	0.438931i
$764$	−12.0000	−	6.92820i	−0.434145	−	0.250654i
$765$			20.7846i			0.751469i
$766$	−36.0000			−1.30073
$767$	−6.00000	−	3.46410i	−0.216647	−	0.125081i
$768$	19.0000	−	32.9090i	0.685603	−	1.18750i
$769$			43.3013i			1.56148i	0.624854	+	0.780742i	$0.285159\pi$
$769$			43.3013i			1.56148i	−0.624854	+	0.780742i	$0.714841\pi$
$770$		−	62.3538i		−	2.24708i
$771$	−15.0000	−	25.9808i	−0.540212	−	0.935674i
$772$	−10.5000	+	6.06218i	−0.377903	+	0.218183i
$773$	−39.0000			−1.40273			−0.701366	−	0.712801i	$-0.747426\pi$
$773$	−39.0000			−1.40273			−0.701366	+	0.712801i	$0.747426\pi$
$774$	−3.00000	+	5.19615i	−0.107833	+	0.186772i
$775$	36.0000	−	20.7846i	1.29316	−	0.746605i
$776$	1.50000	+	0.866025i	0.0538469	+	0.0310885i
$777$	6.00000	+	10.3923i	0.215249	+	0.372822i
$778$	25.5000	+	44.1673i	0.914219	+	1.58347i
$779$	3.00000	−	5.19615i	0.107486	−	0.186171i
$780$	6.00000	+	10.3923i	0.214834	+	0.372104i
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$		0			0
$783$	−6.00000	−	3.46410i	−0.214423	−	0.123797i
$784$	25.0000			0.892857
$785$		−	41.5692i		−	1.48367i
$786$		0			0
$787$	−9.00000	+	5.19615i	−0.320815	+	0.185223i	−0.651756	−	0.758429i	$-0.725967\pi$
$787$	−9.00000	+	5.19615i	−0.320815	+	0.185223i	0.330941	+	0.943652i	$0.392634\pi$
$788$	1.50000	+	2.59808i	0.0534353	+	0.0925526i
$789$	−6.00000	+	10.3923i	−0.213606	+	0.369976i
$790$	−54.0000			−1.92123
$791$	−18.0000	+	10.3923i	−0.640006	+	0.369508i
$792$	6.00000			0.213201
$793$	13.0000	−	8.66025i	0.461644	−	0.307535i
$794$	57.0000			2.02285
$795$	−27.0000	+	15.5885i	−0.957591	+	0.552866i
$796$	4.00000			0.141776
$797$	10.5000	−	18.1865i	0.371929	−	0.644200i	−0.617933	−	0.786231i	$-0.712030\pi$
$797$	10.5000	−	18.1865i	0.371929	−	0.644200i	0.989862	+	0.142031i	$0.0453631\pi$
$798$	12.0000	+	20.7846i	0.424795	+	0.735767i
$799$	72.0000	−	41.5692i	2.54718	−	1.47061i
$800$	18.0000	−	10.3923i	0.636396	−	0.367423i
$801$			15.5885i			0.550791i
$802$	3.00000			0.105934
$803$	21.0000	+	12.1244i	0.741074	+	0.427859i
$804$		−	6.92820i		−	0.244339i
$805$		0			0
$806$	18.0000	+	31.1769i	0.634023	+	1.09816i
$807$	9.00000	−	15.5885i	0.316815	−	0.548740i
$808$	−13.5000	−	23.3827i	−0.474928	−	0.822600i
$809$	1.50000	+	2.59808i	0.0527372	+	0.0913435i	0.891189	−	0.453632i	$-0.149872\pi$
$809$	1.50000	+	2.59808i	0.0527372	+	0.0913435i	−0.838452	+	0.544976i	$0.816539\pi$
$810$	−49.5000	−	28.5788i	−1.73925	−	1.00416i
$811$	−42.0000	+	24.2487i	−1.47482	+	0.851487i	−0.999597	−	0.0283784i	$-0.990966\pi$
$811$	−42.0000	+	24.2487i	−1.47482	+	0.851487i	−0.475222	+	0.879866i	$0.657632\pi$
