LMFDB - Embedded newform 504.2.cz.a.187.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(187,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 5]))

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

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

chi := DirichletCharacter("504.187");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cz (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:	$4.02446026187$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 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			187.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	504.187
Dual form			504.2.cz.a.283.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} -1.73205 q^{5} +(-1.73205 + 1.73205i) q^{6} +(0.866025 - 2.50000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} -1.73205 q^{5} +(-1.73205 + 1.73205i) q^{6} +(0.866025 - 2.50000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.633975 + 2.36603i) q^{10} -5.00000 q^{11} +(1.73205 + 3.00000i) q^{12} +(0.866025 + 1.50000i) q^{13} +(-3.09808 - 2.09808i) q^{14} +(2.59808 + 1.50000i) q^{15} +(2.00000 + 3.46410i) q^{16} +(1.50000 - 0.866025i) q^{17} +(4.09808 - 1.09808i) q^{18} +(-1.50000 - 0.866025i) q^{19} +(3.00000 + 1.73205i) q^{20} +(-3.46410 + 3.00000i) q^{21} +(-1.83013 + 6.83013i) q^{22} +7.00000i q^{23} +(4.73205 - 1.26795i) q^{24} -2.00000 q^{25} +(2.36603 - 0.633975i) q^{26} -5.19615i q^{27} +(-4.00000 + 3.46410i) q^{28} +(6.06218 + 3.50000i) q^{29} +(3.00000 - 3.00000i) q^{30} +(3.46410 - 6.00000i) q^{31} +(5.46410 - 1.46410i) q^{32} +(7.50000 + 4.33013i) q^{33} +(-0.633975 - 2.36603i) q^{34} +(-1.50000 + 4.33013i) q^{35} -6.00000i q^{36} +(0.866025 + 0.500000i) q^{37} +(-1.73205 + 1.73205i) q^{38} -3.00000i q^{39} +(3.46410 - 3.46410i) q^{40} +(-10.5000 + 6.06218i) q^{41} +(2.83013 + 5.83013i) q^{42} +(-4.50000 + 7.79423i) q^{43} +(8.66025 + 5.00000i) q^{44} +(-2.59808 - 4.50000i) q^{45} +(9.56218 + 2.56218i) q^{46} +(-1.73205 - 3.00000i) q^{47} -6.92820i q^{48} +(-5.50000 - 4.33013i) q^{49} +(-0.732051 + 2.73205i) q^{50} -3.00000 q^{51} -3.46410i q^{52} +(-9.52628 + 5.50000i) q^{53} +(-7.09808 - 1.90192i) q^{54} +8.66025 q^{55} +(3.26795 + 6.73205i) q^{56} +(1.50000 + 2.59808i) q^{57} +(7.00000 - 7.00000i) q^{58} +(-6.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(-1.73205 - 3.00000i) q^{61} +(-6.92820 - 6.92820i) q^{62} +(7.79423 - 1.50000i) q^{63} -8.00000i q^{64} +(-1.50000 - 2.59808i) q^{65} +(8.66025 - 8.66025i) q^{66} +(4.00000 - 6.92820i) q^{67} -3.46410 q^{68} +(6.06218 - 10.5000i) q^{69} +(5.36603 + 3.63397i) q^{70} -10.0000i q^{71} +(-8.19615 - 2.19615i) q^{72} +(-7.50000 + 4.33013i) q^{73} +(1.00000 - 1.00000i) q^{74} +(3.00000 + 1.73205i) q^{75} +(1.73205 + 3.00000i) q^{76} +(-4.33013 + 12.5000i) q^{77} +(-4.09808 - 1.09808i) q^{78} +(-5.19615 + 3.00000i) q^{79} +(-3.46410 - 6.00000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(4.43782 + 16.5622i) q^{82} +(-13.5000 - 7.79423i) q^{83} +(9.00000 - 1.73205i) q^{84} +(-2.59808 + 1.50000i) q^{85} +(9.00000 + 9.00000i) q^{86} +(-6.06218 - 10.5000i) q^{87} +(10.0000 - 10.0000i) q^{88} +(7.50000 + 4.33013i) q^{89} +(-7.09808 + 1.90192i) q^{90} +(4.50000 - 0.866025i) q^{91} +(7.00000 - 12.1244i) q^{92} +(-10.3923 + 6.00000i) q^{93} +(-4.73205 + 1.26795i) q^{94} +(2.59808 + 1.50000i) q^{95} +(-9.46410 - 2.53590i) q^{96} +(-1.50000 - 0.866025i) q^{97} +(-7.92820 + 5.92820i) q^{98} +(-7.50000 - 12.9904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{3} - 8 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^3 - 8 * q^8 + 6 * q^9	$ 4 q - 2 q^{2} - 6 q^{3} - 8 q^{8} + 6 q^{9} - 6 q^{10} - 20 q^{11} - 2 q^{14} + 8 q^{16} + 6 q^{17} + 6 q^{18} - 6 q^{19} + 12 q^{20} + 10 q^{22} + 12 q^{24} - 8 q^{25} + 6 q^{26} - 16 q^{28} + 12 q^{30} + 8 q^{32} + 30 q^{33} - 6 q^{34} - 6 q^{35} - 42 q^{41} - 6 q^{42} - 18 q^{43} + 14 q^{46} - 22 q^{49} + 4 q^{50} - 12 q^{51} - 18 q^{54} + 20 q^{56} + 6 q^{57} + 28 q^{58} - 24 q^{59} - 12 q^{60} - 6 q^{65} + 16 q^{67} + 18 q^{70} - 12 q^{72} - 30 q^{73} + 4 q^{74} + 12 q^{75} - 6 q^{78} - 18 q^{81} + 42 q^{82} - 54 q^{83} + 36 q^{84} + 36 q^{86} + 40 q^{88} + 30 q^{89} - 18 q^{90} + 18 q^{91} + 28 q^{92} - 12 q^{94} - 24 q^{96} - 6 q^{97} - 4 q^{98} - 30 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^3 - 8 * q^8 + 6 * q^9 - 6 * q^10 - 20 * q^11 - 2 * q^14 + 8 * q^16 + 6 * q^17 + 6 * q^18 - 6 * q^19 + 12 * q^20 + 10 * q^22 + 12 * q^24 - 8 * q^25 + 6 * q^26 - 16 * q^28 + 12 * q^30 + 8 * q^32 + 30 * q^33 - 6 * q^34 - 6 * q^35 - 42 * q^41 - 6 * q^42 - 18 * q^43 + 14 * q^46 - 22 * q^49 + 4 * q^50 - 12 * q^51 - 18 * q^54 + 20 * q^56 + 6 * q^57 + 28 * q^58 - 24 * q^59 - 12 * q^60 - 6 * q^65 + 16 * q^67 + 18 * q^70 - 12 * q^72 - 30 * q^73 + 4 * q^74 + 12 * q^75 - 6 * q^78 - 18 * q^81 + 42 * q^82 - 54 * q^83 + 36 * q^84 + 36 * q^86 + 40 * q^88 + 30 * q^89 - 18 * q^90 + 18 * q^91 + 28 * q^92 - 12 * q^94 - 24 * q^96 - 6 * q^97 - 4 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$	−1.73205			−0.774597			−0.387298	−	0.921954i	$-0.626592\pi$
$5$	−1.73205			−0.774597			−0.387298	+	0.921954i	$0.626592\pi$
$6$	−1.73205	+	1.73205i	−0.707107	+	0.707107i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−0.633975	+	2.36603i	−0.200480	+	0.748203i
$11$	−5.00000			−1.50756			−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000			−1.50756			−0.753778	+	0.657129i	$0.771771\pi$
$12$	1.73205	+	3.00000i	0.500000	+	0.866025i
$13$	0.866025	+	1.50000i	0.240192	+	0.416025i	0.960769	−	0.277350i	$-0.0894562\pi$
$13$	0.866025	+	1.50000i	0.240192	+	0.416025i	−0.720577	+	0.693375i	$0.756123\pi$
$14$	−3.09808	−	2.09808i	−0.827996	−	0.560734i
$15$	2.59808	+	1.50000i	0.670820	+	0.387298i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	1.50000	−	0.866025i	0.363803	−	0.210042i	−0.306944	−	0.951727i	$-0.599307\pi$
$17$	1.50000	−	0.866025i	0.363803	−	0.210042i	0.670748	+	0.741685i	$0.265973\pi$
$18$	4.09808	−	1.09808i	0.965926	−	0.258819i
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	0.317970	−	0.948101i	$-0.396999\pi$
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	−0.662094	+	0.749421i	$0.730332\pi$
$20$	3.00000	+	1.73205i	0.670820	+	0.387298i
$21$	−3.46410	+	3.00000i	−0.755929	+	0.654654i
$22$	−1.83013	+	6.83013i	−0.390184	+	1.45619i
$23$			7.00000i			1.45960i	0.683660	+	0.729800i	$0.260387\pi$
$23$			7.00000i			1.45960i	−0.683660	+	0.729800i	$0.739613\pi$
$24$	4.73205	−	1.26795i	0.965926	−	0.258819i
$25$	−2.00000			−0.400000
$26$	2.36603	−	0.633975i	0.464016	−	0.124333i
$27$		−	5.19615i		−	1.00000i
$28$	−4.00000	+	3.46410i	−0.755929	+	0.654654i
$29$	6.06218	+	3.50000i	1.12572	+	0.649934i	0.942855	−	0.333205i	$-0.108130\pi$
$29$	6.06218	+	3.50000i	1.12572	+	0.649934i	0.182864	+	0.983138i	$0.441463\pi$
$30$	3.00000	−	3.00000i	0.547723	−	0.547723i
$31$	3.46410	−	6.00000i	0.622171	−	1.07763i	−0.366910	−	0.930257i	$-0.619584\pi$
$31$	3.46410	−	6.00000i	0.622171	−	1.07763i	0.989081	−	0.147375i	$-0.0470825\pi$
$32$	5.46410	−	1.46410i	0.965926	−	0.258819i
$33$	7.50000	+	4.33013i	1.30558	+	0.753778i
$34$	−0.633975	−	2.36603i	−0.108726	−	0.405770i
$35$	−1.50000	+	4.33013i	−0.253546	+	0.731925i
$36$		−	6.00000i		−	1.00000i
$37$	0.866025	+	0.500000i	0.142374	+	0.0821995i	0.569495	−	0.821995i	$-0.307139\pi$
$37$	0.866025	+	0.500000i	0.142374	+	0.0821995i	−0.427121	+	0.904194i	$0.640472\pi$
$38$	−1.73205	+	1.73205i	−0.280976	+	0.280976i
$39$		−	3.00000i		−	0.480384i
$40$	3.46410	−	3.46410i	0.547723	−	0.547723i
$41$	−10.5000	+	6.06218i	−1.63982	+	0.946753i	−0.658932	+	0.752202i	$0.728992\pi$
$41$	−10.5000	+	6.06218i	−1.63982	+	0.946753i	−0.980892	+	0.194551i	$0.937675\pi$
$42$	2.83013	+	5.83013i	0.436698	+	0.899608i
$43$	−4.50000	+	7.79423i	−0.686244	+	1.18861i	0.286801	+	0.957990i	$0.407408\pi$
$43$	−4.50000	+	7.79423i	−0.686244	+	1.18861i	−0.973044	+	0.230618i	$0.925925\pi$
$44$	8.66025	+	5.00000i	1.30558	+	0.753778i
$45$	−2.59808	−	4.50000i	−0.387298	−	0.670820i
$46$	9.56218	+	2.56218i	1.40987	+	0.377773i
$47$	−1.73205	−	3.00000i	−0.252646	−	0.437595i	0.711608	−	0.702577i	$-0.247967\pi$
$47$	−1.73205	−	3.00000i	−0.252646	−	0.437595i	−0.964253	+	0.264982i	$0.914634\pi$
$48$		−	6.92820i		−	1.00000i
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$	−0.732051	+	2.73205i	−0.103528	+	0.386370i
$51$	−3.00000			−0.420084
$52$		−	3.46410i		−	0.480384i
$53$	−9.52628	+	5.50000i	−1.30854	+	0.755483i	−0.981852	−	0.189651i	$-0.939264\pi$
$53$	−9.52628	+	5.50000i	−1.30854	+	0.755483i	−0.326683	+	0.945134i	$0.605931\pi$
$54$	−7.09808	−	1.90192i	−0.965926	−	0.258819i
$55$	8.66025			1.16775
$56$	3.26795	+	6.73205i	0.436698	+	0.899608i
$57$	1.50000	+	2.59808i	0.198680	+	0.344124i
$58$	7.00000	−	7.00000i	0.919145	−	0.919145i
$59$	−6.00000	−	3.46410i	−0.781133	−	0.450988i	0.0556984	−	0.998448i	$-0.482261\pi$
$59$	−6.00000	−	3.46410i	−0.781133	−	0.450988i	−0.836832	+	0.547460i	$0.815595\pi$
$60$	−3.00000	−	5.19615i	−0.387298	−	0.670820i
$61$	−1.73205	−	3.00000i	−0.221766	−	0.384111i	0.733578	−	0.679605i	$-0.237849\pi$
