LMFDB - Embedded newform 504.2.bf.a.115.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(115,504)]

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, 1]))

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

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

chi := DirichletCharacter("504.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bf (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:	$0$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	504.115
Dual form			504.2.bf.a.355.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} -1.73205i q^{3} -2.00000i q^{4} +(0.866025 - 1.50000i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(1.73205 - 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} -1.73205i q^{3} -2.00000i q^{4} +(0.866025 - 1.50000i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(1.73205 - 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} -3.00000 q^{9} +(-0.633975 - 2.36603i) q^{10} +(2.50000 + 4.33013i) q^{11} -3.46410 q^{12} +(0.866025 + 1.50000i) q^{13} +(-0.267949 - 3.73205i) q^{14} +(-2.59808 - 1.50000i) q^{15} -4.00000 q^{16} +(1.50000 + 0.866025i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(-1.50000 + 0.866025i) q^{19} +(-3.00000 - 1.73205i) q^{20} +(-3.46410 - 3.00000i) q^{21} +(6.83013 + 1.83013i) q^{22} +(6.06218 + 3.50000i) q^{23} +(-3.46410 + 3.46410i) q^{24} +(1.00000 + 1.73205i) q^{25} +(2.36603 + 0.633975i) q^{26} +5.19615i q^{27} +(-4.00000 - 3.46410i) q^{28} +(-6.06218 - 3.50000i) q^{29} +(-4.09808 + 1.09808i) q^{30} -6.92820 q^{31} +(-4.00000 + 4.00000i) q^{32} +(7.50000 - 4.33013i) q^{33} +(2.36603 - 0.633975i) q^{34} +(-1.50000 - 4.33013i) q^{35} +6.00000i q^{36} +(0.866025 - 0.500000i) q^{37} +(-0.633975 + 2.36603i) q^{38} +(2.59808 - 1.50000i) q^{39} +(-4.73205 + 1.26795i) q^{40} +(10.5000 - 6.06218i) q^{41} +(-6.46410 + 0.464102i) 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} +3.46410 q^{47} +6.92820i q^{48} +(-1.00000 - 6.92820i) q^{49} +(2.73205 + 0.732051i) q^{50} +(1.50000 - 2.59808i) q^{51} +(3.00000 - 1.73205i) q^{52} +(-9.52628 - 5.50000i) q^{53} +(5.19615 + 5.19615i) q^{54} +8.66025 q^{55} +(-7.46410 + 0.535898i) q^{56} +(1.50000 + 2.59808i) q^{57} +(-9.56218 + 2.56218i) q^{58} -6.92820i q^{59} +(-3.00000 + 5.19615i) q^{60} +3.46410 q^{61} +(-6.92820 + 6.92820i) q^{62} +(-5.19615 + 6.00000i) q^{63} +8.00000i q^{64} +3.00000 q^{65} +(3.16987 - 11.8301i) q^{66} -8.00000 q^{67} +(1.73205 - 3.00000i) q^{68} +(6.06218 - 10.5000i) q^{69} +(-5.83013 - 2.83013i) q^{70} +10.0000i q^{71} +(6.00000 + 6.00000i) q^{72} +(-7.50000 - 4.33013i) q^{73} +(0.366025 - 1.36603i) q^{74} +(3.00000 - 1.73205i) q^{75} +(1.73205 + 3.00000i) q^{76} +(12.9904 + 2.50000i) q^{77} +(1.09808 - 4.09808i) q^{78} +6.00000i q^{79} +(-3.46410 + 6.00000i) q^{80} +9.00000 q^{81} +(4.43782 - 16.5622i) q^{82} +(13.5000 + 7.79423i) q^{83} +(-6.00000 + 6.92820i) q^{84} +(2.59808 - 1.50000i) q^{85} +(3.29423 + 12.2942i) q^{86} +(-6.06218 + 10.5000i) q^{87} +(3.66025 - 13.6603i) q^{88} +(7.50000 - 4.33013i) q^{89} +(1.90192 + 7.09808i) q^{90} +(4.50000 + 0.866025i) q^{91} +(7.00000 - 12.1244i) q^{92} +12.0000i q^{93} +(3.46410 - 3.46410i) q^{94} +3.00000i q^{95} +(6.92820 + 6.92820i) 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 + 4 q^{2} - 8 q^{8} - 12 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^8 - 12 * q^9	$ 4 q + 4 q^{2} - 8 q^{8} - 12 q^{9} - 6 q^{10} + 10 q^{11} - 8 q^{14} - 16 q^{16} + 6 q^{17} - 12 q^{18} - 6 q^{19} - 12 q^{20} + 10 q^{22} + 4 q^{25} + 6 q^{26} - 16 q^{28} - 6 q^{30} - 16 q^{32} + 30 q^{33} + 6 q^{34} - 6 q^{35} - 6 q^{38} - 12 q^{40} + 42 q^{41} - 12 q^{42} - 18 q^{43} + 14 q^{46} - 4 q^{49} + 4 q^{50} + 6 q^{51} + 12 q^{52} - 16 q^{56} + 6 q^{57} - 14 q^{58} - 12 q^{60} + 12 q^{65} + 30 q^{66} - 32 q^{67} - 6 q^{70} + 24 q^{72} - 30 q^{73} - 2 q^{74} + 12 q^{75} - 6 q^{78} + 36 q^{81} + 42 q^{82} + 54 q^{83} - 24 q^{84} - 18 q^{86} - 20 q^{88} + 30 q^{89} + 18 q^{90} + 18 q^{91} + 28 q^{92} + 6 q^{97} - 4 q^{98} - 30 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^8 - 12 * q^9 - 6 * q^10 + 10 * q^11 - 8 * q^14 - 16 * q^16 + 6 * q^17 - 12 * q^18 - 6 * q^19 - 12 * q^20 + 10 * q^22 + 4 * q^25 + 6 * q^26 - 16 * q^28 - 6 * q^30 - 16 * q^32 + 30 * q^33 + 6 * q^34 - 6 * q^35 - 6 * q^38 - 12 * q^40 + 42 * q^41 - 12 * q^42 - 18 * q^43 + 14 * q^46 - 4 * q^49 + 4 * q^50 + 6 * q^51 + 12 * q^52 - 16 * q^56 + 6 * q^57 - 14 * q^58 - 12 * q^60 + 12 * q^65 + 30 * q^66 - 32 * q^67 - 6 * q^70 + 24 * q^72 - 30 * q^73 - 2 * q^74 + 12 * q^75 - 6 * q^78 + 36 * q^81 + 42 * q^82 + 54 * q^83 - 24 * q^84 - 18 * q^86 - 20 * q^88 + 30 * q^89 + 18 * q^90 + 18 * q^91 + 28 * q^92 + 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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.00000	−	1.00000i	0.707107	−	0.707107i
$2$	1.00000	−	1.00000i	0.707107	−	0.707107i
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$		−	2.00000i		−	1.00000i
$5$	0.866025	−	1.50000i	0.387298	−	0.670820i	−0.604787	−	0.796387i	$-0.706742\pi$
$5$	0.866025	−	1.50000i	0.387298	−	0.670820i	0.992085	+	0.125567i	$0.0400750\pi$
$6$	−1.73205	−	1.73205i	−0.707107	−	0.707107i
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$7$	1.73205	−	2.00000i	0.654654	−	0.755929i
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	−3.00000			−1.00000
$10$	−0.633975	−	2.36603i	−0.200480	−	0.748203i
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	0.945979	+	0.324227i	$0.105104\pi$
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	−0.192201	+	0.981356i	$0.561563\pi$
$12$	−3.46410			−1.00000
$13$	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	$0.756123\pi$
$14$	−0.267949	−	3.73205i	−0.0716124	−	0.997433i
$15$	−2.59808	−	1.50000i	−0.670820	−	0.387298i
$16$	−4.00000			−1.00000
$17$	1.50000	+	0.866025i	0.363803	+	0.210042i	0.670748	−	0.741685i	$-0.265973\pi$
$17$	1.50000	+	0.866025i	0.363803	+	0.210042i	−0.306944	+	0.951727i	$0.599307\pi$
$18$	−3.00000	+	3.00000i	−0.707107	+	0.707107i
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	−0.662094	−	0.749421i	$-0.730332\pi$
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	0.317970	+	0.948101i	$0.396999\pi$
$20$	−3.00000	−	1.73205i	−0.670820	−	0.387298i
$21$	−3.46410	−	3.00000i	−0.755929	−	0.654654i
$22$	6.83013	+	1.83013i	1.45619	+	0.390184i
$23$	6.06218	+	3.50000i	1.26405	+	0.729800i	0.973856	−	0.227167i	$-0.0729463\pi$
$23$	6.06218	+	3.50000i	1.26405	+	0.729800i	0.290196	+	0.956967i	$0.406280\pi$
$24$	−3.46410	+	3.46410i	−0.707107	+	0.707107i
$25$	1.00000	+	1.73205i	0.200000	+	0.346410i
$26$	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	−0.182864	−	0.983138i	$-0.558537\pi$
$29$	−6.06218	−	3.50000i	−1.12572	−	0.649934i	−0.942855	+	0.333205i	$0.891870\pi$
$30$	−4.09808	+	1.09808i	−0.748203	+	0.200480i
$31$	−6.92820			−1.24434			−0.622171	−	0.782881i	$-0.713749\pi$
$31$	−6.92820			−1.24434			−0.622171	+	0.782881i	$0.713749\pi$
$32$	−4.00000	+	4.00000i	−0.707107	+	0.707107i
$33$	7.50000	−	4.33013i	1.30558	−	0.753778i
$34$	2.36603	−	0.633975i	0.405770	−	0.108726i
$35$	−1.50000	−	4.33013i	−0.253546	−	0.731925i
$36$			6.00000i			1.00000i
$37$	0.866025	−	0.500000i	0.142374	−	0.0821995i	−0.427121	−	0.904194i	$-0.640472\pi$
$37$	0.866025	−	0.500000i	0.142374	−	0.0821995i	0.569495	+	0.821995i	$0.307139\pi$
$38$	−0.633975	+	2.36603i	−0.102844	+	0.383820i
$39$	2.59808	−	1.50000i	0.416025	−	0.240192i
$40$	−4.73205	+	1.26795i	−0.748203	+	0.200480i
$41$	10.5000	−	6.06218i	1.63982	−	0.946753i	0.658932	−	0.752202i	$-0.271008\pi$
$41$	10.5000	−	6.06218i	1.63982	−	0.946753i	0.980892	−	0.194551i	$-0.0623249\pi$
$42$	−6.46410	+	0.464102i	−0.997433	+	0.0716124i