$812$	3.00000	−	5.19615i	0.105279	−	0.182349i
$813$	20.0000			0.701431
$814$	9.00000	−	5.19615i	0.315450	−	0.182125i
$815$	−6.00000	−	10.3923i	−0.210171	−	0.364027i
$816$			69.2820i			2.42536i
$817$		−	6.92820i		−	0.242387i
$818$	−31.5000	+	54.5596i	−1.10137	+	1.90763i
$819$	−6.00000	−	3.46410i	−0.209657	−	0.121046i
$820$	−9.00000			−0.314294
$821$		−	5.19615i		−	0.181347i	−0.995881	−	0.0906735i	$-0.971098\pi$
$821$		−	5.19615i		−	0.181347i	0.995881	−	0.0906735i	$-0.0289020\pi$
$822$	9.00000	+	5.19615i	0.313911	+	0.181237i
$823$	27.0000	+	15.5885i	0.941161	+	0.543379i	0.890324	−	0.455328i	$-0.150478\pi$
$823$	27.0000	+	15.5885i	0.941161	+	0.543379i	0.0508368	+	0.998707i	$0.483811\pi$
$824$	−12.0000	−	6.92820i	−0.418040	−	0.241355i
$825$	24.0000	+	13.8564i	0.835573	+	0.482418i
$826$			20.7846i			0.723189i
$827$	42.0000			1.46048			0.730242	−	0.683189i	$-0.239408\pi$
$827$	42.0000			1.46048			0.730242	+	0.683189i	$0.239408\pi$
$828$		0			0
$829$	−7.00000	+	12.1244i	−0.243120	+	0.421096i	−0.961601	−	0.274450i	$-0.911504\pi$
$829$	−7.00000	+	12.1244i	−0.243120	+	0.421096i	0.718481	+	0.695546i	$0.244838\pi$
$830$		−	31.1769i		−	1.08217i
$831$		0			0
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$	−30.0000	+	17.3205i	−1.03944	+	0.600120i
$834$	24.0000			0.831052
$835$	−27.0000	+	46.7654i	−0.934374	+	1.61838i
$836$	6.00000	−	3.46410i	0.207514	−	0.119808i
$837$	−36.0000	−	20.7846i	−1.24434	−	0.718421i
$838$	−24.0000	−	41.5692i	−0.829066	−	1.43598i
$839$	15.0000	+	25.9808i	0.517858	+	0.896956i	0.999785	+	0.0207443i	$0.00660359\pi$
$839$	15.0000	+	25.9808i	0.517858	+	0.896956i	−0.481927	+	0.876211i	$0.660063\pi$
$840$	−18.0000	+	31.1769i	−0.621059	+	1.07571i
$841$	−13.0000	−	22.5167i	−0.448276	−	0.776437i
$842$	18.0000	−	31.1769i	0.620321	−	1.07443i
$843$		−	38.1051i		−	1.31241i
$844$	−3.00000	−	1.73205i	−0.103264	−	0.0596196i
$845$	−27.0000			−0.928828
$846$		−	20.7846i		−	0.714590i
$847$	3.00000	−	1.73205i	0.103081	−	0.0595140i
$848$	−22.5000	+	12.9904i	−0.772653	+	0.446092i
$849$	26.0000	+	45.0333i	0.892318	+	1.54554i
$850$	−24.0000	+	41.5692i	−0.823193	+	1.42581i
$851$		0			0
$852$	18.0000	−	10.3923i	0.616670	−	0.356034i
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$	−42.0000	−	20.7846i	−1.43721	−	0.711235i
$855$	−6.00000			−0.205196
$856$		0			0
$857$	−21.0000			−0.717346			−0.358673	−	0.933463i	$-0.616771\pi$
$857$	−21.0000			−0.717346			−0.358673	+	0.933463i	$0.616771\pi$
$858$	−12.0000	+	20.7846i	−0.409673	+	0.709575i
$859$	−22.0000	−	38.1051i	−0.750630	−	1.30013i	−0.947518	−	0.319704i	$-0.896417\pi$