$61$	−1.73205	−	3.00000i	−0.221766	−	0.384111i	−0.955344	+	0.295495i	$0.904516\pi$
$62$	−6.92820	−	6.92820i	−0.879883	−	0.879883i
$63$	7.79423	−	1.50000i	0.981981	−	0.188982i
$64$		−	8.00000i		−	1.00000i
$65$	−1.50000	−	2.59808i	−0.186052	−	0.322252i
$66$	8.66025	−	8.66025i	1.06600	−	1.06600i
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	−0.511237	−	0.859440i	$-0.670813\pi$
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	0.999915	+	0.0130248i	$0.00414604\pi$
$68$	−3.46410			−0.420084
$69$	6.06218	−	10.5000i	0.729800	−	1.26405i
$70$	5.36603	+	3.63397i	0.641363	+	0.434343i
$71$		−	10.0000i		−	1.18678i	−0.804914	−	0.593391i	$-0.797789\pi$
$71$		−	10.0000i		−	1.18678i	0.804914	−	0.593391i	$-0.202211\pi$
$72$	−8.19615	−	2.19615i	−0.965926	−	0.258819i
$73$	−7.50000	+	4.33013i	−0.877809	+	0.506803i	−0.869935	−	0.493166i	$-0.835840\pi$
$73$	−7.50000	+	4.33013i	−0.877809	+	0.506803i	−0.00787336	+	0.999969i	$0.502506\pi$
$74$	1.00000	−	1.00000i	0.116248	−	0.116248i
$75$	3.00000	+	1.73205i	0.346410	+	0.200000i
$76$	1.73205	+	3.00000i	0.198680	+	0.344124i
$77$	−4.33013	+	12.5000i	−0.493464	+	1.42451i
$78$	−4.09808	−	1.09808i	−0.464016	−	0.124333i
$79$	−5.19615	+	3.00000i	−0.584613	+	0.337526i	−0.762964	−	0.646440i	$-0.776257\pi$
$79$	−5.19615	+	3.00000i	−0.584613	+	0.337526i	0.178352	+	0.983967i	$0.442924\pi$
$80$	−3.46410	−	6.00000i	−0.387298	−	0.670820i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	4.43782	+	16.5622i	0.490075	+	1.82899i
$83$	−13.5000	−	7.79423i	−1.48182	−	0.855528i	−0.482030	−	0.876155i	$-0.660100\pi$
$83$	−13.5000	−	7.79423i	−1.48182	−	0.855528i	−0.999787	+	0.0206268i	$0.993434\pi$
$84$	9.00000	−	1.73205i	0.981981	−	0.188982i
$85$	−2.59808	+	1.50000i	−0.281801	+	0.162698i
$86$	9.00000	+	9.00000i	0.970495	+	0.970495i
$87$	−6.06218	−	10.5000i	−0.649934	−	1.12572i
$88$	10.0000	−	10.0000i	1.06600	−	1.06600i
$89$	7.50000	+	4.33013i	0.794998	+	0.458993i	0.841719	−	0.539915i	$-0.181544\pi$
$89$	7.50000	+	4.33013i	0.794998	+	0.458993i	−0.0467209	+	0.998908i	$0.514877\pi$
$90$	−7.09808	+	1.90192i	−0.748203	+	0.200480i
$91$	4.50000	−	0.866025i	0.471728	−	0.0907841i
$92$	7.00000	−	12.1244i	0.729800	−	1.26405i
$93$	−10.3923	+	6.00000i	−1.07763	+	0.622171i
$94$	−4.73205	+	1.26795i	−0.488074	+	0.130779i
$95$	2.59808	+	1.50000i	0.266557	+	0.153897i
$96$	−9.46410	−	2.53590i	−0.965926	−	0.258819i
$97$	−1.50000	−	0.866025i	−0.152302	−	0.0879316i	0.421912	−	0.906637i	$-0.361359\pi$
$97$	−1.50000	−	0.866025i	−0.152302	−	0.0879316i	−0.574214	+	0.818705i	$0.694692\pi$
$98$	−7.92820	+	5.92820i	−0.800869	+	0.598839i
$99$	−7.50000	−	12.9904i	−0.753778	−	1.30558i
$100$	3.46410	+	2.00000i	0.346410	+	0.200000i
$101$	1.73205			0.172345			0.0861727	−	0.996280i	$-0.472536\pi$
$101$	1.73205			0.172345			0.0861727	+	0.996280i	$0.472536\pi$
$102$	−1.09808	+	4.09808i	−0.108726	+	0.405770i
$103$	−5.19615			−0.511992			−0.255996	−	0.966678i	$-0.582403\pi$
$103$	−5.19615			−0.511992			−0.255996	+	0.966678i	$0.582403\pi$
$104$	−4.73205	−	1.26795i	−0.464016	−	0.124333i
$105$	6.00000	−	5.19615i	0.585540	−	0.507093i
$106$	4.02628	+	15.0263i	0.391067	+	1.45948i
$107$	−2.50000	+	4.33013i	−0.241684	+	0.418609i	−0.961194	−	0.275873i	$-0.911033\pi$
$107$	−2.50000	+	4.33013i	−0.241684	+	0.418609i	0.719510	+	0.694482i	$0.244366\pi$
$108$	−5.19615	+	9.00000i	−0.500000	+	0.866025i
$109$	−4.33013	+	2.50000i	−0.414751	+	0.239457i	−0.692829	−	0.721102i	$-0.743636\pi$
$109$	−4.33013	+	2.50000i	−0.414751	+	0.239457i	0.278078	+	0.960558i	$0.410303\pi$
$110$	3.16987	−	11.8301i	0.302236	−	1.12796i
$111$	−0.866025	−	1.50000i	−0.0821995	−	0.142374i
$112$	10.3923	−	2.00000i	0.981981	−	0.188982i
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	0.888585	−	0.458712i	$-0.151689\pi$
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	−0.841549	+	0.540181i	$0.818356\pi$
$114$	4.09808	−	1.09808i	0.383820	−	0.102844i
$115$		−	12.1244i		−	1.13060i
$116$	−7.00000	−	12.1244i	−0.649934	−	1.12572i
$117$	−2.59808	+	4.50000i	−0.240192	+	0.416025i
$118$	−6.92820	+	6.92820i	−0.637793	+	0.637793i
$119$	−0.866025	−	4.50000i	−0.0793884	−	0.412514i
$120$	−8.19615	+	2.19615i	−0.748203	+	0.200480i
$121$	14.0000			1.27273
$122$	−4.73205	+	1.26795i	−0.428420	+	0.114795i
$123$	21.0000			1.89351
$124$	−12.0000	+	6.92820i	−1.07763	+	0.622171i
$125$	12.1244			1.08444
$126$	0.803848	−	11.1962i	0.0716124	−	0.997433i
$127$			18.0000i			1.59724i	0.601834	+	0.798621i	$0.294437\pi$
$127$			18.0000i			1.59724i	−0.601834	+	0.798621i	$0.705563\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$	13.5000	−	7.79423i	1.18861	−	0.686244i
$130$	−4.09808	+	1.09808i	−0.359425	+	0.0963077i
$131$			8.66025i			0.756650i	0.925673	+	0.378325i	$0.123500\pi$
$131$			8.66025i			0.756650i	−0.925673	+	0.378325i	$0.876500\pi$
$132$	−8.66025	−	15.0000i	−0.753778	−	1.30558i
$133$	−3.46410	+	3.00000i	−0.300376	+	0.260133i
$134$	−8.00000	−	8.00000i	−0.691095	−	0.691095i
$135$			9.00000i			0.774597i
$136$	−1.26795	+	4.73205i	−0.108726	+	0.405770i
$137$	−13.0000			−1.11066			−0.555332	−	0.831628i	$-0.687409\pi$
$137$	−13.0000			−1.11066			−0.555332	+	0.831628i	$0.687409\pi$
$138$	−12.1244	−	12.1244i	−1.03209	−	1.03209i
$139$	13.5000	−	7.79423i	1.14506	−	0.661098i	0.197378	−	0.980328i	$-0.436757\pi$
$139$	13.5000	−	7.79423i	1.14506	−	0.661098i	0.947677	+	0.319230i	$0.103424\pi$
$140$	6.92820	−	6.00000i	0.585540	−	0.507093i
$141$			6.00000i			0.505291i
$142$	−13.6603	−	3.66025i	−1.14634	−	0.307162i
$143$	−4.33013	−	7.50000i	−0.362103	−	0.627182i
$144$	−6.00000	+	10.3923i	−0.500000	+	0.866025i
$145$	−10.5000	−	6.06218i	−0.871978	−	0.503436i
$146$	3.16987	+	11.8301i	0.262341	+	0.979068i
$147$	4.50000	+	11.2583i	0.371154	+	0.928571i
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$		−	11.0000i		−	0.901155i	−0.892737	−	0.450578i	$-0.851218\pi$
$149$		−	11.0000i		−	0.901155i	0.892737	−	0.450578i	$-0.148782\pi$
$150$	3.46410	−	3.46410i	0.282843	−	0.282843i
$151$			5.00000i			0.406894i	0.979086	+	0.203447i	$0.0652145\pi$
$151$			5.00000i			0.406894i	−0.979086	+	0.203447i	$0.934786\pi$
$152$	4.73205	−	1.26795i	0.383820	−	0.102844i
$153$	4.50000	+	2.59808i	0.363803	+	0.210042i
$154$	15.4904	+	10.4904i	1.24825	+	0.845339i
$155$	−6.00000	+	10.3923i	−0.481932	+	0.834730i
$156$	−3.00000	+	5.19615i	−0.240192	+	0.416025i
$157$	10.3923	−	18.0000i	0.829396	−	1.43656i	−0.0691164	−	0.997609i	$-0.522018\pi$
$157$	10.3923	−	18.0000i	0.829396	−	1.43656i	0.898513	−	0.438948i	$-0.144649\pi$
$158$	2.19615	+	8.19615i	0.174717	+	0.652051i
$159$	19.0526			1.51097
$160$	−9.46410	+	2.53590i	−0.748203	+	0.200480i
$161$	17.5000	+	6.06218i	1.37919	+	0.477767i
$162$	9.00000	+	9.00000i	0.707107	+	0.707107i
$163$	3.50000	−	6.06218i	0.274141	−	0.474826i	−0.695777	−	0.718258i	$-0.744940\pi$
$163$	3.50000	−	6.06218i	0.274141	−	0.474826i	0.969918	+	0.243432i	$0.0782731\pi$
$164$	24.2487			1.89351
$165$	−12.9904	−	7.50000i	−1.01130	−	0.583874i
$166$	−15.5885	+	15.5885i	−1.20990	+	1.20990i
$167$	−4.33013	−	7.50000i	−0.335075	−	0.580367i	0.648424	−	0.761279i	$-0.275428\pi$
$167$	−4.33013	−	7.50000i	−0.335075	−	0.580367i	−0.983499	+	0.180912i	$0.942095\pi$
$168$	0.928203	−	12.9282i	0.0716124	−	0.997433i
$169$	5.00000	−	8.66025i	0.384615	−	0.666173i
$170$	1.09808	+	4.09808i	0.0842186	+	0.314308i
$171$		−	5.19615i		−	0.397360i
$172$	15.5885	−	9.00000i	1.18861	−	0.686244i
$173$	1.73205	+	3.00000i	0.131685	+	0.228086i	0.924326	−	0.381603i	$-0.124628\pi$
$173$	1.73205	+	3.00000i	0.131685	+	0.228086i	−0.792641	+	0.609689i	$0.791294\pi$
$174$	−16.5622	+	4.43782i	−1.25558	+	0.336430i
$175$	−1.73205	+	5.00000i	−0.130931	+	0.377964i
$176$	−10.0000	−	17.3205i	−0.753778	−	1.30558i
$177$	6.00000	+	10.3923i	0.450988	+	0.781133i
$178$	8.66025	−	8.66025i	0.649113	−	0.649113i
$179$	−5.50000	−	9.52628i	−0.411089	−	0.712028i	0.583920	−	0.811811i	$-0.301518\pi$
$179$	−5.50000	−	9.52628i	−0.411089	−	0.712028i	−0.995009	+	0.0997838i	$0.968185\pi$
$180$			10.3923i			0.774597i
$181$	3.46410			0.257485			0.128742	−	0.991678i	$-0.458906\pi$
$181$	3.46410			0.257485			0.128742	+	0.991678i	$0.458906\pi$
$182$	0.464102	−	6.46410i	0.0344015	−	0.479151i
$183$			6.00000i			0.443533i
$184$	−14.0000	−	14.0000i	−1.03209	−	1.03209i
$185$	−1.50000	−	0.866025i	−0.110282	−	0.0636715i
$186$	4.39230	+	16.3923i	0.322059	+	1.20194i
$187$	−7.50000	+	4.33013i	−0.548454	+	0.316650i
$188$			6.92820i			0.505291i
$189$	−12.9904	−	4.50000i	−0.944911	−	0.327327i
$190$	3.00000	−	3.00000i	0.217643	−	0.217643i
$191$	−12.1244	+	7.00000i	−0.877288	+	0.506502i	−0.869763	−	0.493469i	$-0.835728\pi$
$191$	−12.1244	+	7.00000i	−0.877288	+	0.506502i	−0.00752447	+	0.999972i	$0.502395\pi$
$192$	−6.92820	+	12.0000i	−0.500000	+	0.866025i
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	−0.737620	−	0.675216i	$-0.764050\pi$
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	0.953564	+	0.301189i	$0.0973836\pi$
$194$	−1.73205	+	1.73205i	−0.124354	+	0.124354i
$195$			5.19615i			0.372104i
$196$	5.19615	+	13.0000i	0.371154	+	0.928571i