$43$	−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
$47$	3.46410			0.505291			0.252646	−	0.967559i	$-0.418699\pi$
$47$	3.46410			0.505291			0.252646	+	0.967559i	$0.418699\pi$
$48$			6.92820i			1.00000i
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$	2.73205	+	0.732051i	0.386370	+	0.103528i
$51$	1.50000	−	2.59808i	0.210042	−	0.363803i
$52$	3.00000	−	1.73205i	0.416025	−	0.240192i
$53$	−9.52628	−	5.50000i	−1.30854	−	0.755483i	−0.326683	−	0.945134i	$-0.605931\pi$
$53$	−9.52628	−	5.50000i	−1.30854	−	0.755483i	−0.981852	+	0.189651i	$0.939264\pi$
$54$	5.19615	+	5.19615i	0.707107	+	0.707107i
$55$	8.66025			1.16775
$56$	−7.46410	+	0.535898i	−0.997433	+	0.0716124i
$57$	1.50000	+	2.59808i	0.198680	+	0.344124i
$58$	−9.56218	+	2.56218i	−1.25558	+	0.336430i
$59$		−	6.92820i		−	0.901975i	−0.892530	−	0.450988i	$-0.851072\pi$
$59$		−	6.92820i		−	0.901975i	0.892530	−	0.450988i	$-0.148928\pi$
$60$	−3.00000	+	5.19615i	−0.387298	+	0.670820i
$61$	3.46410			0.443533			0.221766	−	0.975100i	$-0.428818\pi$
$61$	3.46410			0.443533			0.221766	+	0.975100i	$0.428818\pi$
$62$	−6.92820	+	6.92820i	−0.879883	+	0.879883i
$63$	−5.19615	+	6.00000i	−0.654654	+	0.755929i
$64$			8.00000i			1.00000i
$65$	3.00000			0.372104
$66$	3.16987	−	11.8301i	0.390184	−	1.45619i
$67$	−8.00000			−0.977356			−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000			−0.977356			−0.488678	+	0.872464i	$0.662521\pi$
$68$	1.73205	−	3.00000i	0.210042	−	0.363803i
$69$	6.06218	−	10.5000i	0.729800	−	1.26405i
$70$	−5.83013	−	2.83013i	−0.696833	−	0.338265i
$71$			10.0000i			1.18678i	0.804914	+	0.593391i	$0.202211\pi$
$71$			10.0000i			1.18678i	−0.804914	+	0.593391i	$0.797789\pi$
$72$	6.00000	+	6.00000i	0.707107	+	0.707107i
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.00787336	−	0.999969i	$-0.502506\pi$
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.869935	+	0.493166i	$0.835840\pi$
$74$	0.366025	−	1.36603i	0.0425496	−	0.158797i
$75$	3.00000	−	1.73205i	0.346410	−	0.200000i
$76$	1.73205	+	3.00000i	0.198680	+	0.344124i
$77$	12.9904	+	2.50000i	1.48039	+	0.284901i
$78$	1.09808	−	4.09808i	0.124333	−	0.464016i
$79$			6.00000i			0.675053i	0.941316	+	0.337526i	$0.109590\pi$
$79$			6.00000i			0.675053i	−0.941316	+	0.337526i	$0.890410\pi$
$80$	−3.46410	+	6.00000i	−0.387298	+	0.670820i
$81$	9.00000			1.00000
$82$	4.43782	−	16.5622i	0.490075	−	1.82899i
$83$	13.5000	+	7.79423i	1.48182	+	0.855528i	0.999787	−	0.0206268i	$-0.00656619\pi$
$83$	13.5000	+	7.79423i	1.48182	+	0.855528i	0.482030	+	0.876155i	$0.339900\pi$
$84$	−6.00000	+	6.92820i	−0.654654	+	0.755929i
$85$	2.59808	−	1.50000i	0.281801	−	0.162698i
$86$	3.29423	+	12.2942i	0.355226	+	1.32572i
$87$	−6.06218	+	10.5000i	−0.649934	+	1.12572i
$88$	3.66025	−	13.6603i	0.390184	−	1.45619i
$89$	7.50000	−	4.33013i	0.794998	−	0.458993i	−0.0467209	−	0.998908i	$-0.514877\pi$
$89$	7.50000	−	4.33013i	0.794998	−	0.458993i	0.841719	+	0.539915i	$0.181544\pi$
$90$	1.90192	+	7.09808i	0.200480	+	0.748203i
$91$	4.50000	+	0.866025i	0.471728	+	0.0907841i
$92$	7.00000	−	12.1244i	0.729800	−	1.26405i
$93$			12.0000i			1.24434i
$94$	3.46410	−	3.46410i	0.357295	−	0.357295i
$95$			3.00000i			0.307794i
$96$	6.92820	+	6.92820i	0.707107	+	0.707107i
$97$	1.50000	+	0.866025i	0.152302	+	0.0879316i	0.574214	−	0.818705i	$-0.305308\pi$
$97$	1.50000	+	0.866025i	0.152302	+	0.0879316i	−0.421912	+	0.906637i	$0.638641\pi$
$98$	−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
$101$	−0.866025	−	1.50000i	−0.0861727	−	0.149256i	0.819718	−	0.572768i	$-0.194130\pi$
$101$	−0.866025	−	1.50000i	−0.0861727	−	0.149256i	−0.905890	+	0.423512i	$0.860797\pi$
$102$	−1.09808	−	4.09808i	−0.108726	−	0.405770i
$103$	2.59808	−	4.50000i	0.255996	−	0.443398i	−0.709170	−	0.705038i	$-0.750930\pi$
$103$	2.59808	−	4.50000i	0.255996	−	0.443398i	0.965166	+	0.261640i	$0.0842633\pi$
$104$	1.26795	−	4.73205i	0.124333	−	0.464016i
$105$	−7.50000	+	2.59808i	−0.731925	+	0.253546i
$106$	−15.0263	+	4.02628i	−1.45948	+	0.391067i
$107$	−2.50000	−	4.33013i	−0.241684	−	0.418609i	0.719510	−	0.694482i	$-0.244366\pi$
$107$	−2.50000	−	4.33013i	−0.241684	−	0.418609i	−0.961194	+	0.275873i	$0.911033\pi$
$108$	10.3923			1.00000
$109$	−4.33013	−	2.50000i	−0.414751	−	0.239457i	0.278078	−	0.960558i	$-0.410303\pi$
$109$	−4.33013	−	2.50000i	−0.414751	−	0.239457i	−0.692829	+	0.721102i	$0.743636\pi$
$110$	8.66025	−	8.66025i	0.825723	−	0.825723i
$111$	−0.866025	−	1.50000i	−0.0821995	−	0.142374i
$112$	−6.92820	+	8.00000i	−0.654654	+	0.755929i
$113$	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
$115$	10.5000	−	6.06218i	0.979130	−	0.565301i
$116$	−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
$119$	4.33013	−	1.50000i	0.396942	−	0.137505i
$120$	2.19615	+	8.19615i	0.200480	+	0.748203i
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$	3.46410	−	3.46410i	0.313625	−	0.313625i
$123$	−10.5000	−	18.1865i	−0.946753	−	1.63982i
$124$			13.8564i			1.24434i
$125$	12.1244			1.08444
$126$	0.803848	+	11.1962i	0.0716124	+	0.997433i
$127$		−	18.0000i		−	1.59724i	−0.601834	−	0.798621i	$-0.705563\pi$
$127$		−	18.0000i		−	1.59724i	0.601834	−	0.798621i	$-0.294437\pi$
$128$	8.00000	+	8.00000i	0.707107	+	0.707107i
$129$	13.5000	+	7.79423i	1.18861	+	0.686244i
$130$	3.00000	−	3.00000i	0.263117	−	0.263117i
$131$	7.50000	+	4.33013i	0.655278	+	0.378325i	0.790475	−	0.612494i	$-0.209834\pi$
$131$	7.50000	+	4.33013i	0.655278	+	0.378325i	−0.135197	+	0.990819i	$0.543167\pi$
$132$	−8.66025	−	15.0000i	−0.753778	−	1.30558i
$133$	−0.866025	+	4.50000i	−0.0750939	+	0.390199i
$134$	−8.00000	+	8.00000i	−0.691095	+	0.691095i
$135$	7.79423	+	4.50000i	0.670820	+	0.387298i
$136$	−1.26795	−	4.73205i	−0.108726	−	0.405770i
$137$	6.50000	+	11.2583i	0.555332	+	0.961864i	0.997878	+	0.0651178i	$0.0207423\pi$
$137$	6.50000	+	11.2583i	0.555332	+	0.961864i	−0.442545	+	0.896746i	$0.645924\pi$
$138$	−4.43782	−	16.5622i	−0.377773	−	1.40987i
$139$	−13.5000	+	7.79423i	−1.14506	+	0.661098i	−0.947677	−	0.319230i	$-0.896576\pi$
$139$	−13.5000	+	7.79423i	−1.14506	+	0.661098i	−0.197378	+	0.980328i	$0.563243\pi$
$140$	−8.66025	+	3.00000i	−0.731925	+	0.253546i
$141$		−	6.00000i		−	0.505291i
$142$	10.0000	+	10.0000i	0.839181	+	0.839181i
$143$	−4.33013	+	7.50000i	−0.362103	+	0.627182i
$144$	12.0000			1.00000
$145$	−10.5000	+	6.06218i	−0.871978	+	0.503436i
$146$	−11.8301	+	3.16987i	−0.979068	+	0.262341i
$147$	−12.0000	+	1.73205i	−0.989743	+	0.142857i
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	−9.52628	−	5.50000i	−0.780423	−	0.450578i	0.0561570	−	0.998422i	$-0.482115\pi$
$149$	−9.52628	−	5.50000i	−0.780423	−	0.450578i	−0.836580	+	0.547844i	$0.815449\pi$
$150$	1.26795	−	4.73205i	0.103528	−	0.386370i
$151$	−4.33013	+	2.50000i	−0.352381	+	0.203447i	−0.665733	−	0.746190i	$-0.731881\pi$
$151$	−4.33013	+	2.50000i	−0.352381	+	0.203447i	0.313353	+	0.949637i	$0.398548\pi$
$152$	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
$157$	−20.7846			−1.65879			−0.829396	−	0.558661i	$-0.811315\pi$
$157$	−20.7846			−1.65879			−0.829396	+	0.558661i	$0.811315\pi$
$158$	6.00000	+	6.00000i	0.477334	+	0.477334i
$159$	−9.52628	+	16.5000i	−0.755483	+	1.30854i
$160$	2.53590	+	9.46410i	0.200480	+	0.748203i
$161$	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	0.969918	−	0.243432i	$-0.0782731\pi$
$163$	3.50000	+	6.06218i	0.274141	+	0.474826i	−0.695777	+	0.718258i	$0.744940\pi$
$164$	−12.1244	−	21.0000i	−0.946753	−	1.63982i
$165$		−	15.0000i		−	1.16775i
$166$	21.2942	−	5.70577i	1.65275	−	0.442854i
$167$	−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
$171$	4.50000	−	2.59808i	0.344124	−	0.198680i
$172$	15.5885	+	9.00000i	1.18861	+	0.686244i
$173$	−3.46410			−0.263371			−0.131685	−	0.991292i	$-0.542039\pi$
$173$	−3.46410			−0.263371			−0.131685	+	0.991292i	$0.542039\pi$