$859$	−22.0000	−	38.1051i	−0.750630	−	1.30013i	0.196887	−	0.980426i	$-0.436917\pi$
$860$	−9.00000	+	5.19615i	−0.306897	+	0.177187i
$861$	18.0000	−	10.3923i	0.613438	−	0.354169i
$862$		−	20.7846i		−	0.707927i
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$	−18.0000	−	10.3923i	−0.612372	−	0.353553i
$865$			25.9808i			0.883372i
$866$	34.5000	−	59.7558i	1.17236	−	2.03058i
$867$	−31.0000	−	53.6936i	−1.05282	−	1.82353i
$868$	18.0000	−	31.1769i	0.610960	−	1.05821i
$869$	−18.0000	−	31.1769i	−0.610608	−	1.05760i
$870$	9.00000	+	15.5885i	0.305129	+	0.528498i
$871$	−6.00000	−	3.46410i	−0.203302	−	0.117377i
$872$	10.5000	−	6.06218i	0.355575	−	0.205291i
$873$	−0.500000	+	0.866025i	−0.0169224	+	0.0293105i
$874$		0			0
$875$	9.00000	−	5.19615i	0.304256	−	0.175662i
$876$	7.00000	+	12.1244i	0.236508	+	0.409644i
$877$			20.7846i			0.701846i	0.936404	+	0.350923i	$0.114132\pi$
$877$			20.7846i			0.701846i	−0.936404	+	0.350923i	$0.885868\pi$
$878$		−	34.6410i		−	1.16908i
$879$	6.00000	−	10.3923i	0.202375	−	0.350524i
$880$	45.0000	+	25.9808i	1.51695	+	0.875811i
$881$	−39.0000			−1.31394			−0.656972	−	0.753915i	$-0.728163\pi$
$881$	−39.0000			−1.31394			−0.656972	+	0.753915i	$0.728163\pi$
$882$			8.66025i			0.291606i
$883$	−9.00000	−	5.19615i	−0.302874	−	0.174864i	0.340859	−	0.940114i	$-0.389282\pi$
$883$	−9.00000	−	5.19615i	−0.302874	−	0.174864i	−0.643733	+	0.765250i	$0.722615\pi$
$884$	−12.0000	−	6.92820i	−0.403604	−	0.233021i
$885$	−18.0000	−	10.3923i	−0.605063	−	0.349334i
$886$	−9.00000	−	5.19615i	−0.302361	−	0.174568i
$887$			17.3205i			0.581566i	0.956789	+	0.290783i	$0.0939157\pi$
$887$			17.3205i			0.581566i	−0.956789	+	0.290783i	$0.906084\pi$
$888$	−6.00000			−0.201347
$889$	−6.00000	−	3.46410i	−0.201234	−	0.116182i
$890$	−40.5000	+	70.1481i	−1.35756	+	2.35137i
$891$		−	38.1051i		−	1.27657i
$892$			13.8564i			0.463947i
$893$	12.0000	+	20.7846i	0.401565	+	0.695530i
$894$	−45.0000	+	25.9808i	−1.50503	+	0.868927i
$895$	18.0000			0.601674
$896$	−21.0000	+	36.3731i	−0.701561	+	1.21514i
$897$		0			0
$898$	45.0000	+	25.9808i	1.50167	+	0.866989i
$899$	9.00000	+	15.5885i	0.300167	+	0.519904i
$900$	2.00000	+	3.46410i	0.0666667	+	0.115470i
$901$	18.0000	−	31.1769i	0.599667	−	1.03865i
$902$	−9.00000	−	15.5885i	−0.299667	−	0.519039i
$903$	12.0000	−	20.7846i	0.399335	−	0.691669i
$904$		−	10.3923i		−	0.345643i
$905$	58.5000	+	33.7750i	1.94461	+	1.12272i
$906$	−12.0000			−0.398673
$907$			20.7846i			0.690142i	0.938577	+	0.345071i	$0.112145\pi$
$907$			20.7846i			0.690142i	−0.938577	+	0.345071i	$0.887855\pi$