$197$		−	8.00000i		−	0.569976i	−0.958531	−	0.284988i	$-0.908010\pi$
$197$		−	8.00000i		−	0.569976i	0.958531	−	0.284988i	$-0.0919897\pi$
$198$	−20.4904	+	5.49038i	−1.45619	+	0.390184i
$199$	4.33013	+	7.50000i	0.306955	+	0.531661i	0.977695	−	0.210032i	$-0.0673567\pi$
$199$	4.33013	+	7.50000i	0.306955	+	0.531661i	−0.670740	+	0.741693i	$0.734023\pi$
$200$	4.00000	−	4.00000i	0.282843	−	0.282843i
$201$	−12.0000	+	6.92820i	−0.846415	+	0.488678i
$202$	0.633975	−	2.36603i	0.0446063	−	0.166473i
$203$	14.0000	−	12.1244i	0.982607	−	0.850963i
$204$	5.19615	+	3.00000i	0.363803	+	0.210042i
$205$	18.1865	−	10.5000i	1.27020	−	0.733352i
$206$	−1.90192	+	7.09808i	−0.132513	+	0.494546i
$207$	−18.1865	+	10.5000i	−1.26405	+	0.729800i
$208$	−3.46410	+	6.00000i	−0.240192	+	0.416025i
$209$	7.50000	+	4.33013i	0.518786	+	0.299521i
$210$	−4.90192	−	10.0981i	−0.338265	−	0.696833i
$211$	4.50000	+	7.79423i	0.309793	+	0.536577i	0.978317	−	0.207114i	$-0.0664070\pi$
$211$	4.50000	+	7.79423i	0.309793	+	0.536577i	−0.668524	+	0.743690i	$0.733074\pi$
$212$	22.0000			1.51097
$213$	−8.66025	+	15.0000i	−0.593391	+	1.02778i
$214$	5.00000	+	5.00000i	0.341793	+	0.341793i
$215$	7.79423	−	13.5000i	0.531562	−	0.920692i
$216$	10.3923	+	10.3923i	0.707107	+	0.707107i
$217$	−12.0000	−	13.8564i	−0.814613	−	0.940634i
$218$	1.83013	+	6.83013i	0.123952	+	0.462595i
$219$	15.0000			1.01361
$220$	−15.0000	−	8.66025i	−1.01130	−	0.583874i
$221$	2.59808	+	1.50000i	0.174766	+	0.100901i
$222$	−2.36603	+	0.633975i	−0.158797	+	0.0425496i
$223$	−6.06218	+	10.5000i	−0.405953	+	0.703132i	−0.994432	−	0.105381i	$-0.966394\pi$
$223$	−6.06218	+	10.5000i	−0.405953	+	0.703132i	0.588478	+	0.808513i	$0.299727\pi$
$224$	1.07180	−	14.9282i	0.0716124	−	0.997433i
$225$	−3.00000	−	5.19615i	−0.200000	−	0.346410i
$226$	1.36603	−	0.366025i	0.0908667	−	0.0243476i
$227$			19.0526i			1.26456i	0.774739	+	0.632281i	$0.217881\pi$
$227$			19.0526i			1.26456i	−0.774739	+	0.632281i	$0.782119\pi$
$228$		−	6.00000i		−	0.397360i
$229$	−12.1244			−0.801200			−0.400600	−	0.916253i	$-0.631198\pi$
$229$	−12.1244			−0.801200			−0.400600	+	0.916253i	$0.631198\pi$
$230$	−16.5622	−	4.43782i	−1.09208	−	0.292621i
$231$	17.3205	−	15.0000i	1.13961	−	0.986928i
$232$	−19.1244	+	5.12436i	−1.25558	+	0.336430i
$233$	5.50000	−	9.52628i	0.360317	−	0.624087i	−0.627696	−	0.778459i	$-0.716002\pi$
$233$	5.50000	−	9.52628i	0.360317	−	0.624087i	0.988013	+	0.154371i	$0.0493352\pi$
$234$	5.19615	+	5.19615i	0.339683	+	0.339683i
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$	6.92820	+	12.0000i	0.450988	+	0.781133i
$237$	10.3923			0.675053
$238$	−6.46410	−	0.464102i	−0.419005	−	0.0300832i
$239$	4.33013	−	2.50000i	0.280093	−	0.161712i	−0.353373	−	0.935483i	$-0.614965\pi$
$239$	4.33013	−	2.50000i	0.280093	−	0.161712i	0.633465	+	0.773771i	$0.281632\pi$
$240$			12.0000i			0.774597i
$241$			5.19615i			0.334714i	0.985896	+	0.167357i	$0.0535232\pi$
$241$			5.19615i			0.334714i	−0.985896	+	0.167357i	$0.946477\pi$
$242$	5.12436	−	19.1244i	0.329406	−	1.22936i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$			6.92820i			0.443533i
$245$	9.52628	+	7.50000i	0.608612	+	0.479157i
$246$	7.68653	−	28.6865i	0.490075	−	1.82899i
$247$		−	3.00000i		−	0.190885i
$248$	5.07180	+	18.9282i	0.322059	+	1.20194i
$249$	13.5000	+	23.3827i	0.855528	+	1.48182i
$250$	4.43782	−	16.5622i	0.280673	−	1.04748i
$251$			13.8564i			0.874609i	0.899314	+	0.437304i	$0.144067\pi$
$251$			13.8564i			0.874609i	−0.899314	+	0.437304i	$0.855933\pi$
$252$	−15.0000	−	5.19615i	−0.944911	−	0.327327i
$253$		−	35.0000i		−	2.20043i
$254$	24.5885	+	6.58846i	1.54282	+	0.413397i
$255$	5.19615			0.325396
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		−	22.5167i		−	1.40455i	−0.711905	−	0.702275i	$-0.752168\pi$
$257$		−	22.5167i		−	1.40455i	0.711905	−	0.702275i	$-0.247832\pi$
$258$	−5.70577	−	21.2942i	−0.355226	−	1.32572i
$259$	2.00000	−	1.73205i	0.124274	−	0.107624i
$260$			6.00000i			0.372104i
$261$			21.0000i			1.29987i
$262$	11.8301	+	3.16987i	0.730868	+	0.195835i
$263$		−	13.0000i		−	0.801614i	−0.916162	−	0.400807i	$-0.868730\pi$
$263$		−	13.0000i		−	0.801614i	0.916162	−	0.400807i	$-0.131270\pi$
$264$	−23.6603	+	6.33975i	−1.45619	+	0.390184i
$265$	16.5000	−	9.52628i	1.01359	−	0.585195i
$266$	2.83013	+	5.83013i	0.173526	+	0.357468i
$267$	−7.50000	−	12.9904i	−0.458993	−	0.794998i
$268$	−13.8564	+	8.00000i	−0.846415	+	0.488678i
$269$	−0.866025	−	1.50000i	−0.0528025	−	0.0914566i	0.838416	−	0.545031i	$-0.183482\pi$
$269$	−0.866025	−	1.50000i	−0.0528025	−	0.0914566i	−0.891219	+	0.453574i	$0.850149\pi$
$270$	12.2942	+	3.29423i	0.748203	+	0.200480i
$271$	7.79423	−	13.5000i	0.473466	−	0.820067i	−0.526073	−	0.850439i	$-0.676336\pi$
$271$	7.79423	−	13.5000i	0.473466	−	0.820067i	0.999539	+	0.0303728i	$0.00966946\pi$
$272$	6.00000	+	3.46410i	0.363803	+	0.210042i
$273$	−7.50000	−	2.59808i	−0.453921	−	0.157243i
$274$	−4.75833	+	17.7583i	−0.287461	+	1.07282i
$275$	10.0000			0.603023
$276$	−21.0000	+	12.1244i	−1.26405	+	0.729800i
$277$			21.0000i			1.26177i	0.775877	+	0.630884i	$0.217308\pi$
$277$			21.0000i			1.26177i	−0.775877	+	0.630884i	$0.782692\pi$
$278$	−5.70577	−	21.2942i	−0.342209	−	1.27714i
$279$	20.7846			1.24434
$280$	−5.66025	−	11.6603i	−0.338265	−	0.696833i
$281$	5.50000	−	9.52628i	0.328102	−	0.568290i	−0.654033	−	0.756466i	$-0.726924\pi$
$281$	5.50000	−	9.52628i	0.328102	−	0.568290i	0.982135	+	0.188176i	$0.0602575\pi$
$282$	8.19615	+	2.19615i	0.488074	+	0.130779i
$283$	−12.0000	−	6.92820i	−0.713326	−	0.411839i	0.0989653	−	0.995091i	$-0.468447\pi$
$283$	−12.0000	−	6.92820i	−0.713326	−	0.411839i	−0.812291	+	0.583252i	$0.801780\pi$
$284$	−10.0000	+	17.3205i	−0.593391	+	1.02778i
$285$	−2.59808	−	4.50000i	−0.153897	−	0.266557i
$286$	−11.8301	+	3.16987i	−0.699530	+	0.187439i
$287$	6.06218	+	31.5000i	0.357839	+	1.85939i
$288$	12.0000	+	12.0000i	0.707107	+	0.707107i
$289$	−7.00000	+	12.1244i	−0.411765	+	0.713197i
$290$	−12.1244	+	12.1244i	−0.711967	+	0.711967i
$291$	1.50000	+	2.59808i	0.0879316	+	0.152302i
$292$	17.3205			1.01361
$293$	0.866025	+	1.50000i	0.0505937	+	0.0876309i	0.890213	−	0.455544i	$-0.150555\pi$
$293$	0.866025	+	1.50000i	0.0505937	+	0.0876309i	−0.839619	+	0.543175i	$0.817222\pi$
$294$	17.0263	−	2.02628i	0.992993	−	0.118175i
$295$	10.3923	+	6.00000i	0.605063	+	0.349334i
$296$	−2.73205	+	0.732051i	−0.158797	+	0.0425496i
$297$			25.9808i			1.50756i
$298$	−15.0263	−	4.02628i	−0.870449	−	0.233236i
$299$	−10.5000	+	6.06218i	−0.607231	+	0.350585i
$300$	−3.46410	−	6.00000i	−0.200000	−	0.346410i
$301$	15.5885	+	18.0000i	0.898504	+	1.03750i
$302$	6.83013	+	1.83013i	0.393030	+	0.105312i
$303$	−2.59808	−	1.50000i	−0.149256	−	0.0861727i
$304$		−	6.92820i		−	0.397360i
$305$	3.00000	+	5.19615i	0.171780	+	0.297531i
$306$	5.19615	−	5.19615i	0.297044	−	0.297044i
$307$			6.92820i			0.395413i	0.980261	+	0.197707i	$0.0633494\pi$
$307$			6.92820i			0.395413i	−0.980261	+	0.197707i	$0.936651\pi$
$308$	20.0000	−	17.3205i	1.13961	−	0.986928i
$309$	7.79423	+	4.50000i	0.443398	+	0.255996i
$310$	12.0000	+	12.0000i	0.681554	+	0.681554i
$311$	10.3923	−	18.0000i	0.589294	−	1.02069i	−0.405032	−	0.914303i	$-0.632739\pi$
$311$	10.3923	−	18.0000i	0.589294	−	1.02069i	0.994325	−	0.106384i	$-0.0339272\pi$
$312$	6.00000	+	6.00000i	0.339683	+	0.339683i
$313$	−9.00000	+	5.19615i	−0.508710	+	0.293704i	−0.732303	−	0.680979i	$-0.761555\pi$
$313$	−9.00000	+	5.19615i	−0.508710	+	0.293704i	0.223593	+	0.974683i	$0.428221\pi$
$314$	−20.7846	−	20.7846i	−1.17294	−	1.17294i
$315$	−13.5000	+	2.59808i	−0.760639	+	0.146385i
$316$	12.0000			0.675053
$317$	12.1244	−	7.00000i	0.680972	−	0.393159i	−0.119249	−	0.992864i	$-0.538049\pi$
$317$	12.1244	−	7.00000i	0.680972	−	0.393159i	0.800221	+	0.599705i	$0.204715\pi$
$318$	6.97372	−	26.0263i	0.391067	−	1.45948i
$319$	−30.3109	−	17.5000i	−1.69708	−	0.979812i
$320$			13.8564i			0.774597i
$321$	7.50000	−	4.33013i	0.418609	−	0.241684i
$322$	14.6865	−	21.6865i	0.818449	−	1.20854i
$323$	−3.00000			−0.166924
$324$	15.5885	−	9.00000i	0.866025	−	0.500000i
$325$	−1.73205	−	3.00000i	−0.0960769	−	0.166410i
$326$	−7.00000	−	7.00000i	−0.387694	−	0.387694i
$327$	8.66025			0.478913
$328$	8.87564	−	33.1244i	0.490075	−	1.82899i
$329$	−9.00000	+	1.73205i	−0.496186	+	0.0954911i
$330$	−15.0000	+	15.0000i	−0.825723	+	0.825723i
$331$	−3.00000	−	5.19615i	−0.164895	−	0.285606i	0.771723	−	0.635959i	$-0.219395\pi$
$331$	−3.00000	−	5.19615i	−0.164895	−	0.285606i	−0.936618	+	0.350352i	$0.886062\pi$
$332$	15.5885	+	27.0000i	0.855528	+	1.48182i
$333$			3.00000i			0.164399i
$334$	−11.8301	+	3.16987i	−0.647316	+	0.173448i
$335$	−6.92820	+	12.0000i	−0.378528	+	0.655630i
$336$	−17.3205	−	6.00000i	−0.944911	−	0.327327i
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	0.962168	−	0.272456i	$-0.0878358\pi$
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	−0.717038	+	0.697034i	$0.754502\pi$
$338$	−10.0000	−	10.0000i	−0.543928	−	0.543928i
$339$		−	1.73205i		−	0.0940721i
$340$	6.00000			0.325396
$341$	−17.3205	+	30.0000i	−0.937958	+	1.62459i
$342$	−7.09808	−	1.90192i	−0.383820	−	0.102844i