$174$	4.43782	+	16.5622i	0.336430	+	1.25558i
$175$	5.19615	+	1.00000i	0.392792	+	0.0755929i
$176$	−10.0000	−	17.3205i	−0.753778	−	1.30558i
$177$	−12.0000			−0.901975
$178$	3.16987	−	11.8301i	0.237592	−	0.886706i
$179$	−5.50000	+	9.52628i	−0.411089	+	0.712028i	−0.995009	−	0.0997838i	$-0.968185\pi$
$179$	−5.50000	+	9.52628i	−0.411089	+	0.712028i	0.583920	+	0.811811i	$0.301518\pi$
$180$	9.00000	+	5.19615i	0.670820	+	0.387298i
$181$	3.46410			0.257485			0.128742	−	0.991678i	$-0.458906\pi$
$181$	3.46410			0.257485			0.128742	+	0.991678i	$0.458906\pi$
$182$	5.36603	−	3.63397i	0.397756	−	0.269368i
$183$		−	6.00000i		−	0.443533i
$184$	−5.12436	−	19.1244i	−0.377773	−	1.40987i
$185$		−	1.73205i		−	0.127343i
$186$	12.0000	+	12.0000i	0.879883	+	0.879883i
$187$			8.66025i			0.633300i
$188$		−	6.92820i		−	0.505291i
$189$	10.3923	+	9.00000i	0.755929	+	0.654654i
$190$	3.00000	+	3.00000i	0.217643	+	0.217643i
$191$			14.0000i			1.01300i	0.862239	+	0.506502i	$0.169062\pi$
$191$			14.0000i			1.01300i	−0.862239	+	0.506502i	$0.830938\pi$
$192$	13.8564			1.00000
$193$	−6.00000			−0.431889			−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000			−0.431889			−0.215945	+	0.976406i	$0.569283\pi$
$194$	2.36603	−	0.633975i	0.169871	−	0.0455167i
$195$		−	5.19615i		−	0.372104i
$196$	−13.8564	+	2.00000i	−0.989743	+	0.142857i
$197$			8.00000i			0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$			8.00000i			0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$	−20.4904	−	5.49038i	−1.45619	−	0.390184i
$199$	4.33013	−	7.50000i	0.306955	−	0.531661i	−0.670740	−	0.741693i	$-0.734023\pi$
$199$	4.33013	−	7.50000i	0.306955	−	0.531661i	0.977695	+	0.210032i	$0.0673567\pi$
$200$	1.46410	−	5.46410i	0.103528	−	0.386370i
$201$			13.8564i			0.977356i
$202$	−2.36603	−	0.633975i	−0.166473	−	0.0446063i
$203$	−17.5000	+	6.06218i	−1.22826	+	0.425481i
$204$	−5.19615	−	3.00000i	−0.363803	−	0.210042i
$205$		−	21.0000i		−	1.46670i
$206$	−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	$0.733074\pi$
$212$	−11.0000	+	19.0526i	−0.755483	+	1.30854i
$213$	17.3205			1.18678
$214$	−6.83013	−	1.83013i	−0.466898	−	0.125105i
$215$	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
$218$	−6.83013	+	1.83013i	−0.462595	+	0.123952i
$219$	−7.50000	+	12.9904i	−0.506803	+	0.877809i
$220$		−	17.3205i		−	1.16775i
$221$			3.00000i			0.201802i
$222$	−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
$227$	−16.5000	+	9.52628i	−1.09514	+	0.632281i	−0.934941	−	0.354803i	$-0.884548\pi$
$227$	−16.5000	+	9.52628i	−1.09514	+	0.632281i	−0.160202	+	0.987084i	$0.551215\pi$
$228$	5.19615	−	3.00000i	0.344124	−	0.198680i
$229$	6.06218	−	10.5000i	0.400600	−	0.693860i	−0.593198	−	0.805056i	$-0.702135\pi$
$229$	6.06218	−	10.5000i	0.400600	−	0.693860i	0.993798	+	0.111197i	$0.0354684\pi$
$230$	4.43782	−	16.5622i	0.292621	−	1.09208i
$231$	4.33013	−	22.5000i	0.284901	−	1.48039i
$232$	5.12436	+	19.1244i	0.336430	+	1.25558i
$233$	5.50000	+	9.52628i	0.360317	+	0.624087i	0.988013	−	0.154371i	$-0.0493352\pi$
$233$	5.50000	+	9.52628i	0.360317	+	0.624087i	−0.627696	+	0.778459i	$0.716002\pi$
$234$	−7.09808	−	1.90192i	−0.464016	−	0.124333i
$235$	3.00000	−	5.19615i	0.195698	−	0.338960i
$236$	−13.8564			−0.901975
$237$	10.3923			0.675053
$238$	2.83013	−	5.83013i	0.183450	−	0.377911i
$239$	−4.33013	+	2.50000i	−0.280093	+	0.161712i	−0.633465	−	0.773771i	$-0.718368\pi$
$239$	−4.33013	+	2.50000i	−0.280093	+	0.161712i	0.353373	+	0.935483i	$0.385035\pi$
$240$	10.3923	+	6.00000i	0.670820	+	0.387298i
$241$	−4.50000	+	2.59808i	−0.289870	+	0.167357i	−0.637883	−	0.770133i	$-0.720190\pi$
$241$	−4.50000	+	2.59808i	−0.289870	+	0.167357i	0.348013	+	0.937490i	$0.386857\pi$
$242$	5.12436	+	19.1244i	0.329406	+	1.22936i
$243$		−	15.5885i		−	1.00000i
$244$		−	6.92820i		−	0.443533i
$245$	−11.2583	−	4.50000i	−0.719268	−	0.287494i
$246$	−28.6865	−	7.68653i	−1.82899	−	0.490075i
$247$	−2.59808	−	1.50000i	−0.165312	−	0.0954427i
$248$	13.8564	+	13.8564i	0.879883	+	0.879883i
$249$	13.5000	−	23.3827i	0.855528	−	1.48182i
$250$	12.1244	−	12.1244i	0.766812	−	0.766812i
$251$		−	13.8564i		−	0.874609i	−0.899314	−	0.437304i	$-0.855933\pi$
$251$		−	13.8564i		−	0.874609i	0.899314	−	0.437304i	$-0.144067\pi$
$252$	12.0000	+	10.3923i	0.755929	+	0.654654i
$253$			35.0000i			2.20043i
$254$	−18.0000	−	18.0000i	−1.12942	−	1.12942i
$255$	−2.59808	−	4.50000i	−0.162698	−	0.281801i
$256$	16.0000			1.00000
$257$	−19.5000	−	11.2583i	−1.21638	−	0.702275i	−0.252236	−	0.967666i	$-0.581166\pi$
$257$	−19.5000	−	11.2583i	−1.21638	−	0.702275i	−0.964141	+	0.265391i	$0.914499\pi$
$258$	21.2942	−	5.70577i	1.32572	−	0.355226i
$259$	0.500000	−	2.59808i	0.0310685	−	0.161437i
$260$		−	6.00000i		−	0.372104i
$261$	18.1865	+	10.5000i	1.12572	+	0.649934i
$262$	11.8301	−	3.16987i	0.730868	−	0.195835i
$263$	11.2583	−	6.50000i	0.694218	−	0.400807i	−0.110972	−	0.993824i	$-0.535396\pi$
$263$	11.2583	−	6.50000i	0.694218	−	0.400807i	0.805190	+	0.593016i	$0.202063\pi$
$264$	−23.6603	−	6.33975i	−1.45619	−	0.390184i
$265$	−16.5000	+	9.52628i	−1.01359	+	0.585195i
$266$	3.63397	+	5.36603i	0.222813	+	0.329012i
$267$	−7.50000	−	12.9904i	−0.458993	−	0.794998i
$268$			16.0000i			0.977356i
$269$	−0.866025	+	1.50000i	−0.0528025	+	0.0914566i	−0.891219	−	0.453574i	$-0.850149\pi$
$269$	−0.866025	+	1.50000i	−0.0528025	+	0.0914566i	0.838416	+	0.545031i	$0.183482\pi$
$270$	12.2942	−	3.29423i	0.748203	−	0.200480i
$271$	7.79423	+	13.5000i	0.473466	+	0.820067i	0.999539	−	0.0303728i	$-0.00966946\pi$
$271$	7.79423	+	13.5000i	0.473466	+	0.820067i	−0.526073	+	0.850439i	$0.676336\pi$
$272$	−6.00000	−	3.46410i	−0.363803	−	0.210042i
$273$	1.50000	−	7.79423i	0.0907841	−	0.471728i
$274$	17.7583	+	4.75833i	1.07282	+	0.287461i
$275$	−5.00000	+	8.66025i	−0.301511	+	0.522233i
$276$	−21.0000	−	12.1244i	−1.26405	−	0.729800i
$277$	−18.1865	+	10.5000i	−1.09272	+	0.630884i	−0.934300	−	0.356488i	$-0.883974\pi$
$277$	−18.1865	+	10.5000i	−1.09272	+	0.630884i	−0.158423	+	0.987371i	$0.550641\pi$
$278$	−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	$0.0602575\pi$
$282$	−6.00000	−	6.00000i	−0.357295	−	0.357295i
$283$		−	13.8564i		−	0.823678i	−0.911257	−	0.411839i	$-0.864887\pi$
$283$		−	13.8564i		−	0.823678i	0.911257	−	0.411839i	$-0.135113\pi$
$284$	20.0000			1.18678
$285$	5.19615			0.307794
$286$	3.16987	+	11.8301i	0.187439	+	0.699530i
$287$	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
$290$	−4.43782	+	16.5622i	−0.260598	+	0.972565i
$291$	1.50000	−	2.59808i	0.0879316	−	0.152302i
$292$	−8.66025	+	15.0000i	−0.506803	+	0.877809i
$293$	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	$0.817222\pi$
$294$	−10.2679	+	13.7321i	−0.598839	+	0.800869i
$295$	−10.3923	−	6.00000i	−0.605063	−	0.349334i
$296$	−2.73205	−	0.732051i	−0.158797	−	0.0425496i
$297$	−22.5000	+	12.9904i	−1.30558	+	0.753778i
$298$	−15.0263	+	4.02628i	−0.870449	+	0.233236i
$299$			12.1244i			0.701170i
$300$	−3.46410	−	6.00000i	−0.200000	−	0.346410i
$301$	7.79423	+	22.5000i	0.449252	+	1.29688i
$302$	−1.83013	+	6.83013i	−0.105312	+	0.393030i
$303$	−2.59808	+	1.50000i	−0.149256	+	0.0861727i
$304$	6.00000	−	3.46410i	0.344124	−	0.198680i
$305$	3.00000	−	5.19615i	0.171780	−	0.297531i
$306$	−7.09808	+	1.90192i	−0.405770	+	0.108726i
$307$		−	6.92820i		−	0.395413i	−0.980261	−	0.197707i	$-0.936651\pi$
$307$		−	6.92820i		−	0.395413i	0.980261	−	0.197707i	$-0.0633494\pi$
$308$	5.00000	−	25.9808i	0.284901	−	1.48039i
$309$	−7.79423	−	4.50000i	−0.443398	−	0.255996i
$310$	4.39230	+	16.3923i	0.249466	+	0.931020i
$311$	−20.7846			−1.17859			−0.589294	−	0.807919i	$-0.700594\pi$
$311$	−20.7846			−1.17859			−0.589294	+	0.807919i	$0.700594\pi$
$312$	−8.19615	−	2.19615i	−0.464016	−	0.124333i