$908$	6.00000	−	3.46410i	0.199117	−	0.114960i
$909$	13.5000	−	7.79423i	0.447767	−	0.258518i
$910$	−18.0000	−	31.1769i	−0.596694	−	1.03350i
$911$	9.00000	−	15.5885i	0.298183	−	0.516469i	−0.677537	−	0.735489i	$-0.736953\pi$
$911$	9.00000	−	15.5885i	0.298183	−	0.516469i	0.975720	+	0.219020i	$0.0702860\pi$
$912$	−20.0000			−0.662266
$913$	18.0000	−	10.3923i	0.595713	−	0.343935i
$914$	39.0000			1.29001
$915$	39.0000	−	25.9808i	1.28930	−	0.858898i
$916$	−19.0000			−0.627778
$917$		0			0
$918$	48.0000			1.58424
$919$	−22.0000	+	38.1051i	−0.725713	+	1.25697i	0.232967	+	0.972485i	$0.425157\pi$
$919$	−22.0000	+	38.1051i	−0.725713	+	1.25697i	−0.958680	+	0.284487i	$0.908177\pi$
$920$		0			0
$921$	6.00000	−	3.46410i	0.197707	−	0.114146i
$922$	−40.5000	+	23.3827i	−1.33380	+	0.770068i
$923$		−	20.7846i		−	0.684134i
$924$	24.0000			0.789542
$925$	−6.00000	−	3.46410i	−0.197279	−	0.113899i
$926$		−	69.2820i		−	2.27675i
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$	4.50000	+	7.79423i	0.147720	+	0.255858i
$929$	22.5000	−	38.9711i	0.738201	−	1.27860i	−0.215104	−	0.976591i	$-0.569009\pi$
$929$	22.5000	−	38.9711i	0.738201	−	1.27860i	0.953305	−	0.302010i	$-0.0976578\pi$
$930$	54.0000	+	93.5307i	1.77073	+	3.06699i
$931$	−5.00000	−	8.66025i	−0.163868	−	0.283828i
$932$	10.5000	+	6.06218i	0.343939	+	0.198573i
$933$	−24.0000	+	13.8564i	−0.785725	+	0.453638i
$934$	−18.0000	+	31.1769i	−0.588978	+	1.02014i
$935$	−72.0000			−2.35465
$936$	3.00000	−	1.73205i	0.0980581	−	0.0566139i
$937$	2.50000	+	4.33013i	0.0816714	+	0.141459i	0.903968	−	0.427600i	$-0.140641\pi$
$937$	2.50000	+	4.33013i	0.0816714	+	0.141459i	−0.822297	+	0.569059i	$0.807308\pi$
$938$			20.7846i			0.678642i
$939$		−	41.5692i		−	1.35656i
$940$	18.0000	−	31.1769i	0.587095	−	1.01688i
$941$	34.5000	+	19.9186i	1.12467	+	0.649327i	0.942588	−	0.333957i	$-0.108384\pi$
$941$	34.5000	+	19.9186i	1.12467	+	0.649327i	0.182079	+	0.983284i	$0.441717\pi$
$942$	48.0000			1.56392
$943$		0			0
$944$	−15.0000	−	8.66025i	−0.488208	−	0.281867i
$945$	36.0000	+	20.7846i	1.17108	+	0.676123i
$946$	−18.0000	−	10.3923i	−0.585230	−	0.337883i
$947$	15.0000	+	8.66025i	0.487435	+	0.281420i	0.723510	−	0.690314i	$-0.242528\pi$
$947$	15.0000	+	8.66025i	0.487435	+	0.281420i	−0.236075	+	0.971735i	$0.575861\pi$
$948$		−	20.7846i		−	0.675053i
$949$	14.0000			0.454459
$950$	−12.0000	−	6.92820i	−0.389331	−	0.224781i
$951$	−6.00000	+	10.3923i	−0.194563	+	0.336994i
$952$		−	41.5692i		−	1.34727i
$953$		−	32.9090i		−	1.06603i	−0.846107	−	0.533013i	$-0.821060\pi$
$953$		−	32.9090i		−	1.06603i	0.846107	−	0.533013i	$-0.178940\pi$