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	−6.58846	−	24.5885i	−0.355226	−	1.32572i
$345$	−10.5000	+	18.1865i	−0.565301	+	0.979130i
$346$	4.73205	−	1.26795i	0.254397	−	0.0681654i
$347$	−8.00000	+	13.8564i	−0.429463	+	0.743851i	−0.996826	−	0.0796169i	$-0.974630\pi$
$347$	−8.00000	+	13.8564i	−0.429463	+	0.743851i	0.567363	+	0.823468i	$0.307964\pi$
$348$			24.2487i			1.29987i
$349$	−6.06218	+	10.5000i	−0.324501	+	0.562052i	−0.981411	−	0.191917i	$-0.938530\pi$
$349$	−6.06218	+	10.5000i	−0.324501	+	0.562052i	0.656910	+	0.753969i	$0.271863\pi$
$350$	6.19615	+	4.19615i	0.331198	+	0.224294i
$351$	7.79423	−	4.50000i	0.416025	−	0.240192i
$352$	−27.3205	+	7.32051i	−1.45619	+	0.390184i
$353$			5.19615i			0.276563i	0.990393	+	0.138282i	$0.0441579\pi$
$353$			5.19615i			0.276563i	−0.990393	+	0.138282i	$0.955842\pi$
$354$	16.3923	−	4.39230i	0.871241	−	0.233448i
$355$			17.3205i			0.919277i
$356$	−8.66025	−	15.0000i	−0.458993	−	0.794998i
$357$	−2.59808	+	7.50000i	−0.137505	+	0.396942i
$358$	−15.0263	+	4.02628i	−0.794164	+	0.212795i
$359$	6.06218	+	3.50000i	0.319950	+	0.184723i	0.651370	−	0.758760i	$-0.274195\pi$
$359$	6.06218	+	3.50000i	0.319950	+	0.184723i	−0.331421	+	0.943483i	$0.607528\pi$
$360$	14.1962	+	3.80385i	0.748203	+	0.200480i
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$	1.26795	−	4.73205i	0.0666419	−	0.248711i
$363$	−21.0000	−	12.1244i	−1.10221	−	0.636364i
$364$	−8.66025	−	3.00000i	−0.453921	−	0.157243i
$365$	12.9904	−	7.50000i	0.679948	−	0.392568i
$366$	8.19615	+	2.19615i	0.428420	+	0.114795i
$367$	−36.3731			−1.89866			−0.949329	−	0.314283i	$-0.898236\pi$
$367$	−36.3731			−1.89866			−0.949329	+	0.314283i	$0.898236\pi$
$368$	−24.2487	+	14.0000i	−1.26405	+	0.729800i
$369$	−31.5000	−	18.1865i	−1.63982	−	0.946753i
$370$	−1.73205	+	1.73205i	−0.0900450	+	0.0900450i
$371$	5.50000	+	28.5788i	0.285546	+	1.48374i
$372$	24.0000			1.24434
$373$			3.00000i			0.155334i	0.996979	+	0.0776671i	$0.0247471\pi$
$373$			3.00000i			0.155334i	−0.996979	+	0.0776671i	$0.975253\pi$
$374$	3.16987	+	11.8301i	0.163910	+	0.611721i
$375$	−18.1865	−	10.5000i	−0.939149	−	0.542218i
$376$	9.46410	+	2.53590i	0.488074	+	0.130779i
$377$			12.1244i			0.624436i
$378$	−10.9019	+	16.0981i	−0.560734	+	0.827996i
$379$	18.0000			0.924598			0.462299	−	0.886724i	$-0.347025\pi$
$379$	18.0000			0.924598			0.462299	+	0.886724i	$0.347025\pi$
$380$	−3.00000	−	5.19615i	−0.153897	−	0.266557i
$381$	15.5885	−	27.0000i	0.798621	−	1.38325i
$382$	5.12436	+	19.1244i	0.262185	+	0.978487i
$383$	−36.3731			−1.85858			−0.929288	−	0.369355i	$-0.879579\pi$
$383$	−36.3731			−1.85858			−0.929288	+	0.369355i	$0.879579\pi$
$384$	13.8564	+	13.8564i	0.707107	+	0.707107i
$385$	7.50000	−	21.6506i	0.382235	−	1.10342i
$386$	−6.00000	−	6.00000i	−0.305392	−	0.305392i
$387$	−27.0000			−1.37249
$388$	1.73205	+	3.00000i	0.0879316	+	0.152302i
$389$			1.00000i			0.0507020i	0.999679	+	0.0253510i	$0.00807034\pi$
$389$			1.00000i			0.0507020i	−0.999679	+	0.0253510i	$0.991930\pi$
$390$	7.09808	+	1.90192i	0.359425	+	0.0963077i
$391$	6.06218	+	10.5000i	0.306578	+	0.531008i
$392$	19.6603	−	2.33975i	0.992993	−	0.118175i
$393$	7.50000	−	12.9904i	0.378325	−	0.655278i
$394$	−10.9282	−	2.92820i	−0.550555	−	0.147521i
$395$	9.00000	−	5.19615i	0.452839	−	0.261447i
$396$			30.0000i			1.50756i
$397$	16.4545	−	28.5000i	0.825827	−	1.43037i	−0.0754589	−	0.997149i	$-0.524042\pi$
$397$	16.4545	−	28.5000i	0.825827	−	1.43037i	0.901286	−	0.433225i	$-0.142624\pi$
$398$	11.8301	−	3.16987i	0.592991	−	0.158891i
$399$	7.79423	−	1.50000i	0.390199	−	0.0750939i
$400$	−4.00000	−	6.92820i	−0.200000	−	0.346410i
$401$	25.0000			1.24844			0.624220	−	0.781248i	$-0.285417\pi$
$401$	25.0000			1.24844			0.624220	+	0.781248i	$0.285417\pi$
$402$	5.07180	+	18.9282i	0.252958	+	0.944053i
$403$	12.0000			0.597763
$404$	−3.00000	−	1.73205i	−0.149256	−	0.0861727i
$405$	7.79423	−	13.5000i	0.387298	−	0.670820i
$406$	−11.4378	−	23.5622i	−0.567650	−	1.16937i
$407$	−4.33013	−	2.50000i	−0.214636	−	0.123920i
$408$	6.00000	−	6.00000i	0.297044	−	0.297044i
$409$	−27.0000	−	15.5885i	−1.33506	−	0.770800i	−0.348993	−	0.937125i	$-0.613476\pi$
$409$	−27.0000	−	15.5885i	−1.33506	−	0.770800i	−0.986071	+	0.166326i	$0.946810\pi$
$410$	−7.68653	−	28.6865i	−0.379611	−	1.41673i
$411$	19.5000	+	11.2583i	0.961864	+	0.555332i
$412$	9.00000	+	5.19615i	0.443398	+	0.255996i
$413$	−13.8564	+	12.0000i	−0.681829	+	0.590481i
$414$	7.68653	+	28.6865i	0.377773	+	1.40987i
$415$	23.3827	+	13.5000i	1.14781	+	0.662689i
$416$	6.92820	+	6.92820i	0.339683	+	0.339683i
$417$	−27.0000			−1.32220
$418$	8.66025	−	8.66025i	0.423587	−	0.423587i
$419$	−1.50000	+	0.866025i	−0.0732798	+	0.0423081i	−0.536192	−	0.844096i	$-0.680138\pi$
$419$	−1.50000	+	0.866025i	−0.0732798	+	0.0423081i	0.462912	+	0.886404i	$0.346804\pi$
$420$	−15.5885	+	3.00000i	−0.760639	+	0.146385i
$421$	−12.9904	−	7.50000i	−0.633112	−	0.365528i	0.148844	−	0.988861i	$-0.452445\pi$
$421$	−12.9904	−	7.50000i	−0.633112	−	0.365528i	−0.781956	+	0.623333i	$0.785778\pi$
$422$	12.2942	−	3.29423i	0.598474	−	0.160361i
$423$	5.19615	−	9.00000i	0.252646	−	0.437595i
$424$	8.05256	−	30.0526i	0.391067	−	1.45948i
$425$	−3.00000	+	1.73205i	−0.145521	+	0.0840168i
$426$	17.3205	+	17.3205i	0.839181	+	0.839181i
$427$	−9.00000	+	1.73205i	−0.435541	+	0.0838198i
$428$	8.66025	−	5.00000i	0.418609	−	0.241684i
$429$			15.0000i			0.724207i
$430$	−15.5885	−	15.5885i	−0.751742	−	0.751742i
$431$	4.33013	−	2.50000i	0.208575	−	0.120421i	−0.392074	−	0.919934i	$-0.628242\pi$
$431$	4.33013	−	2.50000i	0.208575	−	0.120421i	0.600649	+	0.799513i	$0.294909\pi$
$432$	18.0000	−	10.3923i	0.866025	−	0.500000i
$433$			31.1769i			1.49827i	0.662419	+	0.749133i	$0.269530\pi$
$433$			31.1769i			1.49827i	−0.662419	+	0.749133i	$0.730470\pi$
$434$	−23.3205	+	11.3205i	−1.11942	+	0.543402i
$435$	10.5000	+	18.1865i	0.503436	+	0.871978i
$436$	10.0000			0.478913
$437$	6.06218	−	10.5000i	0.289993	−	0.502283i
$438$	5.49038	−	20.4904i	0.262341	−	0.979068i
$439$	−13.8564	−	24.0000i	−0.661330	−	1.14546i	−0.980266	−	0.197681i	$-0.936659\pi$
$439$	−13.8564	−	24.0000i	−0.661330	−	1.14546i	0.318936	−	0.947776i	$-0.396674\pi$
$440$	−17.3205	+	17.3205i	−0.825723	+	0.825723i
$441$	3.00000	−	20.7846i	0.142857	−	0.989743i
$442$	3.00000	−	3.00000i	0.142695	−	0.142695i
$443$	−13.0000	−	22.5167i	−0.617649	−	1.06980i	−0.989914	−	0.141672i	$-0.954752\pi$
$443$	−13.0000	−	22.5167i	−0.617649	−	1.06980i	0.372265	−	0.928126i	$-0.378581\pi$
$444$			3.46410i			0.164399i
$445$	−12.9904	−	7.50000i	−0.615803	−	0.355534i
$446$	12.1244	+	12.1244i	0.574105	+	0.574105i
$447$	−9.52628	+	16.5000i	−0.450578	+	0.780423i
$448$	−20.0000	−	6.92820i	−0.944911	−	0.327327i
$449$	22.0000			1.03824			0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000			1.03824			0.519122	+	0.854700i	$0.326259\pi$
$450$	−8.19615	+	2.19615i	−0.386370	+	0.103528i
$451$	52.5000	−	30.3109i	2.47213	−	1.42728i
$452$		−	2.00000i		−	0.0940721i
$453$	4.33013	−	7.50000i	0.203447	−	0.352381i
$454$	26.0263	+	6.97372i	1.22147	+	0.327293i
$455$	−7.79423	+	1.50000i	−0.365399	+	0.0703211i
$456$	−8.19615	−	2.19615i	−0.383820	−	0.102844i
$457$	−12.0000	−	20.7846i	−0.561336	−	0.972263i	−0.997380	−	0.0723376i	$-0.976954\pi$
$457$	−12.0000	−	20.7846i	−0.561336	−	0.972263i	0.436044	−	0.899925i	$-0.356379\pi$
$458$	−4.43782	+	16.5622i	−0.207366	+	0.773900i
$459$	−4.50000	−	7.79423i	−0.210042	−	0.363803i
$460$	−12.1244	+	21.0000i	−0.565301	+	0.979130i
$461$	2.59808	−	4.50000i	0.121004	−	0.209586i	−0.799160	−	0.601119i	$-0.794722\pi$
$461$	2.59808	−	4.50000i	0.121004	−	0.209586i	0.920164	+	0.391533i	$0.128055\pi$
$462$	−14.1506	−	29.1506i	−0.658347	−	1.35621i
$463$	−7.79423	+	4.50000i	−0.362229	+	0.209133i	−0.670058	−	0.742309i	$-0.733731\pi$
$463$	−7.79423	+	4.50000i	−0.362229	+	0.209133i	0.307829	+	0.951442i	$0.400397\pi$
$464$			28.0000i			1.29987i
$465$	18.0000	−	10.3923i	0.834730	−	0.481932i
$466$	−11.0000	−	11.0000i	−0.509565	−	0.509565i
$467$	7.50000	+	4.33013i	0.347059	+	0.200374i	0.663389	−	0.748275i	$-0.269117\pi$
$467$	7.50000	+	4.33013i	0.347059	+	0.200374i	−0.316330	+	0.948649i	$0.602451\pi$
$468$	9.00000	−	5.19615i	0.416025	−	0.240192i
$469$	−13.8564	−	16.0000i	−0.639829	−	0.738811i
$470$	8.19615	−	2.19615i	0.378060	−	0.101301i
$471$	−31.1769	+	18.0000i	−1.43656	+	0.829396i
$472$	18.9282	−	5.07180i	0.871241	−	0.233448i
$473$	22.5000	−	38.9711i	1.03455	−	1.79190i
$474$	3.80385	−	14.1962i	0.174717	−	0.652051i
$475$	3.00000	+	1.73205i	0.137649	+	0.0794719i
$476$	−3.00000	+	8.66025i	−0.137505	+	0.396942i
$477$	−28.5788	−	16.5000i	−1.30854	−	0.755483i
$478$	−1.83013	−	6.83013i	−0.0837081	−	0.312403i
$479$	−1.73205			−0.0791394			−0.0395697	−	0.999217i	$-0.512599\pi$
$479$	−1.73205			−0.0791394			−0.0395697	+	0.999217i	$0.512599\pi$
$480$	16.3923	+	4.39230i	0.748203	+	0.200480i
$481$			1.73205i			0.0789747i
$482$	7.09808	+	1.90192i	0.323309	+	0.0866303i
$483$	−21.0000	−	24.2487i	−0.955533	−	1.10335i
$484$	−24.2487	−	14.0000i	−1.10221	−	0.636364i
$485$	2.59808	+	1.50000i	0.117973	+	0.0681115i