$313$			10.3923i			0.587408i	0.955896	+	0.293704i	$0.0948880\pi$
$313$			10.3923i			0.587408i	−0.955896	+	0.293704i	$0.905112\pi$
$314$	−20.7846	+	20.7846i	−1.17294	+	1.17294i
$315$	4.50000	+	12.9904i	0.253546	+	0.731925i
$316$	12.0000			0.675053
$317$		−	14.0000i		−	0.786318i	−0.919470	−	0.393159i	$-0.871382\pi$
$317$		−	14.0000i		−	0.786318i	0.919470	−	0.393159i	$-0.128618\pi$
$318$	6.97372	+	26.0263i	0.391067	+	1.45948i
$319$		−	35.0000i		−	1.95962i
$320$	12.0000	+	6.92820i	0.670820	+	0.387298i
$321$	−7.50000	+	4.33013i	−0.418609	+	0.241684i
$322$	11.4378	−	23.5622i	0.637405	−	1.31307i
$323$	−3.00000			−0.166924
$324$		−	18.0000i		−	1.00000i
$325$	−1.73205	+	3.00000i	−0.0960769	+	0.166410i
$326$	9.56218	+	2.56218i	0.529600	+	0.141906i
$327$	−4.33013	+	7.50000i	−0.239457	+	0.414751i
$328$	−33.1244	−	8.87564i	−1.82899	−	0.490075i
$329$	6.00000	−	6.92820i	0.330791	−	0.381964i
$330$	−15.0000	−	15.0000i	−0.825723	−	0.825723i
$331$	6.00000			0.329790			0.164895	−	0.986311i	$-0.447272\pi$
$331$	6.00000			0.329790			0.164895	+	0.986311i	$0.447272\pi$
$332$	15.5885	−	27.0000i	0.855528	−	1.48182i
$333$	−2.59808	+	1.50000i	−0.142374	+	0.0821995i
$334$	−11.8301	−	3.16987i	−0.647316	−	0.173448i
$335$	−6.92820	+	12.0000i	−0.378528	+	0.655630i
$336$	13.8564	+	12.0000i	0.755929	+	0.654654i
$337$	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	$0.754502\pi$
$338$	−3.66025	−	13.6603i	−0.199092	−	0.743020i
$339$	1.50000	−	0.866025i	0.0814688	−	0.0470360i
$340$	−3.00000	−	5.19615i	−0.162698	−	0.281801i
$341$	−17.3205	−	30.0000i	−0.937958	−	1.62459i
$342$	1.90192	−	7.09808i	0.102844	−	0.383820i
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$	24.5885	−	6.58846i	1.32572	−	0.355226i
$345$	−10.5000	−	18.1865i	−0.565301	−	0.979130i
$346$	−3.46410	+	3.46410i	−0.186231	+	0.186231i
$347$	16.0000			0.858925			0.429463	−	0.903085i	$-0.358703\pi$
$347$	16.0000			0.858925			0.429463	+	0.903085i	$0.358703\pi$
$348$	21.0000	+	12.1244i	1.12572	+	0.649934i
$349$	−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
$353$	−4.50000	+	2.59808i	−0.239511	+	0.138282i	−0.614952	−	0.788565i	$-0.710825\pi$
$353$	−4.50000	+	2.59808i	−0.239511	+	0.138282i	0.375441	+	0.926846i	$0.377491\pi$
$354$	−12.0000	+	12.0000i	−0.637793	+	0.637793i
$355$	15.0000	+	8.66025i	0.796117	+	0.459639i
$356$	−8.66025	−	15.0000i	−0.458993	−	0.794998i
$357$	−2.59808	−	7.50000i	−0.137505	−	0.396942i
$358$	4.02628	+	15.0263i	0.212795	+	0.794164i
$359$	6.06218	−	3.50000i	0.319950	−	0.184723i	−0.331421	−	0.943483i	$-0.607528\pi$
$359$	6.06218	−	3.50000i	0.319950	−	0.184723i	0.651370	+	0.758760i	$0.274195\pi$
$360$	14.1962	−	3.80385i	0.748203	−	0.200480i
$361$	−8.00000	+	13.8564i	−0.421053	+	0.729285i
$362$	3.46410	−	3.46410i	0.182069	−	0.182069i
$363$	21.0000	+	12.1244i	1.10221	+	0.636364i
$364$	1.73205	−	9.00000i	0.0907841	−	0.471728i
$365$	−12.9904	+	7.50000i	−0.679948	+	0.392568i
$366$	−6.00000	−	6.00000i	−0.313625	−	0.313625i
$367$	18.1865	+	31.5000i	0.949329	+	1.64429i	0.746842	+	0.665002i	$0.231569\pi$
$367$	18.1865	+	31.5000i	0.949329	+	1.64429i	0.202488	+	0.979285i	$0.435097\pi$
$368$	−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
$371$	−27.5000	+	9.52628i	−1.42773	+	0.494580i
$372$	24.0000			1.24434
$373$	2.59808	+	1.50000i	0.134523	+	0.0776671i	0.565751	−	0.824576i	$-0.308586\pi$
$373$	2.59808	+	1.50000i	0.134523	+	0.0776671i	−0.431228	+	0.902243i	$0.641920\pi$
$374$	8.66025	+	8.66025i	0.447811	+	0.447811i
$375$		−	21.0000i		−	1.08444i
$376$	−6.92820	−	6.92820i	−0.357295	−	0.357295i
$377$		−	12.1244i		−	0.624436i
$378$	19.3923	−	1.39230i	0.997433	−	0.0716124i
$379$	18.0000			0.924598			0.462299	−	0.886724i	$-0.347025\pi$
$379$	18.0000			0.924598			0.462299	+	0.886724i	$0.347025\pi$
$380$	6.00000			0.307794
$381$	−31.1769			−1.59724
$382$	14.0000	+	14.0000i	0.716302	+	0.716302i
$383$	18.1865	−	31.5000i	0.929288	−	1.60957i	0.144774	−	0.989465i	$-0.453755\pi$
$383$	18.1865	−	31.5000i	0.929288	−	1.60957i	0.784515	−	0.620110i	$-0.212912\pi$
$384$	13.8564	−	13.8564i	0.707107	−	0.707107i
$385$	15.0000	−	17.3205i	0.764471	−	0.882735i
$386$	−6.00000	+	6.00000i	−0.305392	+	0.305392i
$387$	13.5000	−	23.3827i	0.686244	−	1.18861i
$388$	1.73205	−	3.00000i	0.0879316	−	0.152302i
$389$	−0.866025	+	0.500000i	−0.0439092	+	0.0253510i	−0.521794	−	0.853072i	$-0.674737\pi$
$389$	−0.866025	+	0.500000i	−0.0439092	+	0.0253510i	0.477885	+	0.878423i	$0.341404\pi$
$390$	−5.19615	−	5.19615i	−0.263117	−	0.263117i
$391$	6.06218	+	10.5000i	0.306578	+	0.531008i
$392$	−11.8564	+	15.8564i	−0.598839	+	0.800869i
$393$	7.50000	−	12.9904i	0.378325	−	0.655278i
$394$	8.00000	+	8.00000i	0.403034	+	0.403034i
$395$	9.00000	+	5.19615i	0.452839	+	0.261447i
$396$	−25.9808	+	15.0000i	−1.30558	+	0.753778i
$397$	16.4545	+	28.5000i	0.825827	+	1.43037i	0.901286	+	0.433225i	$0.142624\pi$
$397$	16.4545	+	28.5000i	0.825827	+	1.43037i	−0.0754589	+	0.997149i	$0.524042\pi$
$398$	−3.16987	−	11.8301i	−0.158891	−	0.592991i
$399$	7.79423	+	1.50000i	0.390199	+	0.0750939i
$400$	−4.00000	−	6.92820i	−0.200000	−	0.346410i
$401$	−12.5000	+	21.6506i	−0.624220	+	1.08118i	0.364471	+	0.931215i	$0.381250\pi$
$401$	−12.5000	+	21.6506i	−0.624220	+	1.08118i	−0.988691	+	0.149966i	$0.952083\pi$
$402$	13.8564	+	13.8564i	0.691095	+	0.691095i
$403$	−6.00000	−	10.3923i	−0.298881	−	0.517678i
$404$	−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
$408$	−8.19615	+	2.19615i	−0.405770	+	0.108726i
$409$		−	31.1769i		−	1.54160i	−0.637078	−	0.770800i	$-0.719857\pi$
$409$		−	31.1769i		−	1.54160i	0.637078	−	0.770800i	$-0.280143\pi$
$410$	−21.0000	−	21.0000i	−1.03712	−	1.03712i
$411$	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
$414$	−28.6865	+	7.68653i	−1.40987	+	0.377773i
$415$	23.3827	−	13.5000i	1.14781	−	0.662689i
$416$	−9.46410	−	2.53590i	−0.464016	−	0.124333i
$417$	13.5000	+	23.3827i	0.661098	+	1.14506i
$418$	−11.8301	+	3.16987i	−0.578630	+	0.155044i
$419$	1.50000	−	0.866025i	0.0732798	−	0.0423081i	−0.462912	−	0.886404i	$-0.653196\pi$
$419$	1.50000	−	0.866025i	0.0732798	−	0.0423081i	0.536192	+	0.844096i	$0.319862\pi$
$420$	5.19615	+	15.0000i	0.253546	+	0.731925i
$421$	12.9904	+	7.50000i	0.633112	+	0.365528i	0.781956	−	0.623333i	$-0.214222\pi$
$421$	12.9904	+	7.50000i	0.633112	+	0.365528i	−0.148844	+	0.988861i	$0.547555\pi$
$422$	12.2942	+	3.29423i	0.598474	+	0.160361i
$423$	−10.3923			−0.505291
$424$	8.05256	+	30.0526i	0.391067	+	1.45948i
$425$			3.46410i			0.168034i
$426$	17.3205	−	17.3205i	0.839181	−	0.839181i
$427$	6.00000	−	6.92820i	0.290360	−	0.335279i
$428$	−8.66025	+	5.00000i	−0.418609	+	0.241684i
$429$	12.9904	+	7.50000i	0.627182	+	0.362103i
$430$	21.2942	+	5.70577i	1.02690	+	0.275157i
$431$	4.33013	+	2.50000i	0.208575	+	0.120421i	0.600649	−	0.799513i	$-0.294909\pi$
$431$	4.33013	+	2.50000i	0.208575	+	0.120421i	−0.392074	+	0.919934i	$0.628242\pi$
$432$		−	20.7846i		−	1.00000i
$433$		−	31.1769i		−	1.49827i	−0.662419	−	0.749133i	$-0.730470\pi$
$433$		−	31.1769i		−	1.49827i	0.662419	−	0.749133i	$-0.269530\pi$
$434$	1.85641	+	25.8564i	0.0891104	+	1.24115i
$435$	10.5000	+	18.1865i	0.503436	+	0.871978i
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$	−12.1244			−0.579987
$438$	5.49038	+	20.4904i	0.262341	+	0.979068i
$439$	27.7128			1.32266			0.661330	−	0.750095i	$-0.269992\pi$
$439$	27.7128			1.32266			0.661330	+	0.750095i	$0.269992\pi$
$440$	−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
$443$	26.0000			1.23530			0.617649	−	0.786454i	$-0.288085\pi$
$443$	26.0000			1.23530			0.617649	+	0.786454i	$0.288085\pi$
$444$	−3.00000	+	1.73205i	−0.142374	+	0.0821995i
$445$		−	15.0000i		−	0.711068i
$446$	4.43782	+	16.5622i	0.210137	+	0.784242i
$447$	−9.52628	+	16.5000i	−0.450578	+	0.780423i