$954$	−4.50000	−	7.79423i	−0.145693	−	0.252347i
$955$	−36.0000	+	20.7846i	−1.16493	+	0.672574i
$956$	−6.00000			−0.194054
$957$	−6.00000	+	10.3923i	−0.193952	+	0.335936i
$958$	9.00000	−	5.19615i	0.290777	−	0.167880i
$959$	−9.00000	−	5.19615i	−0.290625	−	0.167793i
$960$	−3.00000	−	5.19615i	−0.0968246	−	0.167705i
$961$	38.5000	+	66.6840i	1.24194	+	2.15110i
$962$	3.00000	−	5.19615i	0.0967239	−	0.167531i
$963$		0			0
$964$	−5.50000	+	9.52628i	−0.177143	+	0.306821i
$965$			36.3731i			1.17089i
$966$		0			0
$967$	50.0000			1.60789			0.803946	−	0.594703i	$-0.202730\pi$
$967$	50.0000			1.60789			0.803946	+	0.594703i	$0.202730\pi$
$968$			1.73205i			0.0556702i
$969$	24.0000	−	13.8564i	0.770991	−	0.445132i
$970$	−4.50000	+	2.59808i	−0.144486	+	0.0834192i
$971$	−21.0000	−	36.3731i	−0.673922	−	1.16727i	−0.976783	−	0.214232i	$-0.931275\pi$
$971$	−21.0000	−	36.3731i	−0.673922	−	1.16727i	0.302861	−	0.953035i	$-0.402058\pi$
$972$	5.00000	−	8.66025i	0.160375	−	0.277778i
$973$	−24.0000			−0.769405
$974$	−3.00000	+	1.73205i	−0.0961262	+	0.0554985i
$975$	16.0000			0.512410
$976$	32.5000	−	21.6506i	1.04030	−	0.693020i
$977$	−57.0000			−1.82359			−0.911796	−	0.410644i	$-0.865304\pi$
$977$	−57.0000			−1.82359			−0.911796	+	0.410644i	$0.865304\pi$
$978$	12.0000	−	6.92820i	0.383718	−	0.221540i
$979$	−54.0000			−1.72585
$980$	−7.50000	+	12.9904i	−0.239579	+	0.414963i
$981$	3.50000	+	6.06218i	0.111746	+	0.193550i
$982$	−45.0000	+	25.9808i	−1.43601	+	0.829079i
$983$	3.00000	−	1.73205i	0.0956851	−	0.0552438i	−0.451394	−	0.892325i	$-0.649073\pi$
$983$	3.00000	−	1.73205i	0.0956851	−	0.0552438i	0.547079	+	0.837081i	$0.315740\pi$
$984$			10.3923i			0.331295i
$985$	9.00000			0.286764
$986$	−18.0000	−	10.3923i	−0.573237	−	0.330958i
$987$			83.1384i			2.64633i
$988$	2.00000	−	3.46410i	0.0636285	−	0.110208i
$989$		0			0
$990$	−9.00000	+	15.5885i	−0.286039	+	0.495434i
$991$	10.0000	+	17.3205i	0.317660	+	0.550204i	0.979999	−	0.199000i	$-0.0637695\pi$
$991$	10.0000	+	17.3205i	0.317660	+	0.550204i	−0.662339	+	0.749204i	$0.730436\pi$
$992$	27.0000	+	46.7654i	0.857251	+	1.48480i
$993$		0			0
$994$	−54.0000	+	31.1769i	−1.71278	+	0.988872i
$995$	6.00000	−	10.3923i	0.190213	−	0.329458i
$996$	12.0000			0.380235
$997$	6.00000	−	3.46410i	0.190022	−	0.109709i	−0.401971	−	0.915652i	$-0.631675\pi$
$997$	6.00000	−	3.46410i	0.190022	−	0.109709i	0.591993	+	0.805943i	$0.298341\pi$
$998$	30.0000	+	51.9615i	0.949633	+	1.64481i
$999$			6.92820i			0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.f.a.14.1	✓	2
3.2	odd	2		549.2.s.c.136.1		2
4.3	odd	2		976.2.ba.a.929.1		2