$486$	−5.70577	−	21.2942i	−0.258819	−	0.965926i
$487$	−19.9186	+	11.5000i	−0.902597	+	0.521115i	−0.878042	−	0.478584i	$-0.841150\pi$
$487$	−19.9186	+	11.5000i	−0.902597	+	0.521115i	−0.0245553	+	0.999698i	$0.507817\pi$
$488$	9.46410	+	2.53590i	0.428420	+	0.114795i
$489$	−10.5000	+	6.06218i	−0.474826	+	0.274141i
$490$	13.7321	−	10.2679i	0.620351	−	0.463859i
$491$	−18.5000	−	32.0429i	−0.834893	−	1.44608i	−0.894117	−	0.447833i	$-0.852196\pi$
$491$	−18.5000	−	32.0429i	−0.834893	−	1.44608i	0.0592240	−	0.998245i	$-0.481137\pi$
$492$	−36.3731	−	21.0000i	−1.63982	−	0.946753i
$493$	12.1244			0.546054
$494$	−4.09808	−	1.09808i	−0.184381	−	0.0494048i
$495$	12.9904	+	22.5000i	0.583874	+	1.01130i
$496$	27.7128			1.24434
$497$	−25.0000	−	8.66025i	−1.12140	−	0.388465i
$498$	36.8827	−	9.88269i	1.65275	−	0.442854i
$499$	−15.0000			−0.671492			−0.335746	−	0.941953i	$-0.608988\pi$
$499$	−15.0000			−0.671492			−0.335746	+	0.941953i	$0.608988\pi$
$500$	−21.0000	−	12.1244i	−0.939149	−	0.542218i
$501$			15.0000i			0.670151i
$502$	18.9282	+	5.07180i	0.844807	+	0.226365i
$503$	−6.92820			−0.308913			−0.154457	−	0.988000i	$-0.549363\pi$
$503$	−6.92820			−0.308913			−0.154457	+	0.988000i	$0.549363\pi$
$504$	−12.5885	+	18.5885i	−0.560734	+	0.827996i
$505$	−3.00000			−0.133498
$506$	−47.8109	−	12.8109i	−2.12545	−	0.569513i
$507$	−15.0000	+	8.66025i	−0.666173	+	0.384615i
$508$	18.0000	−	31.1769i	0.798621	−	1.38325i
$509$	32.9090			1.45866			0.729332	−	0.684160i	$-0.239831\pi$
$509$	32.9090			1.45866			0.729332	+	0.684160i	$0.239831\pi$
$510$	1.90192	−	7.09808i	0.0842186	−	0.314308i
$511$	4.33013	+	22.5000i	0.191554	+	0.995341i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−4.50000	+	7.79423i	−0.198680	+	0.344124i
$514$	−30.7583	−	8.24167i	−1.35669	−	0.363524i
$515$	9.00000			0.396587
$516$	−31.1769			−1.37249
$517$	8.66025	+	15.0000i	0.380878	+	0.659699i
$518$	−1.63397	−	3.36603i	−0.0717927	−	0.147895i
$519$		−	6.00000i		−	0.263371i
$520$	8.19615	+	2.19615i	0.359425	+	0.0963077i
$521$	−4.50000	+	2.59808i	−0.197149	+	0.113824i	−0.595325	−	0.803485i	$-0.702977\pi$
$521$	−4.50000	+	2.59808i	−0.197149	+	0.113824i	0.398176	+	0.917309i	$0.369643\pi$
$522$	28.6865	+	7.68653i	1.25558	+	0.336430i
$523$	10.5000	+	6.06218i	0.459133	+	0.265081i	0.711680	−	0.702504i	$-0.247935\pi$
$523$	10.5000	+	6.06218i	0.459133	+	0.265081i	−0.252547	+	0.967585i	$0.581268\pi$
$524$	8.66025	−	15.0000i	0.378325	−	0.655278i
$525$	6.92820	−	6.00000i	0.302372	−	0.261861i
$526$	−17.7583	−	4.75833i	−0.774300	−	0.207473i
$527$		−	12.0000i		−	0.522728i
$528$			34.6410i			1.50756i
$529$	−26.0000			−1.13043
$530$	−6.97372	−	26.0263i	−0.302919	−	1.13051i
$531$		−	20.7846i		−	0.901975i
$532$	9.00000	−	1.73205i	0.390199	−	0.0750939i
$533$	−18.1865	−	10.5000i	−0.787746	−	0.454805i
$534$	−20.4904	+	5.49038i	−0.886706	+	0.237592i
$535$	4.33013	−	7.50000i	0.187208	−	0.324253i
$536$	5.85641	+	21.8564i	0.252958	+	0.944053i
$537$			19.0526i			0.822179i
$538$	−2.36603	+	0.633975i	−0.102007	+	0.0273326i
$539$	27.5000	+	21.6506i	1.18451	+	0.932559i
$540$	9.00000	−	15.5885i	0.387298	−	0.670820i
$541$	−2.59808	−	1.50000i	−0.111700	−	0.0644900i	0.443109	−	0.896468i	$-0.353875\pi$
$541$	−2.59808	−	1.50000i	−0.111700	−	0.0644900i	−0.554809	+	0.831978i	$0.687209\pi$
$542$	−15.5885	−	15.5885i	−0.669582	−	0.669582i
$543$	−5.19615	−	3.00000i	−0.222988	−	0.128742i
$544$	6.92820	−	6.92820i	0.297044	−	0.297044i
$545$	7.50000	−	4.33013i	0.321265	−	0.185482i
$546$	−6.29423	+	9.29423i	−0.269368	+	0.397756i
$547$	−18.5000	+	32.0429i	−0.791003	+	1.37006i	0.134344	+	0.990935i	$0.457107\pi$
$547$	−18.5000	+	32.0429i	−0.791003	+	1.37006i	−0.925347	+	0.379122i	$0.876226\pi$
$548$	22.5167	+	13.0000i	0.961864	+	0.555332i
$549$	5.19615	−	9.00000i	0.221766	−	0.384111i
$550$	3.66025	−	13.6603i	0.156074	−	0.582475i
$551$	−6.06218	−	10.5000i	−0.258257	−	0.447315i
$552$	8.87564	+	33.1244i	0.377773	+	1.40987i
$553$	3.00000	+	15.5885i	0.127573	+	0.662889i
$554$	28.6865	+	7.68653i	1.21877	+	0.326570i
$555$	1.50000	+	2.59808i	0.0636715	+	0.110282i
$556$	−31.1769			−1.32220
$557$	40.7032	−	23.5000i	1.72465	−	0.995727i	0.816152	−	0.577838i	$-0.196103\pi$
$557$	40.7032	−	23.5000i	1.72465	−	0.995727i	0.908498	−	0.417889i	$-0.137230\pi$
$558$	7.60770	−	28.3923i	0.322059	−	1.20194i
$559$	−15.5885			−0.659321
$560$	−18.0000	+	3.46410i	−0.760639	+	0.146385i
$561$	15.0000			0.633300
$562$	−11.0000	−	11.0000i	−0.464007	−	0.464007i
$563$	3.00000	+	1.73205i	0.126435	+	0.0729972i	0.561884	−	0.827216i	$-0.310077\pi$
$563$	3.00000	+	1.73205i	0.126435	+	0.0729972i	−0.435449	+	0.900214i	$0.643410\pi$
$564$	6.00000	−	10.3923i	0.252646	−	0.437595i
$565$	−0.866025	−	1.50000i	−0.0364340	−	0.0631055i
$566$	−13.8564	+	13.8564i	−0.582428	+	0.582428i
$567$	15.5885	+	18.0000i	0.654654	+	0.755929i
$568$	20.0000	+	20.0000i	0.839181	+	0.839181i
$569$	−10.0000	−	17.3205i	−0.419222	−	0.726113i	0.576640	−	0.816999i	$-0.304364\pi$
$569$	−10.0000	−	17.3205i	−0.419222	−	0.726113i	−0.995861	+	0.0908852i	$0.971030\pi$
$570$	−7.09808	+	1.90192i	−0.297306	+	0.0796628i
$571$	−13.0000	+	22.5167i	−0.544033	+	0.942293i	0.454634	+	0.890678i	$0.349770\pi$
$571$	−13.0000	+	22.5167i	−0.544033	+	0.942293i	−0.998667	+	0.0516146i	$0.983563\pi$
$572$			17.3205i			0.724207i
$573$	24.2487			1.01300
$574$	45.2487	+	3.24871i	1.88864	+	0.135599i
$575$		−	14.0000i		−	0.583840i
$576$	20.7846	−	12.0000i	0.866025	−	0.500000i
$577$	−28.5000	+	16.4545i	−1.18647	+	0.685009i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−28.5000	+	16.4545i	−1.18647	+	0.685009i	−0.228968	+	0.973434i	$0.573535\pi$
$578$	14.0000	+	14.0000i	0.582323	+	0.582323i
$579$	−9.00000	+	5.19615i	−0.374027	+	0.215945i
$580$	12.1244	+	21.0000i	0.503436	+	0.871978i
$581$	−31.1769	+	27.0000i	−1.29344	+	1.12015i
$582$	4.09808	−	1.09808i	0.169871	−	0.0455167i
$583$	47.6314	−	27.5000i	1.97269	−	1.13893i
$584$	6.33975	−	23.6603i	0.262341	−	0.979068i
$585$	4.50000	−	7.79423i	0.186052	−	0.322252i
$586$	2.36603	−	0.633975i	0.0977396	−	0.0261892i
$587$	−7.50000	−	4.33013i	−0.309558	−	0.178723i	0.337171	−	0.941444i	$-0.390530\pi$
$587$	−7.50000	−	4.33013i	−0.309558	−	0.178723i	−0.646729	+	0.762720i	$0.723863\pi$
$588$	3.46410	−	24.0000i	0.142857	−	0.989743i
$589$	−10.3923	+	6.00000i	−0.428207	+	0.247226i
$590$	12.0000	−	12.0000i	0.494032	−	0.494032i
$591$	−6.92820	+	12.0000i	−0.284988	+	0.493614i
$592$			4.00000i			0.164399i
$593$	−25.5000	−	14.7224i	−1.04716	−	0.604578i	−0.125307	−	0.992118i	$-0.539991\pi$
$593$	−25.5000	−	14.7224i	−1.04716	−	0.604578i	−0.921853	+	0.387540i	$0.873325\pi$
$594$	35.4904	+	9.50962i	1.45619	+	0.390184i
$595$	1.50000	+	7.79423i	0.0614940	+	0.319532i
$596$	−11.0000	+	19.0526i	−0.450578	+	0.780423i
$597$		−	15.0000i		−	0.613909i
$598$	4.43782	+	16.5622i	0.181476	+	0.677278i
$599$	38.1051	+	22.0000i	1.55693	+	0.898896i	0.997548	+	0.0699877i	$0.0222960\pi$
$599$	38.1051	+	22.0000i	1.55693	+	0.898896i	0.559385	+	0.828908i	$0.311037\pi$
$600$	−9.46410	+	2.53590i	−0.386370	+	0.103528i
$601$	7.50000	+	4.33013i	0.305931	+	0.176630i	0.645104	−	0.764094i	$-0.276814\pi$
$601$	7.50000	+	4.33013i	0.305931	+	0.176630i	−0.339173	+	0.940724i	$0.610147\pi$
$602$	30.2942	−	14.7058i	1.23470	−	0.599362i
$603$	24.0000			0.977356
$604$	5.00000	−	8.66025i	0.203447	−	0.352381i
$605$	−24.2487			−0.985850
$606$	−3.00000	+	3.00000i	−0.121867	+	0.121867i
$607$	36.3731			1.47634			0.738169	−	0.674616i	$-0.235691\pi$
$607$	36.3731			1.47634			0.738169	+	0.674616i	$0.235691\pi$
$608$	−9.46410	−	2.53590i	−0.383820	−	0.102844i
$609$	−31.5000	+	6.06218i	−1.27644	+	0.245652i
$610$	8.19615	−	2.19615i	0.331853	−	0.0889196i
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$	−5.19615	−	9.00000i	−0.210042	−	0.363803i
$613$	−18.1865	+	10.5000i	−0.734547	+	0.424091i	−0.820083	−	0.572244i	$-0.806073\pi$
$613$	−18.1865	+	10.5000i	−0.734547	+	0.424091i	0.0855362	+	0.996335i	$0.472740\pi$
$614$	9.46410	+	2.53590i	0.381940	+	0.102341i
$615$	−36.3731			−1.46670
$616$	−16.3397	−	33.6603i	−0.658347	−	1.35621i
$617$	−11.5000	−	19.9186i	−0.462973	−	0.801892i	0.536135	−	0.844132i	$-0.319884\pi$
$617$	−11.5000	−	19.9186i	−0.462973	−	0.801892i	−0.999107	+	0.0422403i	$0.986550\pi$
$618$	9.00000	−	9.00000i	0.362033	−	0.362033i
$619$			32.9090i			1.32272i	0.750067	+	0.661361i	$0.230021\pi$
$619$			32.9090i			1.32272i	−0.750067	+	0.661361i	$0.769979\pi$
$620$	20.7846	−	12.0000i	0.834730	−	0.481932i
$621$	36.3731			1.45960
$622$	−20.7846	−	20.7846i	−0.833387	−	0.833387i
$623$	17.3205	−	15.0000i	0.693932	−	0.600962i
$624$	10.3923	−	6.00000i	0.416025	−	0.240192i
$625$	−11.0000			−0.440000
$626$	3.80385	+	14.1962i	0.152032	+	0.567392i
$627$	−7.50000	−	12.9904i	−0.299521	−	0.518786i
$628$	−36.0000	+	20.7846i	−1.43656	+	0.829396i
$629$	1.73205			0.0690614
$630$	−1.39230	+	19.3923i	−0.0554708	+	0.772608i
$631$			42.0000i			1.67199i	0.548734	+	0.835997i	$0.315110\pi$
$631$			42.0000i			1.67199i	−0.548734	+	0.835997i	$0.684890\pi$
$632$	4.39230	−	16.3923i	0.174717	−	0.652051i
$633$		−	15.5885i		−	0.619586i