$448$	16.0000	+	13.8564i	0.755929	+	0.654654i
$449$	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
$452$	1.73205	−	1.00000i	0.0814688	−	0.0470360i
$453$	4.33013	+	7.50000i	0.203447	+	0.352381i
$454$	−6.97372	+	26.0263i	−0.327293	+	1.22147i
$455$	5.19615	−	6.00000i	0.243599	−	0.281284i
$456$	2.19615	−	8.19615i	0.102844	−	0.383820i
$457$	24.0000			1.12267			0.561336	−	0.827588i	$-0.310287\pi$
$457$	24.0000			1.12267			0.561336	+	0.827588i	$0.310287\pi$
$458$	−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	$0.128055\pi$
$462$	−18.1699	−	26.8301i	−0.845339	−	1.24825i
$463$	7.79423	−	4.50000i	0.362229	−	0.209133i	−0.307829	−	0.951442i	$-0.599603\pi$
$463$	7.79423	−	4.50000i	0.362229	−	0.209133i	0.670058	+	0.742309i	$0.266269\pi$
$464$	24.2487	+	14.0000i	1.12572	+	0.649934i
$465$	18.0000	+	10.3923i	0.834730	+	0.481932i
$466$	15.0263	+	4.02628i	0.696079	+	0.186514i
$467$	7.50000	−	4.33013i	0.347059	−	0.200374i	−0.316330	−	0.948649i	$-0.602451\pi$
$467$	7.50000	−	4.33013i	0.347059	−	0.200374i	0.663389	+	0.748275i	$0.269117\pi$
$468$	−9.00000	+	5.19615i	−0.416025	+	0.240192i
$469$	−13.8564	+	16.0000i	−0.639829	+	0.738811i
$470$	−2.19615	−	8.19615i	−0.101301	−	0.378060i
$471$			36.0000i			1.65879i
$472$	−13.8564	+	13.8564i	−0.637793	+	0.637793i
$473$	−45.0000			−2.06910
$474$	10.3923	−	10.3923i	0.477334	−	0.477334i
$475$	−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
$479$	0.866025	+	1.50000i	0.0395697	+	0.0685367i	0.885132	−	0.465340i	$-0.154068\pi$
$479$	0.866025	+	1.50000i	0.0395697	+	0.0685367i	−0.845562	+	0.533877i	$0.820735\pi$
$480$	16.3923	−	4.39230i	0.748203	−	0.200480i
$481$	1.50000	+	0.866025i	0.0683941	+	0.0394874i
$482$	−1.90192	+	7.09808i	−0.0866303	+	0.323309i
$483$	−10.5000	−	30.3109i	−0.477767	−	1.37919i
$484$	24.2487	+	14.0000i	1.10221	+	0.636364i
$485$	2.59808	−	1.50000i	0.117973	−	0.0681115i
$486$	−15.5885	−	15.5885i	−0.707107	−	0.707107i
$487$	−19.9186	−	11.5000i	−0.902597	−	0.521115i	−0.0245553	−	0.999698i	$-0.507817\pi$
$487$	−19.9186	−	11.5000i	−0.902597	−	0.521115i	−0.878042	+	0.478584i	$0.841150\pi$
$488$	−6.92820	−	6.92820i	−0.313625	−	0.313625i
$489$	10.5000	−	6.06218i	0.474826	−	0.274141i
$490$	−15.7583	+	6.75833i	−0.711889	+	0.305310i
$491$	−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
$493$	−6.06218	−	10.5000i	−0.273027	−	0.472896i
$494$	−4.09808	+	1.09808i	−0.184381	+	0.0494048i
$495$	−25.9808			−1.16775
$496$	27.7128			1.24434
$497$	20.0000	+	17.3205i	0.897123	+	0.776931i
$498$	−9.88269	−	36.8827i	−0.442854	−	1.65275i
$499$	7.50000	−	12.9904i	0.335746	−	0.581529i	−0.647882	−	0.761741i	$-0.724345\pi$
$499$	7.50000	−	12.9904i	0.335746	−	0.581529i	0.983628	+	0.180212i	$0.0576783\pi$
$500$		−	24.2487i		−	1.08444i
$501$	−12.9904	+	7.50000i	−0.580367	+	0.335075i
$502$	−13.8564	−	13.8564i	−0.618442	−	0.618442i
$503$	−6.92820			−0.308913			−0.154457	−	0.988000i	$-0.549363\pi$
$503$	−6.92820			−0.308913			−0.154457	+	0.988000i	$0.549363\pi$
$504$	22.3923	−	1.60770i	0.997433	−	0.0716124i
$505$	−3.00000			−0.133498
$506$	35.0000	+	35.0000i	1.55594	+	1.55594i
$507$	−15.0000	−	8.66025i	−0.666173	−	0.384615i
$508$	−36.0000			−1.59724
$509$	−16.4545	+	28.5000i	−0.729332	+	1.26324i	0.227834	+	0.973700i	$0.426836\pi$
$509$	−16.4545	+	28.5000i	−0.729332	+	1.26324i	−0.957166	+	0.289540i	$0.906498\pi$
$510$	−7.09808	−	1.90192i	−0.314308	−	0.0842186i
$511$	−21.6506	+	7.50000i	−0.957768	+	0.331780i
$512$	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
$515$	−4.50000	−	7.79423i	−0.198294	−	0.343455i
$516$	15.5885	−	27.0000i	0.686244	−	1.18861i
$517$	8.66025	+	15.0000i	0.380878	+	0.659699i
$518$	−2.09808	−	3.09808i	−0.0921842	−	0.136122i
$519$			6.00000i			0.263371i
$520$	−6.00000	−	6.00000i	−0.263117	−	0.263117i
$521$	−4.50000	−	2.59808i	−0.197149	−	0.113824i	0.398176	−	0.917309i	$-0.369643\pi$
$521$	−4.50000	−	2.59808i	−0.197149	−	0.113824i	−0.595325	+	0.803485i	$0.702977\pi$
$522$	28.6865	−	7.68653i	1.25558	−	0.336430i
$523$	10.5000	−	6.06218i	0.459133	−	0.265081i	−0.252547	−	0.967585i	$-0.581268\pi$
$523$	10.5000	−	6.06218i	0.459133	−	0.265081i	0.711680	+	0.702504i	$0.247935\pi$
$524$	8.66025	−	15.0000i	0.378325	−	0.655278i
$525$	1.73205	−	9.00000i	0.0755929	−	0.392792i
$526$	4.75833	−	17.7583i	0.207473	−	0.774300i
$527$	−10.3923	−	6.00000i	−0.452696	−	0.261364i
$528$	−30.0000	+	17.3205i	−1.30558	+	0.753778i
$529$	13.0000	+	22.5167i	0.565217	+	0.978985i
$530$	−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
$535$	−8.66025			−0.374415
$536$	16.0000	+	16.0000i	0.691095	+	0.691095i
$537$	16.5000	+	9.52628i	0.712028	+	0.411089i
$538$	0.633975	+	2.36603i	0.0273326	+	0.102007i
$539$	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	−0.554809	−	0.831978i	$-0.687209\pi$
$541$	−2.59808	+	1.50000i	−0.111700	+	0.0644900i	0.443109	+	0.896468i	$0.353875\pi$
$542$	21.2942	+	5.70577i	0.914665	+	0.245084i
$543$		−	6.00000i		−	0.257485i
$544$	−9.46410	+	2.53590i	−0.405770	+	0.108726i
$545$	−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
$549$	−10.3923			−0.443533
$550$	3.66025	+	13.6603i	0.156074	+	0.582475i
$551$	12.1244			0.516515
$552$	−33.1244	+	8.87564i	−1.40987	+	0.377773i
$553$	12.0000	+	10.3923i	0.510292	+	0.441926i
$554$	−7.68653	+	28.6865i	−0.326570	+	1.21877i
$555$	−3.00000			−0.127343
$556$	15.5885	+	27.0000i	0.661098	+	1.14506i
$557$	40.7032	+	23.5000i	1.72465	+	0.995727i	0.908498	+	0.417889i	$0.137230\pi$
$557$	40.7032	+	23.5000i	1.72465	+	0.995727i	0.816152	+	0.577838i	$0.196103\pi$
$558$	20.7846	−	20.7846i	0.879883	−	0.879883i
$559$	−15.5885			−0.659321
$560$	6.00000	+	17.3205i	0.253546	+	0.731925i
$561$	15.0000			0.633300
$562$	−4.02628	−	15.0263i	−0.169838	−	0.633845i
$563$			3.46410i			0.145994i	0.997332	+	0.0729972i	$0.0232564\pi$
$563$			3.46410i			0.145994i	−0.997332	+	0.0729972i	$0.976744\pi$
$564$	−12.0000			−0.505291
$565$	1.73205			0.0728679
$566$	−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
$569$	20.0000			0.838444			0.419222	−	0.907884i	$-0.362303\pi$
$569$	20.0000			0.838444			0.419222	+	0.907884i	$0.362303\pi$
$570$	5.19615	−	5.19615i	0.217643	−	0.217643i
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$	15.0000	+	8.66025i	0.627182	+	0.362103i
$573$	24.2487			1.01300
$574$	−25.4378	−	37.5622i	−1.06175	−	1.56782i
$575$			14.0000i			0.583840i
$576$		−	24.0000i		−	1.00000i
$577$	−28.5000	−	16.4545i	−1.18647	−	0.685009i	−0.228968	−	0.973434i	$-0.573535\pi$
$577$	−28.5000	−	16.4545i	−1.18647	−	0.685009i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	−19.1244	−	5.12436i	−0.795468	−	0.213145i
$579$			10.3923i			0.431889i
$580$	12.1244	+	21.0000i	0.503436	+	0.871978i
$581$	38.9711	−	13.5000i	1.61680	−	0.560074i
$582$	−1.09808	−	4.09808i	−0.0455167	−	0.169871i
$583$		−	55.0000i		−	2.27787i
$584$	6.33975	+	23.6603i	0.262341	+	0.979068i
$585$	−9.00000			−0.372104
$586$	2.36603	+	0.633975i	0.0977396	+	0.0261892i
$587$	7.50000	+	4.33013i	0.309558	+	0.178723i	0.646729	−	0.762720i	$-0.276137\pi$
$587$	7.50000	+	4.33013i	0.309558	+	0.178723i	−0.337171	+	0.941444i	$0.609470\pi$
$588$	3.46410	+	24.0000i	0.142857	+	0.989743i
$589$	10.3923	−	6.00000i	0.428207	−	0.247226i
$590$	−16.3923	+	4.39230i	−0.674861	+	0.180828i
$591$	13.8564			0.569976
$592$	−3.46410	+	2.00000i	−0.142374	+	0.0821995i
$593$	−25.5000	+	14.7224i	−1.04716	+	0.604578i	−0.921853	−	0.387540i	$-0.873325\pi$
$593$	−25.5000	+	14.7224i	−1.04716	+	0.604578i	−0.125307	+	0.992118i	$0.539991\pi$
$594$	−9.50962	+	35.4904i	−0.390184	+	1.45619i
$595$	1.50000	−	7.79423i	0.0614940	−	0.319532i
$596$	−11.0000	+	19.0526i	−0.450578	+	0.780423i
$597$	−12.9904	−	7.50000i	−0.531661	−	0.306955i
$598$	12.1244	+	12.1244i	0.495802	+	0.495802i
$599$			44.0000i			1.79779i	0.438163	+	0.898896i	$0.355629\pi$