61.29	odd	12		3721.2.a.b.1.2		2
61.32	odd	12		3721.2.a.b.1.1		2
61.48	even	6	inner	61.2.f.a.48.1	yes	2
183.170	odd	6		549.2.s.c.109.1		2
244.231	odd	6		976.2.ba.a.353.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.f.a.14.1	✓	2	1.1	even	1	trivial
61.2.f.a.48.1	yes	2	61.48	even	6	inner
549.2.s.c.109.1		2	183.170	odd	6
549.2.s.c.136.1		2	3.2	odd	2
976.2.ba.a.353.1		2	244.231	odd	6
976.2.ba.a.929.1		2	4.3	odd	2
3721.2.a.b.1.1		2	61.32	odd	12
3721.2.a.b.1.2		2	61.29	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{2} -2.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(3.00000 - 1.73205i) q^{6} +(-3.00000 + 1.73205i) q^{7} -1.73205i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{2} -2.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(3.00000 - 1.73205i) q^{6} +(-3.00000 + 1.73205i) q^{7} -1.73205i q^{8} +1.00000 q^{9} +(4.50000 + 2.59808i) q^{10} +3.46410i q^{11} +(-1.00000 + 1.73205i) q^{12} +(1.00000 + 1.73205i) q^{13} +(3.00000 - 5.19615i) q^{14} +(3.00000 + 5.19615i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-6.00000 - 3.46410i) q^{17} +(-1.50000 + 0.866025i) q^{18} +(1.00000 - 1.73205i) q^{19} -3.00000 q^{20} +(6.00000 - 3.46410i) q^{21} +(-3.00000 - 5.19615i) q^{22} +3.46410i q^{24} +(-2.00000 + 3.46410i) q^{25} +(-3.00000 - 1.73205i) q^{26} +4.00000 q^{27} +3.46410i q^{28} +(-1.50000 - 0.866025i) q^{29} +(-9.00000 - 5.19615i) q^{30} +(-9.00000 - 5.19615i) q^{31} +(-4.50000 - 2.59808i) q^{32} -6.92820i q^{33} +12.0000 q^{34} +(9.00000 + 5.19615i) q^{35} +(0.500000 - 0.866025i) q^{36} +1.73205i q^{37} +3.46410i q^{38} +(-2.00000 - 3.46410i) q^{39} +(-4.50000 + 2.59808i) q^{40} +3.00000 q^{41} +(-6.00000 + 10.3923i) q^{42} +(3.00000 - 1.73205i) q^{43} +(3.00000 + 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{45} +(-6.00000 + 10.3923i) q^{47} +(-5.00000 - 8.66025i) q^{48} +(2.50000 - 4.33013i) q^{49} -6.92820i q^{50} +(12.0000 + 6.92820i) q^{51} +2.00000 q^{52} +5.19615i q^{53} +(-6.00000 + 3.46410i) q^{54} +(9.00000 - 5.19615i) q^{55} +(3.00000 + 5.19615i) q^{56} +(-2.00000 + 3.46410i) q^{57} +3.00000 q^{58} +(-3.00000 + 1.73205i) q^{59} +6.00000 q^{60} +(-0.500000 - 7.79423i) q^{61} +18.0000 q^{62} +(-3.00000 + 1.73205i) q^{63} -1.00000 q^{64} +(3.00000 - 5.19615i) q^{65} +(6.00000 + 10.3923i) q^{66} +(-3.00000 + 1.73205i) q^{67} +(-6.00000 + 3.46410i) q^{68} -18.0000 q^{70} +(-9.00000 - 5.19615i) q^{71} -1.73205i q^{72} +(3.50000 - 6.06218i) q^{73} +(-1.50000 - 2.59808i) q^{74} +(4.00000 - 6.92820i) q^{75} +(-1.00000 - 1.73205i) q^{76} +(-6.00000 - 