$634$	−5.12436	−	19.1244i	−0.203514	−	0.759525i
$635$		−	31.1769i		−	1.23722i
$636$	−33.0000	−	19.0526i	−1.30854	−	0.755483i
$637$	1.73205	−	12.0000i	0.0686264	−	0.475457i
$638$	−35.0000	+	35.0000i	−1.38566	+	1.38566i
$639$	25.9808	−	15.0000i	1.02778	−	0.593391i
$640$	18.9282	+	5.07180i	0.748203	+	0.200480i
$641$	11.0000			0.434474			0.217237	−	0.976119i	$-0.430296\pi$
$641$	11.0000			0.434474			0.217237	+	0.976119i	$0.430296\pi$
$642$	−3.16987	−	11.8301i	−0.125105	−	0.466898i
$643$	−10.5000	+	6.06218i	−0.414080	+	0.239069i	−0.692541	−	0.721378i	$-0.743509\pi$
$643$	−10.5000	+	6.06218i	−0.414080	+	0.239069i	0.278462	+	0.960447i	$0.410176\pi$
$644$	−24.2487	−	28.0000i	−0.955533	−	1.10335i
$645$	−23.3827	+	13.5000i	−0.920692	+	0.531562i
$646$	−1.09808	+	4.09808i	−0.0432032	+	0.161237i
$647$	−16.4545	−	28.5000i	−0.646892	−	1.12045i	−0.983861	−	0.178935i	$-0.942735\pi$
$647$	−16.4545	−	28.5000i	−0.646892	−	1.12045i	0.336968	−	0.941516i	$-0.390598\pi$
$648$	−6.58846	−	24.5885i	−0.258819	−	0.965926i
$649$	30.0000	+	17.3205i	1.17760	+	0.679889i
$650$	−4.73205	+	1.26795i	−0.185606	+	0.0497331i
$651$	6.00000	+	31.1769i	0.235159	+	1.22192i
$652$	−12.1244	+	7.00000i	−0.474826	+	0.274141i
$653$		−	13.0000i		−	0.508729i	−0.967108	−	0.254365i	$-0.918134\pi$
$653$		−	13.0000i		−	0.508729i	0.967108	−	0.254365i	$-0.0818663\pi$
$654$	3.16987	−	11.8301i	0.123952	−	0.462595i
$655$		−	15.0000i		−	0.586098i
$656$	−42.0000	−	24.2487i	−1.63982	−	0.946753i
$657$	−22.5000	−	12.9904i	−0.877809	−	0.506803i
$658$	−0.928203	+	12.9282i	−0.0361851	+	0.503994i
$659$	−2.50000	+	4.33013i	−0.0973862	+	0.168678i	−0.910602	−	0.413284i	$-0.864382\pi$
$659$	−2.50000	+	4.33013i	−0.0973862	+	0.168678i	0.813216	+	0.581962i	$0.197715\pi$
$660$	15.0000	+	25.9808i	0.583874	+	1.01130i
$661$	1.73205	−	3.00000i	0.0673690	−	0.116686i	−0.830373	−	0.557207i	$-0.811873\pi$
$661$	1.73205	−	3.00000i	0.0673690	−	0.116686i	0.897742	+	0.440521i	$0.145206\pi$
$662$	−8.19615	+	2.19615i	−0.318553	+	0.0853559i
$663$	−2.59808	−	4.50000i	−0.100901	−	0.174766i
$664$	42.5885	−	11.4115i	1.65275	−	0.442854i
$665$	6.00000	−	5.19615i	0.232670	−	0.201498i
$666$	4.09808	+	1.09808i	0.158797	+	0.0425496i
$667$	−24.5000	+	42.4352i	−0.948644	+	1.64310i
$668$			17.3205i			0.670151i
$669$	18.1865	−	10.5000i	0.703132	−	0.405953i
$670$	13.8564	+	13.8564i	0.535320	+	0.535320i
$671$	8.66025	+	15.0000i	0.334325	+	0.579069i
$672$	−14.5359	+	21.4641i	−0.560734	+	0.827996i
$673$	7.50000	−	12.9904i	0.289104	−	0.500742i	−0.684492	−	0.729020i	$-0.739976\pi$
$673$	7.50000	−	12.9904i	0.289104	−	0.500742i	0.973596	+	0.228278i	$0.0733094\pi$
$674$	12.2942	−	3.29423i	0.473556	−	0.126889i
$675$			10.3923i			0.400000i
$676$	−17.3205	+	10.0000i	−0.666173	+	0.384615i
$677$	10.3923	+	18.0000i	0.399409	+	0.691796i	0.993653	−	0.112488i	$-0.0358821\pi$
$677$	10.3923	+	18.0000i	0.399409	+	0.691796i	−0.594244	+	0.804285i	$0.702549\pi$
$678$	−2.36603	−	0.633975i	−0.0908667	−	0.0243476i
$679$	−3.46410	+	3.00000i	−0.132940	+	0.115129i
$680$	2.19615	−	8.19615i	0.0842186	−	0.314308i
$681$	16.5000	−	28.5788i	0.632281	−	1.09514i
$682$	34.6410	+	34.6410i	1.32647	+	1.32647i
$683$	−0.500000	−	0.866025i	−0.0191320	−	0.0331375i	0.856301	−	0.516477i	$-0.172757\pi$
$683$	−0.500000	−	0.866025i	−0.0191320	−	0.0331375i	−0.875433	+	0.483340i	$0.839424\pi$
$684$	−5.19615	+	9.00000i	−0.198680	+	0.344124i
$685$	22.5167			0.860317
$686$	7.95448	+	24.9545i	0.303704	+	0.952767i
$687$	18.1865	+	10.5000i	0.693860	+	0.400600i
$688$	−36.0000			−1.37249
$689$	−16.5000	−	9.52628i	−0.628600	−	0.362922i
$690$	21.0000	+	21.0000i	0.799456	+	0.799456i
$691$	33.0000	−	19.0526i	1.25538	−	0.724793i	0.283206	−	0.959059i	$-0.408602\pi$
$691$	33.0000	−	19.0526i	1.25538	−	0.724793i	0.972173	+	0.234265i	$0.0752685\pi$
$692$		−	6.92820i		−	0.263371i
$693$	−38.9711	+	7.50000i	−1.48039	+	0.284901i
$694$	16.0000	+	16.0000i	0.607352	+	0.607352i
$695$	−23.3827	+	13.5000i	−0.886956	+	0.512084i
$696$	33.1244	+	8.87564i	1.25558	+	0.336430i
$697$	−10.5000	+	18.1865i	−0.397716	+	0.688864i
$698$	12.1244	+	12.1244i	0.458914	+	0.458914i
$699$	−16.5000	+	9.52628i	−0.624087	+	0.360317i
$700$	8.00000	−	6.92820i	0.302372	−	0.261861i
$701$		−	44.0000i		−	1.66186i	−0.556379	−	0.830929i	$-0.687810\pi$
$701$		−	44.0000i		−	1.66186i	0.556379	−	0.830929i	$-0.312190\pi$
$702$	−3.29423	−	12.2942i	−0.124333	−	0.464016i
$703$	−0.866025	−	1.50000i	−0.0326628	−	0.0565736i
$704$			40.0000i			1.50756i
$705$		−	10.3923i		−	0.391397i
$706$	7.09808	+	1.90192i	0.267140	+	0.0715798i
$707$	1.50000	−	4.33013i	0.0564133	−	0.162851i
$708$		−	24.0000i		−	0.901975i
$709$	45.0333	−	26.0000i	1.69126	−	0.976450i	0.737760	−	0.675063i	$-0.235884\pi$
$709$	45.0333	−	26.0000i	1.69126	−	0.976450i	0.953502	−	0.301388i	$-0.0974498\pi$
$710$	23.6603	+	6.33975i	0.887954	+	0.237926i
$711$	−15.5885	−	9.00000i	−0.584613	−	0.337526i
$712$	−23.6603	+	6.33975i	−0.886706	+	0.237592i
$713$	42.0000	+	24.2487i	1.57291	+	0.908121i
$714$	9.29423	+	6.29423i	0.347828	+	0.235556i
$715$	7.50000	+	12.9904i	0.280484	+	0.485813i
$716$			22.0000i			0.822179i
$717$	−8.66025			−0.323423
$718$	7.00000	−	7.00000i	0.261238	−	0.261238i
$719$	−23.3827	+	40.5000i	−0.872027	+	1.51040i	−0.0121307	+	0.999926i	$0.503861\pi$
$719$	−23.3827	+	40.5000i	−0.872027	+	1.51040i	−0.859896	+	0.510469i	$0.829472\pi$
$720$	10.3923	−	18.0000i	0.387298	−	0.670820i
$721$	−4.50000	+	12.9904i	−0.167589	+	0.483787i
$722$	−21.8564	+	5.85641i	−0.813411	+	0.217953i
$723$	4.50000	−	7.79423i	0.167357	−	0.289870i
$724$	−6.00000	−	3.46410i	−0.222988	−	0.128742i
$725$	−12.1244	−	7.00000i	−0.450287	−	0.259973i
$726$	−24.2487	+	24.2487i	−0.899954	+	0.899954i
$727$	−16.4545	+	28.5000i	−0.610263	+	1.05701i	0.380933	+	0.924603i	$0.375603\pi$
$727$	−16.4545	+	28.5000i	−0.610263	+	1.05701i	−0.991196	+	0.132404i	$0.957730\pi$
$728$	−7.26795	+	10.7321i	−0.269368	+	0.397756i
$729$	−27.0000			−1.00000
$730$	−5.49038	−	20.4904i	−0.203208	−	0.758383i
$731$			15.5885i			0.576560i
$732$	6.00000	−	10.3923i	0.221766	−	0.384111i
$733$	8.66025			0.319874			0.159937	−	0.987127i	$-0.448871\pi$
$733$	8.66025			0.319874			0.159937	+	0.987127i	$0.448871\pi$
$734$	−13.3135	+	49.6865i	−0.491409	+	1.83396i
$735$	−7.79423	−	19.5000i	−0.287494	−	0.719268i
$736$	10.2487	+	38.2487i	0.377773	+	1.40987i
$737$	−20.0000	+	34.6410i	−0.736709	+	1.27602i
$738$	−36.3731	+	36.3731i	−1.33891	+	1.33891i
$739$	11.5000	+	19.9186i	0.423034	+	0.732717i	0.996235	−	0.0866983i	$-0.0276316\pi$
$739$	11.5000	+	19.9186i	0.423034	+	0.732717i	−0.573200	+	0.819415i	$0.694298\pi$
$740$	1.73205	+	3.00000i	0.0636715	+	0.110282i
$741$	−2.59808	+	4.50000i	−0.0954427	+	0.165312i
$742$	41.0526	+	2.94744i	1.50709	+	0.108204i
$743$	−16.4545	+	9.50000i	−0.603656	+	0.348521i	−0.770479	−	0.637466i	$-0.779983\pi$
$743$	−16.4545	+	9.50000i	−0.603656	+	0.348521i	0.166822	+	0.985987i	$0.446649\pi$
$744$	8.78461	−	32.7846i	0.322059	−	1.20194i
$745$			19.0526i			0.698032i
$746$	4.09808	+	1.09808i	0.150041	+	0.0402034i
$747$		−	46.7654i		−	1.71106i
$748$	17.3205			0.633300
$749$	8.66025	+	10.0000i	0.316439	+	0.365392i
$750$	−21.0000	+	21.0000i	−0.766812	+	0.766812i
$751$		−	47.0000i		−	1.71505i	−0.514439	−	0.857527i	$-0.672000\pi$
$751$		−	47.0000i		−	1.71505i	0.514439	−	0.857527i	$-0.328000\pi$
$752$	6.92820	−	12.0000i	0.252646	−	0.437595i
$753$	12.0000	−	20.7846i	0.437304	−	0.757433i
$754$	16.5622	+	4.43782i	0.603159	+	0.161616i
$755$		−	8.66025i		−	0.315179i
$756$	18.0000	+	20.7846i	0.654654	+	0.755929i
$757$			26.0000i			0.944986i	0.881334	+	0.472493i	$0.156646\pi$
$757$			26.0000i			0.944986i	−0.881334	+	0.472493i	$0.843354\pi$
$758$	6.58846	−	24.5885i	0.239304	−	0.893093i
$759$	−30.3109	+	52.5000i	−1.10022	+	1.90563i
$760$	−8.19615	+	2.19615i	−0.297306	+	0.0796628i
$761$			43.3013i			1.56967i	0.619705	+	0.784835i	$0.287252\pi$
$761$			43.3013i			1.56967i	−0.619705	+	0.784835i	$0.712748\pi$
$762$	−31.1769	−	31.1769i	−1.12942	−	1.12942i
$763$	2.50000	+	12.9904i	0.0905061	+	0.470283i
$764$	28.0000			1.01300
$765$	−7.79423	−	4.50000i	−0.281801	−	0.162698i
$766$	−13.3135	+	49.6865i	−0.481035	+	1.79525i
$767$		−	12.0000i		−	0.433295i
$768$	24.0000	−	13.8564i	0.866025	−	0.500000i
$769$	19.5000	−	11.2583i	0.703188	−	0.405986i	−0.105346	−	0.994436i	$-0.533595\pi$
$769$	19.5000	−	11.2583i	0.703188	−	0.405986i	0.808534	+	0.588450i	$0.200262\pi$
$770$	−26.8301	−	18.1699i	−0.966891	−	0.654797i
$771$	−19.5000	+	33.7750i	−0.702275	+	1.21638i
$772$	−10.3923	+	6.00000i	−0.374027	+	0.215945i
$773$	25.1147	+	43.5000i	0.903314	+	1.56459i	0.823164	+	0.567803i	$0.192207\pi$
$773$	25.1147	+	43.5000i	0.903314	+	1.56459i	0.0801501	+	0.996783i	$0.474460\pi$
$774$	−9.88269	+	36.8827i	−0.355226	+	1.32572i
$775$	−6.92820	+	12.0000i	−0.248868	+	0.431053i
$776$	4.73205	−	1.26795i	0.169871	−	0.0455167i
$777$	−4.50000	+	0.866025i	−0.161437	+	0.0310685i
$778$	1.36603	+	0.366025i	0.0489744	+	0.0131226i
$779$	21.0000			0.752403
$780$	5.19615	−	9.00000i	0.186052	−	0.322252i
$781$			50.0000i			1.78914i
$782$	16.5622	−	4.43782i	0.592262	−	0.158696i