$599$			44.0000i			1.79779i	−0.438163	+	0.898896i	$0.644371\pi$
$600$	−9.46410	−	2.53590i	−0.386370	−	0.103528i
$601$	−7.50000	−	4.33013i	−0.305931	−	0.176630i	0.339173	−	0.940724i	$-0.389853\pi$
$601$	−7.50000	−	4.33013i	−0.305931	−	0.176630i	−0.645104	+	0.764094i	$0.723186\pi$
$602$	30.2942	+	14.7058i	1.23470	+	0.599362i
$603$	24.0000			0.977356
$604$	5.00000	+	8.66025i	0.203447	+	0.352381i
$605$	12.1244	+	21.0000i	0.492925	+	0.853771i
$606$	−1.09808	+	4.09808i	−0.0446063	+	0.166473i
$607$	−18.1865	+	31.5000i	−0.738169	+	1.27855i	0.215150	+	0.976581i	$0.430976\pi$
$607$	−18.1865	+	31.5000i	−0.738169	+	1.27855i	−0.953319	+	0.301965i	$0.902358\pi$
$608$	2.53590	−	9.46410i	0.102844	−	0.383820i
$609$	10.5000	+	30.3109i	0.425481	+	1.22826i
$610$	−2.19615	−	8.19615i	−0.0889196	−	0.331853i
$611$	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	0.0855362	−	0.996335i	$-0.472740\pi$
$613$	−18.1865	−	10.5000i	−0.734547	−	0.424091i	−0.820083	+	0.572244i	$0.806073\pi$
$614$	−6.92820	−	6.92820i	−0.279600	−	0.279600i
$615$	−36.3731			−1.46670
$616$	−20.9808	−	30.9808i	−0.845339	−	1.24825i
$617$	−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	$0.986550\pi$
$618$	−12.2942	+	3.29423i	−0.494546	+	0.132513i
$619$	−28.5000	+	16.4545i	−1.14551	+	0.661361i	−0.947790	−	0.318897i	$-0.896688\pi$
$619$	−28.5000	+	16.4545i	−1.14551	+	0.661361i	−0.197722	+	0.980258i	$0.563354\pi$
$620$	20.7846	+	12.0000i	0.834730	+	0.481932i
$621$	−18.1865	+	31.5000i	−0.729800	+	1.26405i
$622$	−20.7846	+	20.7846i	−0.833387	+	0.833387i
$623$	4.33013	−	22.5000i	0.173483	−	0.901443i
$624$	−10.3923	+	6.00000i	−0.416025	+	0.240192i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	10.3923	+	10.3923i	0.415360	+	0.415360i
$627$	−7.50000	+	12.9904i	−0.299521	+	0.518786i
$628$			41.5692i			1.65879i
$629$	1.73205			0.0690614
$630$	17.4904	+	8.49038i	0.696833	+	0.338265i
$631$		−	42.0000i		−	1.67199i	−0.548734	−	0.835997i	$-0.684890\pi$
$631$		−	42.0000i		−	1.67199i	0.548734	−	0.835997i	$-0.315110\pi$
$632$	12.0000	−	12.0000i	0.477334	−	0.477334i
$633$	13.5000	−	7.79423i	0.536577	−	0.309793i
$634$	−14.0000	−	14.0000i	−0.556011	−	0.556011i
$635$	−27.0000	−	15.5885i	−1.07146	−	0.618609i
$636$	33.0000	+	19.0526i	1.30854	+	0.755483i
$637$	9.52628	−	7.50000i	0.377445	−	0.297161i
$638$	−35.0000	−	35.0000i	−1.38566	−	1.38566i
$639$		−	30.0000i		−	1.18678i
$640$	18.9282	−	5.07180i	0.748203	−	0.200480i
$641$	−5.50000	−	9.52628i	−0.217237	−	0.376265i	0.736725	−	0.676192i	$-0.236371\pi$
$641$	−5.50000	−	9.52628i	−0.217237	−	0.376265i	−0.953962	+	0.299927i	$0.903038\pi$
$642$	−3.16987	+	11.8301i	−0.125105	+	0.466898i
$643$	10.5000	−	6.06218i	0.414080	−	0.239069i	−0.278462	−	0.960447i	$-0.589824\pi$
$643$	10.5000	−	6.06218i	0.414080	−	0.239069i	0.692541	+	0.721378i	$0.256491\pi$
$644$	−12.1244	−	35.0000i	−0.477767	−	1.37919i
$645$	23.3827	−	13.5000i	0.920692	−	0.531562i
$646$	−3.00000	+	3.00000i	−0.118033	+	0.118033i
$647$	−16.4545	+	28.5000i	−0.646892	+	1.12045i	0.336968	+	0.941516i	$0.390598\pi$
$647$	−16.4545	+	28.5000i	−0.646892	+	1.12045i	−0.983861	+	0.178935i	$0.942735\pi$
$648$	−18.0000	−	18.0000i	−0.707107	−	0.707107i
$649$	30.0000	−	17.3205i	1.17760	−	0.679889i
$650$	1.26795	+	4.73205i	0.0497331	+	0.185606i
$651$	24.0000	+	20.7846i	0.940634	+	0.814613i
$652$	12.1244	−	7.00000i	0.474826	−	0.274141i
$653$	−11.2583	−	6.50000i	−0.440573	−	0.254365i	0.263268	−	0.964723i	$-0.415200\pi$
$653$	−11.2583	−	6.50000i	−0.440573	−	0.254365i	−0.703840	+	0.710358i	$0.748533\pi$
$654$	3.16987	+	11.8301i	0.123952	+	0.462595i
$655$	12.9904	−	7.50000i	0.507576	−	0.293049i
$656$	−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	$0.197715\pi$
$660$	−30.0000			−1.16775
$661$	−3.46410			−0.134738			−0.0673690	−	0.997728i	$-0.521460\pi$
$661$	−3.46410			−0.134738			−0.0673690	+	0.997728i	$0.521460\pi$
$662$	6.00000	−	6.00000i	0.233197	−	0.233197i
$663$	5.19615			0.201802
$664$	−11.4115	−	42.5885i	−0.442854	−	1.65275i
$665$	6.00000	+	5.19615i	0.232670	+	0.201498i
$666$	−1.09808	+	4.09808i	−0.0425496	+	0.158797i
$667$	−24.5000	−	42.4352i	−0.948644	−	1.64310i
$668$	−15.0000	+	8.66025i	−0.580367	+	0.335075i
$669$	18.1865	+	10.5000i	0.703132	+	0.405953i
$670$	5.07180	+	18.9282i	0.195941	+	0.731260i
$671$	8.66025	+	15.0000i	0.334325	+	0.579069i
$672$	25.8564	−	1.85641i	0.997433	−	0.0716124i
$673$	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
$675$	−9.00000	+	5.19615i	−0.346410	+	0.200000i
$676$	−17.3205	−	10.0000i	−0.666173	−	0.384615i
$677$	−20.7846			−0.798817			−0.399409	−	0.916773i	$-0.630785\pi$
$677$	−20.7846			−0.798817			−0.399409	+	0.916773i	$0.630785\pi$
$678$	0.633975	−	2.36603i	0.0243476	−	0.0908667i
$679$	4.33013	−	1.50000i	0.166175	−	0.0575647i
$680$	−8.19615	−	2.19615i	−0.314308	−	0.0842186i
$681$	16.5000	+	28.5788i	0.632281	+	1.09514i
$682$	−47.3205	−	12.6795i	−1.81200	−	0.485523i
$683$	−0.500000	+	0.866025i	−0.0191320	+	0.0331375i	−0.875433	−	0.483340i	$-0.839424\pi$
$683$	−0.500000	+	0.866025i	−0.0191320	+	0.0331375i	0.856301	+	0.516477i	$0.172757\pi$
$684$	−5.19615	−	9.00000i	−0.198680	−	0.344124i
$685$	22.5167			0.860317
$686$	−25.5885	+	5.58846i	−0.976972	+	0.213368i
$687$	−18.1865	−	10.5000i	−0.693860	−	0.400600i
$688$	18.0000	−	31.1769i	0.686244	−	1.18861i
$689$		−	19.0526i		−	0.725845i
$690$	−28.6865	−	7.68653i	−1.09208	−	0.292621i
$691$		−	38.1051i		−	1.44959i	−0.688966	−	0.724793i	$-0.741935\pi$
$691$		−	38.1051i		−	1.44959i	0.688966	−	0.724793i	$-0.258065\pi$
$692$			6.92820i			0.263371i
$693$	−38.9711	−	7.50000i	−1.48039	−	0.284901i
$694$	16.0000	−	16.0000i	0.607352	−	0.607352i
$695$			27.0000i			1.02417i
$696$	33.1244	−	8.87564i	1.25558	−	0.336430i
$697$	21.0000			0.795432
$698$	4.43782	+	16.5622i	0.167974	+	0.626888i
$699$	16.5000	−	9.52628i	0.624087	−	0.360317i
$700$	2.00000	−	10.3923i	0.0755929	−	0.392792i
$701$			44.0000i			1.66186i	0.556379	+	0.830929i	$0.312190\pi$
$701$			44.0000i			1.66186i	−0.556379	+	0.830929i	$0.687810\pi$
$702$	−3.29423	+	12.2942i	−0.124333	+	0.464016i
$703$	−0.866025	+	1.50000i	−0.0326628	+	0.0565736i
$704$	−34.6410	+	20.0000i	−1.30558	+	0.753778i
$705$	−9.00000	−	5.19615i	−0.338960	−	0.195698i
$706$	−1.90192	+	7.09808i	−0.0715798	+	0.267140i
$707$	−4.50000	−	0.866025i	−0.169240	−	0.0325702i
$708$			24.0000i			0.901975i
$709$		−	52.0000i		−	1.95290i	−0.215742	−	0.976450i	$-0.569217\pi$
$709$		−	52.0000i		−	1.95290i	0.215742	−	0.976450i	$-0.430783\pi$
$710$	23.6603	−	6.33975i	0.887954	−	0.237926i
$711$		−	18.0000i		−	0.675053i
$712$	−23.6603	−	6.33975i	−0.886706	−	0.237592i
$713$	−42.0000	−	24.2487i	−1.57291	−	0.908121i
$714$	−10.0981	−	4.90192i	−0.377911	−	0.183450i
$715$	7.50000	+	12.9904i	0.280484	+	0.485813i
$716$	19.0526	+	11.0000i	0.712028	+	0.411089i
$717$	4.33013	+	7.50000i	0.161712	+	0.280093i
$718$	2.56218	−	9.56218i	0.0956196	−	0.356857i
$719$	−23.3827	−	40.5000i	−0.872027	−	1.51040i	−0.859896	−	0.510469i	$-0.829472\pi$
$719$	−23.3827	−	40.5000i	−0.872027	−	1.51040i	−0.0121307	−	0.999926i	$-0.503861\pi$
$720$	10.3923	−	18.0000i	0.387298	−	0.670820i
$721$	−4.50000	−	12.9904i	−0.167589	−	0.483787i
$722$	5.85641	+	21.8564i	0.217953	+	0.813411i
$723$	4.50000	+	7.79423i	0.167357	+	0.289870i
$724$		−	6.92820i		−	0.257485i
$725$		−	14.0000i		−	0.519947i
$726$	33.1244	−	8.87564i	1.22936	−	0.329406i
$727$	−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
$731$	−13.5000	+	7.79423i	−0.499316	+	0.288280i
$732$	−12.0000			−0.443533
$733$	−4.33013	+	7.50000i	−0.159937	+	0.277019i	−0.934846	−	0.355054i	$-0.884462\pi$
$733$	−4.33013	+	7.50000i	−0.159937	+	0.277019i	0.774909	+	0.632073i	$0.217796\pi$
$734$	49.6865	+	13.3135i	1.83396	+	0.491409i