10.3923i) q^{77} +(6.00000 + 3.46410i) q^{78} +(-9.00000 + 5.19615i) q^{79} +(7.50000 - 12.9904i) q^{80} -11.0000 q^{81} +(-4.50000 + 2.59808i) q^{82} +(-3.00000 - 5.19615i) q^{83} -6.92820i q^{84} +20.7846i q^{85} +(-3.00000 + 5.19615i) q^{86} +(3.00000 + 1.73205i) q^{87} +6.00000 q^{88} +15.5885i q^{89} +(4.50000 + 2.59808i) q^{90} +(-6.00000 - 3.46410i) q^{91} +(18.0000 + 10.3923i) q^{93} -20.7846i q^{94} -6.00000 q^{95} +(9.00000 + 5.19615i) q^{96} +(-0.500000 + 0.866025i) q^{97} +8.66025i q^{98} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 4 q^{3} + q^{4} - 3 q^{5} + 6 q^{6} - 6 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 4 * q^3 + q^4 - 3 * q^5 + 6 * q^6 - 6 * q^7 + 2 * q^9	\( 2 q - 3 q^{2} - 4 q^{3} + q^{4} - 3 q^{5} + 6 q^{6} - 6 q^{7} + 2 q^{9} + 9 q^{10} - 2 q^{12} + 2 q^{13} + 6 q^{14} + 6 q^{15} + 5 q^{16} - 12 q^{17} - 3 q^{18} + 2 q^{19} - 6 q^{20} + 12 q^{21} - 6 q^{22} - 4 q^{25} - 6 q^{26} + 8 q^{27} - 3 q^{29} - 18 q^{30} - 18 q^{31} - 9 q^{32} + 24 q^{34} + 18 q^{35} + q^{36} - 4 q^{39} - 9 q^{40} + 6 q^{41} - 12 q^{42} + 6 q^{43} + 6 q^{44} - 3 q^{45} - 12 q^{47} - 10 q^{48} + 5 q^{49} + 24 q^{51} + 4 q^{52} - 12 q^{54} + 18 q^{55} + 6 q^{56} - 4 q^{57} + 6 q^{58} - 6 q^{59} + 12 q^{60} - q^{61} + 36 q^{62} - 6 q^{63} - 2 q^{64} + 6 q^{65} + 12 q^{66} - 6 q^{67} - 12 q^{68} - 36 q^{70} - 18 q^{71} + 7 q^{73} - 3 q^{74} + 8 q^{75} - 2 q^{76} - 12 q^{77} + 12 q^{78} - 18 q^{79} + 15 q^{80} - 22 q^{81} - 9 q^{82} - 6 q^{83} - 6 q^{86} + 6 q^{87} + 12 q^{88} + 9 q^{90} - 12 q^{91} + 36 q^{93} - 12 q^{95} + 18 q^{96} - q^{97}+O(q^{100}) \) 2 * q - 3 * q^2 - 4 * q^3 + q^4 - 3 * q^5 + 6 * q^6 - 6 * q^7 + 2 * q^9 + 9 * q^10 - 2 * q^12 + 2 * q^13 + 6 * q^14 + 6 * q^15 + 5 * q^16 - 12 * q^17 - 3 * q^18 + 2 * q^19 - 6 * q^20 + 12 * q^21 - 6 * q^22 - 4 * q^25 - 6 * q^26 + 8 * q^27 - 3 * q^29 - 18 * q^30 - 18 * q^31 - 9 * q^32 + 24 * q^34 + 18 * q^35 + q^36 - 4 * q^39 - 9 * q^40 + 6 * q^41 - 12 * q^42 + 6 * q^43 + 6 * q^44 - 3 * q^45 - 12 * q^47 - 10 * q^48 + 5 * q^49 + 24 * q^51 + 4 * q^52 - 12 * q^54 + 18 * q^55 + 6 * q^56 - 4 * q^57 + 6 * q^58 - 6 * q^59 + 12 * q^60 - q^61 + 36 * q^62 - 6 * q^63 - 2 * q^64 + 6 * q^65 + 12 * q^66 - 6 * q^67 - 12 * q^68 - 36 * q^70 - 18 * q^71 + 7 * q^73 - 3 * q^74 + 8 * q^75 - 2 * q^76 - 12 * q^77 + 12 * q^78 - 18 * q^79 + 15 * q^80 - 22 * q^81 - 9 * q^82 - 6 * q^83 - 6 * q^86 + 6 * q^87 + 12 * q^88 + 9 * q^90 - 12 * q^91 + 36 * q^93 - 12 * q^95 + 18 * q^96 - q^97

Introduction

L-functions

Modular forms

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