$783$	18.1865	−	31.5000i	0.649934	−	1.12572i
$784$	4.00000	−	27.7128i	0.142857	−	0.989743i
$785$	−18.0000	+	31.1769i	−0.642448	+	1.11275i
$786$	−15.0000	−	15.0000i	−0.535032	−	0.535032i
$787$	−36.0000	−	20.7846i	−1.28326	−	0.740891i	−0.305818	−	0.952090i	$-0.598930\pi$
$787$	−36.0000	−	20.7846i	−1.28326	−	0.740891i	−0.977443	+	0.211199i	$0.932263\pi$
$788$	−8.00000	+	13.8564i	−0.284988	+	0.493614i
$789$	−11.2583	+	19.5000i	−0.400807	+	0.694218i
$790$	−3.80385	−	14.1962i	−0.135335	−	0.505076i
$791$	2.59808	−	0.500000i	0.0923770	−	0.0177780i
$792$	40.9808	+	10.9808i	1.45619	+	0.390184i
$793$	3.00000	−	5.19615i	0.106533	−	0.184521i
$794$	−32.9090	−	32.9090i	−1.16790	−	1.16790i
$795$	−33.0000			−1.17039
$796$		−	17.3205i		−	0.613909i
$797$	−12.9904	−	22.5000i	−0.460143	−	0.796991i	0.538825	−	0.842418i	$-0.318868\pi$
$797$	−12.9904	−	22.5000i	−0.460143	−	0.796991i	−0.998968	+	0.0454270i	$0.985535\pi$
$798$	0.803848	−	11.1962i	0.0284559	−	0.396339i
$799$	−5.19615	−	3.00000i	−0.183827	−	0.106132i
$800$	−10.9282	+	2.92820i	−0.386370	+	0.103528i
$801$			25.9808i			0.917985i
$802$	9.15064	−	34.1506i	0.323120	−	1.20590i
$803$	37.5000	−	21.6506i	1.32335	−	0.764034i
$804$	27.7128			0.977356
$805$	−30.3109	−	10.5000i	−1.06832	−	0.370076i
$806$	4.39230	−	16.3923i	0.154712	−	0.577394i
$807$			3.00000i			0.105605i
$808$	−3.46410	+	3.46410i	−0.121867	+	0.121867i
$809$	2.50000	+	4.33013i	0.0878953	+	0.152239i	0.906621	−	0.421945i	$-0.138653\pi$
$809$	2.50000	+	4.33013i	0.0878953	+	0.152239i	−0.818726	+	0.574184i	$0.805319\pi$
$810$	−15.5885	−	15.5885i	−0.547723	−	0.547723i
$811$		−	41.5692i		−	1.45969i	−0.683611	−	0.729846i	$-0.739592\pi$
$811$		−	41.5692i		−	1.45969i	0.683611	−	0.729846i	$-0.260408\pi$
$812$	−36.3731	+	7.00000i	−1.27644	+	0.245652i
$813$	−23.3827	+	13.5000i	−0.820067	+	0.473466i
$814$	−5.00000	+	5.00000i	−0.175250	+	0.175250i
$815$	−6.06218	+	10.5000i	−0.212349	+	0.367799i
$816$	−6.00000	−	10.3923i	−0.210042	−	0.363803i
$817$	13.5000	−	7.79423i	0.472305	−	0.272686i
$818$	−31.1769	+	31.1769i	−1.09008	+	1.09008i
$819$	9.00000	+	10.3923i	0.314485	+	0.363137i
$820$	−42.0000			−1.46670
$821$	1.73205	−	1.00000i	0.0604490	−	0.0349002i	−0.469471	−	0.882948i	$-0.655555\pi$
$821$	1.73205	−	1.00000i	0.0604490	−	0.0349002i	0.529920	+	0.848048i	$0.322222\pi$
$822$	22.5167	−	22.5167i	0.785359	−	0.785359i
$823$	46.7654	+	27.0000i	1.63014	+	0.941161i	0.984049	+	0.177899i	$0.0569301\pi$
$823$	46.7654	+	27.0000i	1.63014	+	0.941161i	0.646090	+	0.763261i	$0.276403\pi$
$824$	10.3923	−	10.3923i	0.362033	−	0.362033i
$825$	−15.0000	−	8.66025i	−0.522233	−	0.301511i
$826$	11.3205	+	23.3205i	0.393891	+	0.811424i
$827$	−38.0000			−1.32139			−0.660695	−	0.750655i	$-0.729738\pi$
$827$	−38.0000			−1.32139			−0.660695	+	0.750655i	$0.729738\pi$
$828$	42.0000			1.45960
$829$	11.2583	+	19.5000i	0.391018	+	0.677263i	0.992584	−	0.121560i	$-0.0387897\pi$
$829$	11.2583	+	19.5000i	0.391018	+	0.677263i	−0.601566	+	0.798823i	$0.705456\pi$
$830$	27.0000	−	27.0000i	0.937184	−	0.937184i
$831$	18.1865	−	31.5000i	0.630884	−	1.09272i
$832$	12.0000	−	6.92820i	0.416025	−	0.240192i
$833$	−12.0000	−	1.73205i	−0.415775	−	0.0600120i
$834$	−9.88269	+	36.8827i	−0.342209	+	1.27714i
$835$	7.50000	+	12.9904i	0.259548	+	0.449551i
$836$	−8.66025	−	15.0000i	−0.299521	−	0.518786i
$837$	−31.1769	−	18.0000i	−1.07763	−	0.622171i
$838$	0.633975	+	2.36603i	0.0219003	+	0.0817330i
$839$	−7.79423	+	13.5000i	−0.269087	+	0.466072i	−0.968626	−	0.248522i	$-0.920055\pi$
$839$	−7.79423	+	13.5000i	−0.269087	+	0.466072i	0.699540	+	0.714594i	$0.253388\pi$
$840$	−1.60770	+	22.3923i	−0.0554708	+	0.772608i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	−15.0000	+	15.0000i	−0.516934	+	0.516934i
$843$	−16.5000	+	9.52628i	−0.568290	+	0.328102i
$844$		−	18.0000i		−	0.619586i
$845$	−8.66025	+	15.0000i	−0.297922	+	0.516016i
$846$	−10.3923	−	10.3923i	−0.357295	−	0.357295i
$847$	12.1244	−	35.0000i	0.416598	−	1.20261i
$848$	−38.1051	−	22.0000i	−1.30854	−	0.755483i
$849$	12.0000	+	20.7846i	0.411839	+	0.713326i
$850$	1.26795	+	4.73205i	0.0434903	+	0.162308i
$851$	−3.50000	+	6.06218i	−0.119978	+	0.207809i
$852$	30.0000	−	17.3205i	1.02778	−	0.593391i
$853$	9.52628	−	16.5000i	0.326174	−	0.564949i	−0.655576	−	0.755130i	$-0.727574\pi$
$853$	9.52628	−	16.5000i	0.326174	−	0.564949i	0.981749	+	0.190180i	$0.0609073\pi$
$854$	−0.928203	+	12.9282i	−0.0317625	+	0.442394i
$855$			9.00000i			0.307794i
$856$	−3.66025	−	13.6603i	−0.125105	−	0.466898i
$857$		−	15.5885i		−	0.532492i	−0.963905	−	0.266246i	$-0.914217\pi$
$857$		−	15.5885i		−	0.532492i	0.963905	−	0.266246i	$-0.0857833\pi$
$858$	20.4904	+	5.49038i	0.699530	+	0.187439i
$859$		−	29.4449i		−	1.00465i	−0.864680	−	0.502323i	$-0.832479\pi$
$859$		−	29.4449i		−	1.00465i	0.864680	−	0.502323i	$-0.167521\pi$
$860$	−27.0000	+	15.5885i	−0.920692	+	0.531562i
$861$	18.1865	−	52.5000i	0.619795	−	1.78920i
$862$	−1.83013	−	6.83013i	−0.0623344	−	0.232635i
$863$	−19.9186	−	11.5000i	−0.678036	−	0.391465i	0.121078	−	0.992643i	$-0.461365\pi$
$863$	−19.9186	−	11.5000i	−0.678036	−	0.391465i	−0.799115	+	0.601178i	$0.794698\pi$
$864$	−7.60770	−	28.3923i	−0.258819	−	0.965926i
$865$	−3.00000	−	5.19615i	−0.102003	−	0.176674i
$866$	42.5885	+	11.4115i	1.44721	+	0.387780i
$867$	21.0000	−	12.1244i	0.713197	−	0.411765i
$868$	6.92820	+	36.0000i	0.235159	+	1.22192i
$869$	25.9808	−	15.0000i	0.881337	−	0.508840i
$870$	28.6865	−	7.68653i	0.972565	−	0.260598i
$871$	13.8564			0.469506
$872$	3.66025	−	13.6603i	0.123952	−	0.462595i
$873$		−	5.19615i		−	0.175863i
$874$	−12.1244	−	12.1244i	−0.410112	−	0.410112i
$875$	10.5000	−	30.3109i	0.354965	−	1.02470i
$876$	−25.9808	−	15.0000i	−0.877809	−	0.506803i
$877$			45.0000i			1.51954i	0.650191	+	0.759771i	$0.274689\pi$
$877$			45.0000i			1.51954i	−0.650191	+	0.759771i	$0.725311\pi$
$878$	−37.8564	+	10.1436i	−1.27759	+	0.342330i
$879$		−	3.00000i		−	0.101187i
$880$	17.3205	+	30.0000i	0.583874	+	1.01130i
$881$		−	10.3923i		−	0.350126i	−0.984557	−	0.175063i	$-0.943987\pi$
$881$		−	10.3923i		−	0.350126i	0.984557	−	0.175063i	$-0.0560129\pi$
$882$	−27.2942	−	11.7058i	−0.919044	−	0.394154i
$883$	−54.0000			−1.81724			−0.908622	−	0.417619i	$-0.862865\pi$
$883$	−54.0000			−1.81724			−0.908622	+	0.417619i	$0.862865\pi$
$884$	−3.00000	−	5.19615i	−0.100901	−	0.174766i
$885$	−10.3923	−	18.0000i	−0.349334	−	0.605063i
$886$	−35.5167	+	9.51666i	−1.19321	+	0.319718i
$887$	25.9808			0.872349			0.436174	−	0.899862i	$-0.356333\pi$
$887$	25.9808			0.872349			0.436174	+	0.899862i	$0.356333\pi$
$888$	4.73205	+	1.26795i	0.158797	+	0.0425496i
$889$	45.0000	+	15.5885i	1.50925	+	0.522820i
$890$	−15.0000	+	15.0000i	−0.502801	+	0.502801i
$891$	22.5000	−	38.9711i	0.753778	−	1.30558i
$892$	21.0000	−	12.1244i	0.703132	−	0.405953i
$893$			6.00000i			0.200782i
$894$	19.0526	+	19.0526i	0.637213	+	0.637213i
$895$	9.52628	+	16.5000i	0.318428	+	0.551534i
$896$	−16.7846	+	24.7846i	−0.560734	+	0.827996i
$897$	21.0000			0.701170
$898$	8.05256	−	30.0526i	0.268717	−	1.00287i
$899$	42.0000	−	24.2487i	1.40078	−	0.808740i
$900$			12.0000i			0.400000i
$901$	−9.52628	+	16.5000i	−0.317366	+	0.549695i
$902$	−22.1891	−	82.8109i	−0.738817	−	2.75730i
$903$	−7.79423	−	40.5000i	−0.259376	−	1.34776i
$904$	−2.73205	−	0.732051i	−0.0908667	−	0.0243476i
$905$	−6.00000			−0.199447
$906$	−8.66025	−	8.66025i	−0.287718	−	0.287718i
$907$	39.0000			1.29497			0.647487	−	0.762077i	$-0.275820\pi$
$907$	39.0000			1.29497			0.647487	+	0.762077i	$0.275820\pi$
$908$	19.0526	−	33.0000i	0.632281	−	1.09514i
$909$	2.59808	+	4.50000i	0.0861727	+	0.149256i
$910$	−0.803848	+	11.1962i	−0.0266473	+	0.371149i
$911$	45.8993	+	26.5000i	1.52071	+	0.877984i	0.999701	+	0.0244347i	$0.00777857\pi$
$911$	45.8993	+	26.5000i	1.52071	+	0.877984i	0.521012	+	0.853549i	$0.325555\pi$
$912$	−6.00000	+	10.3923i	−0.198680	+	0.344124i
$913$	67.5000	+	38.9711i	2.23392	+	1.28976i
$914$	−32.7846	+	8.78461i	−1.08442	+	0.290569i
$915$		−	10.3923i		−	0.343559i
$916$	21.0000	+	12.1244i	0.693860	+	0.400600i
$917$	21.6506	+	7.50000i	0.714967	+	0.247672i
$918$	−12.2942	+	3.29423i	−0.405770	+	0.108726i
$919$	16.4545	+	9.50000i	0.542783	+	0.313376i	0.746206	−	0.665715i	$-0.231873\pi$
$919$	16.4545	+	9.50000i	0.542783	+	0.313376i	−0.203423	+	0.979091i	$0.565207\pi$
$920$	24.2487	+	24.2487i	0.799456	+	0.799456i
$921$	6.00000	−	10.3923i	0.197707	−	0.342438i
$922$	−5.19615	−	5.19615i	−0.171126	−	0.171126i
$923$	15.0000	−	8.66025i	0.493731	−	0.285056i
$924$	−45.0000	+	8.66025i	−1.48039	+	0.284901i
$925$	−1.73205	−	1.00000i	−0.0569495	−	0.0328798i
$926$	3.29423	+	12.2942i	0.108255	+	0.404013i
$927$	−7.79423	−	13.5000i	−0.255996	−	0.443398i
$928$	38.2487	+	10.2487i	1.25558	+	0.336430i
$929$	15.0000	−	8.66025i	0.492134	−	0.284134i	−0.233325	−	0.972399i	$-0.574961\pi$
$929$	15.0000	−	8.66025i	0.492134	−	0.284134i	0.725459	+	0.688265i	$0.241627\pi$
$930$	−7.60770	−	28.3923i	−0.249466	−	0.931020i
$931$	4.50000	+	11.2583i	0.147482	+	0.368977i
$932$	−19.0526	+	11.0000i	−0.624087	+	0.360317i
$933$	−31.1769	+	18.0000i	−1.02069	+	0.589294i