$735$	−7.79423	+	19.5000i	−0.287494	+	0.719268i
$736$	−38.2487	+	10.2487i	−1.40987	+	0.377773i
$737$	−20.0000	−	34.6410i	−0.736709	−	1.27602i
$738$	−13.3135	+	49.6865i	−0.490075	+	1.82899i
$739$	11.5000	−	19.9186i	0.423034	−	0.732717i	−0.573200	−	0.819415i	$-0.694298\pi$
$739$	11.5000	−	19.9186i	0.423034	−	0.732717i	0.996235	+	0.0866983i	$0.0276316\pi$
$740$	−3.46410			−0.127343
$741$	−2.59808	+	4.50000i	−0.0954427	+	0.165312i
$742$	−17.9737	+	37.0263i	−0.659836	+	1.35928i
$743$	16.4545	−	9.50000i	0.603656	−	0.348521i	−0.166822	−	0.985987i	$-0.553351\pi$
$743$	16.4545	−	9.50000i	0.603656	−	0.348521i	0.770479	+	0.637466i	$0.220017\pi$
$744$	24.0000	−	24.0000i	0.879883	−	0.879883i
$745$	−16.5000	+	9.52628i	−0.604513	+	0.349016i
$746$	4.09808	−	1.09808i	0.150041	−	0.0402034i
$747$	−40.5000	−	23.3827i	−1.48182	−	0.855528i
$748$	17.3205			0.633300
$749$	−12.9904	−	2.50000i	−0.474658	−	0.0913480i
$750$	−21.0000	−	21.0000i	−0.766812	−	0.766812i
$751$	−40.7032	−	23.5000i	−1.48528	−	0.857527i	−0.485421	−	0.874281i	$-0.661334\pi$
$751$	−40.7032	−	23.5000i	−1.48528	−	0.857527i	−0.999860	+	0.0167534i	$0.994667\pi$
$752$	−13.8564			−0.505291
$753$	−24.0000			−0.874609
$754$	−12.1244	−	12.1244i	−0.441543	−	0.441543i
$755$			8.66025i			0.315179i
$756$	18.0000	−	20.7846i	0.654654	−	0.755929i
$757$		−	26.0000i		−	0.944986i	−0.881334	−	0.472493i	$-0.843354\pi$
$757$		−	26.0000i		−	0.944986i	0.881334	−	0.472493i	$-0.156646\pi$
$758$	18.0000	−	18.0000i	0.653789	−	0.653789i
$759$	60.6218			2.20043
$760$	6.00000	−	6.00000i	0.217643	−	0.217643i
$761$	37.5000	+	21.6506i	1.35937	+	0.784835i	0.989539	−	0.144263i	$-0.0460810\pi$
$761$	37.5000	+	21.6506i	1.35937	+	0.784835i	0.369835	+	0.929098i	$0.379414\pi$
$762$	−31.1769	+	31.1769i	−1.12942	+	1.12942i
$763$	−12.5000	+	4.33013i	−0.452530	+	0.156761i
$764$	28.0000			1.01300
$765$	−7.79423	+	4.50000i	−0.281801	+	0.162698i
$766$	−13.3135	−	49.6865i	−0.481035	−	1.79525i
$767$	10.3923	−	6.00000i	0.375244	−	0.216647i
$768$		−	27.7128i		−	1.00000i
$769$	−19.5000	+	11.2583i	−0.703188	+	0.405986i	−0.808534	−	0.588450i	$-0.799738\pi$
$769$	−19.5000	+	11.2583i	−0.703188	+	0.405986i	0.105346	+	0.994436i	$0.466405\pi$
$770$	−2.32051	−	32.3205i	−0.0836253	−	1.16475i
$771$	−19.5000	+	33.7750i	−0.702275	+	1.21638i
$772$			12.0000i			0.431889i
$773$	25.1147	−	43.5000i	0.903314	−	1.56459i	0.0801501	−	0.996783i	$-0.474460\pi$
$773$	25.1147	−	43.5000i	0.903314	−	1.56459i	0.823164	−	0.567803i	$-0.192207\pi$
$774$	−9.88269	−	36.8827i	−0.355226	−	1.32572i
$775$	−6.92820	−	12.0000i	−0.248868	−	0.431053i
$776$	−1.26795	−	4.73205i	−0.0455167	−	0.169871i
$777$	−4.50000	−	0.866025i	−0.161437	−	0.0310685i
$778$	−0.366025	+	1.36603i	−0.0131226	+	0.0489744i
$779$	−10.5000	+	18.1865i	−0.376202	+	0.651600i
$780$	−10.3923			−0.372104
$781$	−43.3013	+	25.0000i	−1.54944	+	0.894570i
$782$	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
$786$	−5.49038	−	20.4904i	−0.195835	−	0.730868i
$787$		−	41.5692i		−	1.48178i	−0.671625	−	0.740891i	$-0.734403\pi$
$787$		−	41.5692i		−	1.48178i	0.671625	−	0.740891i	$-0.265597\pi$
$788$	16.0000			0.569976
$789$	−11.2583	−	19.5000i	−0.400807	−	0.694218i
$790$	14.1962	−	3.80385i	0.505076	−	0.135335i
$791$	2.59808	+	0.500000i	0.0923770	+	0.0177780i
$792$	−10.9808	+	40.9808i	−0.390184	+	1.45619i
$793$	3.00000	+	5.19615i	0.106533	+	0.184521i
$794$	44.9545	+	12.0455i	1.59537	+	0.427479i
$795$	16.5000	+	28.5788i	0.585195	+	1.01359i
$796$	−15.0000	−	8.66025i	−0.531661	−	0.306955i
$797$	−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	$0.985535\pi$
$798$	9.29423	−	6.29423i	0.329012	−	0.222813i
$799$	5.19615	+	3.00000i	0.183827	+	0.106132i
$800$	−10.9282	−	2.92820i	−0.386370	−	0.103528i
$801$	−22.5000	+	12.9904i	−0.794998	+	0.458993i
$802$	9.15064	+	34.1506i	0.323120	+	1.20590i
$803$		−	43.3013i		−	1.52807i
$804$	27.7128			0.977356
$805$	6.06218	−	31.5000i	0.213664	−	1.11023i
$806$	−16.3923	−	4.39230i	−0.577394	−	0.154712i
$807$	2.59808	+	1.50000i	0.0914566	+	0.0528025i
$808$	−1.26795	+	4.73205i	−0.0446063	+	0.166473i
$809$	2.50000	−	4.33013i	0.0878953	−	0.152239i	−0.818726	−	0.574184i	$-0.805319\pi$
$809$	2.50000	−	4.33013i	0.0878953	−	0.152239i	0.906621	+	0.421945i	$0.138653\pi$
$810$	−5.70577	−	21.2942i	−0.200480	−	0.748203i
$811$			41.5692i			1.45969i	0.683611	+	0.729846i	$0.260408\pi$
$811$			41.5692i			1.45969i	−0.683611	+	0.729846i	$0.739592\pi$
$812$	12.1244	+	35.0000i	0.425481	+	1.22826i
$813$	23.3827	−	13.5000i	0.820067	−	0.473466i
$814$	6.83013	−	1.83013i	0.239396	−	0.0641459i
$815$	12.1244			0.424698
$816$	−6.00000	+	10.3923i	−0.210042	+	0.363803i
$817$		−	15.5885i		−	0.545371i
$818$	−31.1769	−	31.1769i	−1.09008	−	1.09008i
$819$	−13.5000	−	2.59808i	−0.471728	−	0.0907841i
$820$	−42.0000			−1.46670
$821$		−	2.00000i		−	0.0698005i	−0.999391	−	0.0349002i	$-0.988889\pi$
$821$		−	2.00000i		−	0.0698005i	0.999391	−	0.0349002i	$-0.0111113\pi$
$822$	8.24167	−	30.7583i	0.287461	−	1.07282i
$823$			54.0000i			1.88232i	0.337959	+	0.941161i	$0.390263\pi$
$823$			54.0000i			1.88232i	−0.337959	+	0.941161i	$0.609737\pi$
$824$	−14.1962	+	3.80385i	−0.494546	+	0.132513i
$825$	15.0000	+	8.66025i	0.522233	+	0.301511i
$826$	−25.8564	+	1.85641i	−0.899659	+	0.0645926i
$827$	−38.0000			−1.32139			−0.660695	−	0.750655i	$-0.729738\pi$
$827$	−38.0000			−1.32139			−0.660695	+	0.750655i	$0.729738\pi$
$828$	−21.0000	+	36.3731i	−0.729800	+	1.26405i
$829$	11.2583	−	19.5000i	0.391018	−	0.677263i	−0.601566	−	0.798823i	$-0.705456\pi$
$829$	11.2583	−	19.5000i	0.391018	−	0.677263i	0.992584	+	0.121560i	$0.0387897\pi$
$830$	9.88269	−	36.8827i	0.343033	−	1.28022i
$831$	18.1865	+	31.5000i	0.630884	+	1.09272i
$832$	−12.0000	+	6.92820i	−0.416025	+	0.240192i
$833$	4.50000	−	11.2583i	0.155916	−	0.390078i
$834$	36.8827	+	9.88269i	1.27714	+	0.342209i
$835$	−15.0000			−0.519096
$836$	−8.66025	+	15.0000i	−0.299521	+	0.518786i
$837$		−	36.0000i		−	1.24434i
$838$	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	$0.253388\pi$
$840$	20.1962	+	9.80385i	0.696833	+	0.338265i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	20.4904	−	5.49038i	0.706145	−	0.189211i
$843$	−16.5000	−	9.52628i	−0.568290	−	0.328102i
$844$	15.5885	−	9.00000i	0.536577	−	0.309793i
$845$	−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
$849$	−24.0000			−0.823678
$850$	3.46410	+	3.46410i	0.118818	+	0.118818i
$851$	7.00000			0.239957
$852$		−	34.6410i		−	1.18678i
$853$	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
$857$	13.5000	−	7.79423i	0.461151	−	0.266246i	−0.251377	−	0.967889i	$-0.580883\pi$
$857$	13.5000	−	7.79423i	0.461151	−	0.266246i	0.712528	+	0.701643i	$0.247550\pi$
$858$	20.4904	−	5.49038i	0.699530	−	0.187439i
$859$	−25.5000	−	14.7224i	−0.870049	−	0.502323i	−0.00268433	−	0.999996i	$-0.500854\pi$
$859$	−25.5000	−	14.7224i	−0.870049	−	0.502323i	−0.867364	+	0.497674i	$0.834188\pi$
$860$	27.0000	−	15.5885i	0.920692	−	0.531562i
$861$	−54.5596	−	10.5000i	−1.85939	−	0.357839i
$862$	6.83013	−	1.83013i	0.232635	−	0.0623344i
$863$	−19.9186	+	11.5000i	−0.678036	+	0.391465i	−0.799115	−	0.601178i	$-0.794698\pi$
$863$	−19.9186	+	11.5000i	−0.678036	+	0.391465i	0.121078	+	0.992643i	$0.461365\pi$
$864$	−20.7846	−	20.7846i	−0.707107	−	0.707107i
$865$	−3.00000	+	5.19615i	−0.102003	+	0.176674i
$866$	−31.1769	−	31.1769i	−1.05943	−	1.05943i
$867$	−21.0000	+	12.1244i	−0.713197	+	0.411765i
$868$	27.7128	+	24.0000i	0.940634	+	0.814613i
$869$	−25.9808	+	15.0000i	−0.881337	+	0.508840i
$870$	28.6865	+	7.68653i	0.972565	+	0.260598i
$871$	−6.92820	−	12.0000i	−0.234753	−	0.406604i
$872$	3.66025	+	13.6603i	0.123952	+	0.462595i
$873$	−4.50000	−	2.59808i	−0.152302	−	0.0879316i
$874$	−12.1244	+	12.1244i	−0.410112	+	0.410112i
$875$	21.0000	−	24.2487i	0.709930	−	0.819756i