$934$	8.66025	−	8.66025i	0.283372	−	0.283372i
$935$	12.9904	−	7.50000i	0.424831	−	0.245276i
$936$	−3.80385	−	14.1962i	−0.124333	−	0.464016i
$937$			17.3205i			0.565836i	0.959144	+	0.282918i	$0.0913025\pi$
$937$			17.3205i			0.565836i	−0.959144	+	0.282918i	$0.908698\pi$
$938$	−26.9282	+	13.0718i	−0.879237	+	0.426809i
$939$	18.0000			0.587408
$940$		−	12.0000i		−	0.391397i
$941$	−22.5167	+	39.0000i	−0.734022	+	1.27136i	0.221129	+	0.975245i	$0.429026\pi$
$941$	−22.5167	+	39.0000i	−0.734022	+	1.27136i	−0.955151	+	0.296119i	$0.904307\pi$
$942$	13.1769	+	49.1769i	0.429327	+	1.60227i
$943$	−42.4352	−	73.5000i	−1.38188	−	2.39349i
$944$		−	27.7128i		−	0.901975i
$945$	22.5000	+	7.79423i	0.731925	+	0.253546i
$946$	−45.0000	−	45.0000i	−1.46308	−	1.46308i
$947$	13.0000	+	22.5167i	0.422443	+	0.731693i	0.996178	−	0.0873481i	$-0.0278392\pi$
$947$	13.0000	+	22.5167i	0.422443	+	0.731693i	−0.573735	+	0.819041i	$0.694506\pi$
$948$	−18.0000	−	10.3923i	−0.584613	−	0.337526i
$949$	−12.9904	−	7.50000i	−0.421686	−	0.243460i
$950$	3.46410	−	3.46410i	0.112390	−	0.112390i
$951$	−24.2487			−0.786318
$952$	10.7321	+	7.26795i	0.347828	+	0.235556i
$953$	20.0000			0.647864			0.323932	−	0.946080i	$-0.394995\pi$
$953$	20.0000			0.647864			0.323932	+	0.946080i	$0.394995\pi$
$954$	−33.0000	+	33.0000i	−1.06841	+	1.06841i
$955$	21.0000	−	12.1244i	0.679544	−	0.392335i
$956$	−10.0000			−0.323423
$957$	30.3109	+	52.5000i	0.979812	+	1.69708i
$958$	−0.633975	+	2.36603i	−0.0204828	+	0.0764428i
$959$	−11.2583	+	32.5000i	−0.363550	+	1.04948i
$960$	12.0000	−	20.7846i	0.387298	−	0.670820i
$961$	−8.50000	−	14.7224i	−0.274194	−	0.474917i
$962$	2.36603	+	0.633975i	0.0762837	+	0.0204402i
$963$	−15.0000			−0.483368
$964$	5.19615	−	9.00000i	0.167357	−	0.289870i
$965$	−5.19615	+	9.00000i	−0.167270	+	0.289720i
$966$	−40.8109	+	19.8109i	−1.31307	+	0.637405i
$967$	28.5788	−	16.5000i	0.919033	−	0.530604i	0.0357069	−	0.999362i	$-0.488632\pi$
$967$	28.5788	−	16.5000i	0.919033	−	0.530604i	0.883327	+	0.468758i	$0.155298\pi$
$968$	−28.0000	+	28.0000i	−0.899954	+	0.899954i
$969$	4.50000	+	2.59808i	0.144561	+	0.0834622i
$970$	3.00000	−	3.00000i	0.0963242	−	0.0963242i
$971$	−7.50000	−	4.33013i	−0.240686	−	0.138960i	0.374806	−	0.927103i	$-0.377709\pi$
$971$	−7.50000	−	4.33013i	−0.240686	−	0.138960i	−0.615492	+	0.788143i	$0.711043\pi$
$972$	−31.1769			−1.00000
$973$	−7.79423	−	40.5000i	−0.249871	−	1.29837i
$974$	8.41858	+	31.4186i	0.269749	+	1.00672i
$975$			6.00000i			0.192154i
$976$	6.92820	−	12.0000i	0.221766	−	0.384111i
$977$	10.0000	−	17.3205i	0.319928	−	0.554132i	−0.660544	−	0.750787i	$-0.729674\pi$
$977$	10.0000	−	17.3205i	0.319928	−	0.554132i	0.980473	+	0.196655i	$0.0630078\pi$
$978$	4.43782	+	16.5622i	0.141906	+	0.529600i
$979$	−37.5000	−	21.6506i	−1.19851	−	0.691957i
$980$	−9.00000	−	22.5167i	−0.287494	−	0.719268i
$981$	−12.9904	−	7.50000i	−0.414751	−	0.239457i
$982$	−50.5429	+	13.5429i	−1.61289	+	0.432173i
$983$	29.4449			0.939145			0.469573	−	0.882894i	$-0.344408\pi$
$983$	29.4449			0.939145			0.469573	+	0.882894i	$0.344408\pi$
$984$	−42.0000	+	42.0000i	−1.33891	+	1.33891i
$985$			13.8564i			0.441502i
$986$	4.43782	−	16.5622i	0.141329	−	0.527447i
$987$	15.0000	+	5.19615i	0.477455	+	0.165395i
$988$	−3.00000	+	5.19615i	−0.0954427	+	0.165312i
$989$	−54.5596	−	31.5000i	−1.73489	−	1.00164i
$990$	35.4904	−	9.50962i	1.12796	−	0.302236i
$991$	47.6314	−	27.5000i	1.51306	−	0.873566i	0.513178	−	0.858282i	$-0.328468\pi$
$991$	47.6314	−	27.5000i	1.51306	−	0.873566i	0.999883	−	0.0152841i	$-0.00486527\pi$
$992$	10.1436	−	37.8564i	0.322059	−	1.20194i
$993$			10.3923i			0.329790i
$994$	−20.9808	+	30.9808i	−0.665469	+	0.982650i
$995$	−7.50000	−	12.9904i	−0.237766	−	0.411823i
$996$		−	54.0000i		−	1.71106i
$997$	50.2295			1.59078			0.795392	−	0.606096i	$-0.207265\pi$
$997$	50.2295			1.59078			0.795392	+	0.606096i	$0.207265\pi$
$998$	−5.49038	+	20.4904i	−0.173795	+	0.648612i
$999$	2.59808	−	4.50000i	0.0821995	−	0.142374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cz.a.187.2	yes	4
7.3	odd	6		504.2.bf.a.115.2	yes	4
8.3	odd	2	inner	504.2.cz.a.187.1	yes	4
9.4	even	3		504.2.bf.a.355.2	yes	4
56.3	even	6		504.2.bf.a.115.1	✓	4
63.31	odd	6	inner	504.2.cz.a.283.1	yes	4
72.67	odd	6		504.2.bf.a.355.1	yes	4
504.283	even	6	inner	504.2.cz.a.283.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.a.115.1	✓	4	56.3	even	6
504.2.bf.a.115.2	yes	4	7.3	odd	6
504.2.bf.a.355.1	yes	4	72.67	odd	6
504.2.bf.a.355.2	yes	4	9.4	even	3
504.2.cz.a.187.1	yes	4	8.3	odd	2	inner
504.2.cz.a.187.2	yes	4	1.1	even	1	trivial
504.2.cz.a.283.1	yes	4	63.31	odd	6	inner
504.2.cz.a.283.2	yes	4	504.283	even	6	inner

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} -1.73205 q^{5} +(-1.73205 + 1.73205i) q^{6} +(0.866025 - 2.50000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} -1.73205 q^{5} +(-1.73205 + 1.73205i) q^{6} +(0.866025 - 2.50000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.633975 + 2.36603i) q^{10} -5.00000 q^{11} +(1.73205 + 3.00000i) q^{12} +(0.866025 + 1.50000i) q^{13} +(-3.09808 - 2.09808i) q^{14} +(2.59808 + 1.50000i) q^{15} +(2.00000 + 3.46410i) q^{16} +(1.50000 - 0.866025i) q^{17} +(4.09808 - 1.09808i) q^{18} +(-1.50000 - 0.866025i) q^{19} +(3.00000 + 1.73205i) q^{20} +(-3.46410 + 3.00000i) q^{21} +(-1.83013 + 6.83013i) q^{22} +7.00000i q^{23} +(4.73205 - 1.26795i) q^{24} -2.00000 q^{25} +(2.36603 - 0.633975i) q^{26} -5.19615i q^{27} +(-4.00000 + 3.46410i) q^{28} +(6.06218 + 3.50000i) q^{29} +(3.00000 - 3.00000i) q^{30} +(3.46410 - 6.00000i) q^{31} +(5.46410 - 1.46410i) q^{32} +(7.50000 + 4.33013i) q^{33} +(-0.633975 - 2.36603i) q^{34} +(-1.50000 + 4.33013i) q^{35} -6.00000i q^{36} +(0.866025 + 0.500000i) q^{37} +(-1.73205 + 1.73205i) q^{38} -3.00000i q^{39} +(3.46410 - 3.46410i) q^{40} +(-10.5000 + 6.06218i) q^{41} +(2.83013 + 5.83013i) q^{42} +(-4.50000 + 7.79423i) q^{43} +(8.66025 + 5.00000i) q^{44} +(-2.59808 - 4.50000i) q^{45} +(9.56218 + 2.56218i) q^{46} +(-1.73205 - 3.00000i) q^{47} -6.92820i q^{48} +(-5.50000 - 4.33013i) q^{49} +(-0.732051 + 2.73205i) q^{50} -3.00000 q^{51} -3.46410i q^{52} +(-9.52628 + 5.50000i) q^{53} +(-7.09808 - 1.90192i) q^{54} +8.66025 q^{55} +(3.26795 + 6.73205i) q^{56} +(1.50000 + 2.59808i) q^{57} +(7.00000 - 7.00000i) q^{58} +(-6.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(-1.73205 - 3.00000i) q^{61} +(-6.92820 - 6.92820i) q^{62} +(7.79423 - 1.50000i) q^{63} -8.00000i q^{64} +(-1.50000 - 2.59808i) q^{65} +(8.66025 - 8.66025i) q^{66} +(4.00000 - 6.92820i) q^{67} -3.46410 q^{68} +(6.06218 - 10.5000i) q^{69} +(5.36603 + 3.63397i) q^{70} -10.0000i q^{71} +(-8.19615 - 2.19615i) q^{72} +(-7.50000 + 4.33013i) q^{73} +(1.00000 - 1.00000i) q^{74} +(3.00000 + 1.73205i) q^{75} +(1.73205 + 3.00000i) q^{76} +(-4.33013 + 12.5000i) q^{77} +(-4.09808 - 1.09808i) q^{78} +(-5.19615 + 3.00000i) q^{79} +(-3.46410 - 6.00000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(4.43782 + 16.5622i) q^{82} +(-13.5000 - 7.79423i) q^{83} +(9.00000 - 1.73205i) q^{84} +(-2.59808 + 1.50000i) q^{85} +(9.00000 + 9.00000i) q^{86} +(-6.06218 - 10.5000i) q^{87} +(10.0000 - 10.0000i) q^{88} +(7.50000 + 4.33013i) q^{89} +(-7.09808 + 1.90192i) q^{90} +(4.50000 - 0.866025i) q^{91} +(7.00000 - 12.1244i) q^{92} +(-10.3923 + 6.00000i) q^{93} +(-4.73205 + 1.26795i) q^{94} +(2.59808 + 1.50000i) q^{95} +(-9.46410 - 2.53590i) q^{96} +(-1.50000 - 0.866025i) q^{97} +(-7.92820 + 5.92820i) q^{98} +(-7.50000 - 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{3} - 8 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^3 - 8 * q^8 + 6 * q^9	\( 4 q - 2 q^{2} - 6 q^{3} - 8 q^{8} + 6 q^{9} - 6 q^{10} - 20 q^{11} - 2 q^{14} + 8 q^{16} + 6 q^{17} + 6 q^{18} - 6 q^{19} + 12 q^{20} + 10 q^{22} + 12 q^{24} - 8 q^{25} + 6 q^{26} - 16 q^{28} + 12 q^{30} + 8 q^{32} + 30 q^{33} - 6 q^{34} - 6 q^{35} - 42 q^{41} - 6 q^{42} - 18 q^{43} + 14 q^{46} - 22 q^{49} + 4 q^{50} - 12 q^{51} - 18 q^{54} + 20 q^{56} + 6 q^{57} + 28 q^{58} - 24 q^{59} - 12 q^{60} - 6 q^{65} + 16 q^{67} + 18 q^{70} - 12 q^{72} - 30 q^{73} + 4 q^{74} + 12 q^{75} - 6 q^{78} - 18 q^{81} + 42 q^{82} - 54 q^{83} + 36 q^{84} + 36 q^{86} + 40 q^{88} + 30 q^{89} - 18 q^{90} + 18 q^{91} + 28 q^{92} - 12 q^{94} - 24 q^{96} - 6 q^{97} - 4 q^{98} - 30 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^3 - 8 * q^8 + 6 * q^9 - 6 * q^10 - 20 * q^11 - 2 * q^14 + 8 * q^16 + 6 * q^17 + 6 * q^18 - 6 * q^19 + 12 * q^20 + 10 * q^22 + 12 * q^24 - 8 * q^25 + 6 * q^26 - 16 * q^28 + 12 * q^30 + 8 * q^32 + 30 * q^33 - 6 * q^34 - 6 * q^35 - 42 * q^41 - 6 * q^42 - 18 * q^43 + 14 * q^46 - 22 * q^49 + 4 * q^50 - 12 * q^51 - 18 * q^54 + 20 * q^56 + 6 * q^57 + 28 * q^58 - 24 * q^59 - 12 * q^60 - 6 * q^65 + 16 * q^67 + 18 * q^70 - 12 * q^72 - 30 * q^73 + 4 * q^74 + 12 * q^75 - 6 * q^78 - 18 * q^81 + 42 * q^82 - 54 * q^83 + 36 * q^84 + 36 * q^86 + 40 * q^88 + 30 * q^89 - 18 * q^90 + 18 * q^91 + 28 * q^92 - 12 * q^94 - 24 * q^96 - 6 * q^97 - 4 * q^98 - 30 * q^99

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