$876$	25.9808	+	15.0000i	0.877809	+	0.506803i
$877$	38.9711	+	22.5000i	1.31596	+	0.759771i	0.983076	−	0.183196i	$-0.0586444\pi$
$877$	38.9711	+	22.5000i	1.31596	+	0.759771i	0.332886	+	0.942967i	$0.391978\pi$
$878$	27.7128	−	27.7128i	0.935262	−	0.935262i
$879$	2.59808	−	1.50000i	0.0876309	−	0.0505937i
$880$	−34.6410			−1.16775
$881$			10.3923i			0.350126i	0.984557	+	0.175063i	$0.0560129\pi$
$881$			10.3923i			0.350126i	−0.984557	+	0.175063i	$0.943987\pi$
$882$	23.7846	+	17.7846i	0.800869	+	0.598839i
$883$	−54.0000			−1.81724			−0.908622	−	0.417619i	$-0.862865\pi$
$883$	−54.0000			−1.81724			−0.908622	+	0.417619i	$0.862865\pi$
$884$	6.00000			0.201802
$885$	−10.3923	+	18.0000i	−0.349334	+	0.605063i
$886$	26.0000	−	26.0000i	0.873487	−	0.873487i
$887$	−12.9904	+	22.5000i	−0.436174	+	0.755476i	−0.997391	−	0.0721931i	$-0.977000\pi$
$887$	−12.9904	+	22.5000i	−0.436174	+	0.755476i	0.561216	+	0.827669i	$0.310334\pi$
$888$	−1.26795	+	4.73205i	−0.0425496	+	0.158797i
$889$	−36.0000	−	31.1769i	−1.20740	−	1.04564i
$890$	−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
$893$	−5.19615	+	3.00000i	−0.173883	+	0.100391i
$894$	6.97372	+	26.0263i	0.233236	+	0.870449i
$895$	9.52628	+	16.5000i	0.318428	+	0.551534i
$896$	29.8564	−	2.14359i	0.997433	−	0.0716124i
$897$	21.0000			0.701170
$898$	22.0000	−	22.0000i	0.734150	−	0.734150i
$899$	42.0000	+	24.2487i	1.40078	+	0.808740i
$900$	−10.3923	+	6.00000i	−0.346410	+	0.200000i
$901$	−9.52628	−	16.5000i	−0.317366	−	0.549695i
$902$	82.8109	−	22.1891i	2.75730	−	0.738817i
$903$	38.9711	−	13.5000i	1.29688	−	0.449252i
$904$	0.732051	−	2.73205i	0.0243476	−	0.0908667i
$905$	3.00000	−	5.19615i	0.0997234	−	0.172726i
$906$	11.8301	+	3.16987i	0.393030	+	0.105312i
$907$	−19.5000	−	33.7750i	−0.647487	−	1.12148i	−0.983721	−	0.179702i	$-0.942487\pi$
$907$	−19.5000	−	33.7750i	−0.647487	−	1.12148i	0.336234	−	0.941778i	$-0.390847\pi$
$908$	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	$-0.992221\pi$
$911$	−45.8993	−	26.5000i	−1.52071	−	0.877984i	−0.521012	−	0.853549i	$-0.674445\pi$
$912$	−6.00000	−	10.3923i	−0.198680	−	0.344124i
$913$			77.9423i			2.57951i
$914$	24.0000	−	24.0000i	0.793849	−	0.793849i
$915$	−9.00000	−	5.19615i	−0.297531	−	0.171780i
$916$	−21.0000	−	12.1244i	−0.693860	−	0.400600i
$917$	21.6506	−	7.50000i	0.714967	−	0.247672i
$918$	3.29423	+	12.2942i	0.108726	+	0.405770i
$919$	16.4545	−	9.50000i	0.542783	−	0.313376i	−0.203423	−	0.979091i	$-0.565207\pi$
$919$	16.4545	−	9.50000i	0.542783	−	0.313376i	0.746206	+	0.665715i	$0.231873\pi$
$920$	−33.1244	−	8.87564i	−1.09208	−	0.292621i
$921$	−12.0000			−0.395413
$922$	−1.90192	−	7.09808i	−0.0626365	−	0.233763i
$923$	−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
$929$		−	17.3205i		−	0.568267i	−0.958785	−	0.284134i	$-0.908294\pi$
$929$		−	17.3205i		−	0.568267i	0.958785	−	0.284134i	$-0.0917060\pi$
$930$	28.3923	−	7.60770i	0.931020	−	0.249466i
$931$	7.50000	+	9.52628i	0.245803	+	0.312211i
$932$	19.0526	−	11.0000i	0.624087	−	0.360317i
$933$			36.0000i			1.17859i
$934$	3.16987	−	11.8301i	0.103721	−	0.387094i
$935$	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	$-0.908698\pi$
$937$		−	17.3205i		−	0.565836i	0.959144	−	0.282918i	$-0.0913025\pi$
$938$	2.14359	+	29.8564i	0.0699908	+	0.974846i
$939$	18.0000			0.587408
$940$	−10.3923	−	6.00000i	−0.338960	−	0.195698i
$941$	45.0333			1.46804			0.734022	−	0.679126i	$-0.237641\pi$
$941$	45.0333			1.46804			0.734022	+	0.679126i	$0.237641\pi$
$942$	36.0000	+	36.0000i	1.17294	+	1.17294i
$943$	84.8705			2.76376
$944$			27.7128i			0.901975i
$945$	22.5000	−	7.79423i	0.731925	−	0.253546i
$946$	−45.0000	+	45.0000i	−1.46308	+	1.46308i
$947$	−26.0000			−0.844886			−0.422443	−	0.906389i	$-0.638827\pi$
$947$	−26.0000			−0.844886			−0.422443	+	0.906389i	$0.638827\pi$
$948$		−	20.7846i		−	0.675053i
$949$		−	15.0000i		−	0.486921i
$950$	−4.73205	+	1.26795i	−0.153528	+	0.0411377i
$951$	−24.2487			−0.786318
$952$	−11.6603	−	5.66025i	−0.377911	−	0.183450i
$953$	20.0000			0.647864			0.323932	−	0.946080i	$-0.394995\pi$
$953$	20.0000			0.647864			0.323932	+	0.946080i	$0.394995\pi$
$954$	45.0788	−	12.0788i	1.45948	−	0.391067i
$955$	21.0000	+	12.1244i	0.679544	+	0.392335i
$956$	5.00000	+	8.66025i	0.161712	+	0.280093i
$957$	−60.6218			−1.95962
$958$	2.36603	+	0.633975i	0.0764428	+	0.0204828i
$959$	33.7750	+	6.50000i	1.09065	+	0.209896i
$960$	12.0000	−	20.7846i	0.387298	−	0.670820i
$961$	17.0000			0.548387
$962$	2.36603	−	0.633975i	0.0762837	−	0.0204402i
$963$	7.50000	+	12.9904i	0.241684	+	0.418609i
$964$	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	−0.883327	−	0.468758i	$-0.844702\pi$
$967$	−28.5788	+	16.5000i	−0.919033	+	0.530604i	−0.0357069	+	0.999362i	$0.511368\pi$
$968$	38.2487	−	10.2487i	1.22936	−	0.329406i
$969$			5.19615i			0.166924i
$970$	1.09808	−	4.09808i	0.0352571	−	0.131581i
$971$	−7.50000	+	4.33013i	−0.240686	+	0.138960i	−0.615492	−	0.788143i	$-0.711043\pi$
$971$	−7.50000	+	4.33013i	−0.240686	+	0.138960i	0.374806	+	0.927103i	$0.377709\pi$
$972$	−31.1769			−1.00000
$973$	−7.79423	+	40.5000i	−0.249871	+	1.29837i
$974$	−31.4186	+	8.41858i	−1.00672	+	0.269749i
$975$	5.19615	+	3.00000i	0.166410	+	0.0960769i
$976$	−13.8564			−0.443533
$977$	−20.0000			−0.639857			−0.319928	−	0.947442i	$-0.603659\pi$
$977$	−20.0000			−0.639857			−0.319928	+	0.947442i	$0.603659\pi$
$978$	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
$983$	−14.7224	−	25.5000i	−0.469573	−	0.813324i	0.529822	−	0.848109i	$-0.322259\pi$
$983$	−14.7224	−	25.5000i	−0.469573	−	0.813324i	−0.999395	+	0.0347851i	$0.988925\pi$
$984$	−15.3731	+	57.3731i	−0.490075	+	1.82899i
$985$	12.0000	+	6.92820i	0.382352	+	0.220751i
$986$	−16.5622	−	4.43782i	−0.527447	−	0.141329i
$987$	−12.0000	−	10.3923i	−0.381964	−	0.330791i
$988$	−3.00000	+	5.19615i	−0.0954427	+	0.165312i
$989$	−54.5596	+	31.5000i	−1.73489	+	1.00164i
$990$	−25.9808	+	25.9808i	−0.825723	+	0.825723i
$991$	47.6314	+	27.5000i	1.51306	+	0.873566i	0.999883	+	0.0152841i	$0.00486527\pi$
$991$	47.6314	+	27.5000i	1.51306	+	0.873566i	0.513178	+	0.858282i	$0.328468\pi$
$992$	27.7128	−	27.7128i	0.879883	−	0.879883i
$993$		−	10.3923i		−	0.329790i
$994$	37.3205	−	2.67949i	1.18373	−	0.0849883i
$995$	−7.50000	−	12.9904i	−0.237766	−	0.411823i
$996$	−46.7654	−	27.0000i	−1.48182	−	0.855528i
$997$	−25.1147	−	43.5000i	−0.795392	−	1.37766i	−0.922590	−	0.385782i	$-0.873932\pi$
$997$	−25.1147	−	43.5000i	−0.795392	−	1.37766i	0.127198	−	0.991877i	$-0.459401\pi$
$998$	−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.bf.a.115.1	✓	4
7.5	odd	6		504.2.cz.a.187.1	yes	4
8.3	odd	2	inner	504.2.bf.a.115.2	yes	4
9.4	even	3		504.2.cz.a.283.2	yes	4
56.19	even	6		504.2.cz.a.187.2	yes	4
63.40	odd	6	inner	504.2.bf.a.355.1	yes	4
72.67	odd	6		504.2.cz.a.283.1	yes	4
504.355	even	6	inner	504.2.bf.a.355.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.a.115.1	✓	4	1.1	even	1	trivial
504.2.bf.a.115.2	yes	4	8.3	odd	2	inner
504.2.bf.a.355.1	yes	4	63.40	odd	6	inner
504.2.bf.a.355.2	yes	4	504.355	even	6	inner
504.2.cz.a.187.1	yes	4	7.5	odd	6
504.2.cz.a.187.2	yes	4	56.19	even	6
504.2.cz.a.283.1	yes	4	72.67	odd	6
504.2.cz.a.283.2	yes	4	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -1.73205i q^{3} -2.00000i q^{4} +(0.866025 - 1.50000i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(1.73205 - 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} -1.73205i q^{3} -2.00000i q^{4} +(0.866025 - 1.50000i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(1.73205 - 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} -3.00000 q^{9} +(-0.633975 - 2.36603i) q^{10} +(2.50000 + 4.33013i) q^{11} -3.46410 q^{12} +(0.866025 + 1.50000i) q^{13} +(-0.267949 - 3.73205i) q^{14} +(-2.59808 - 1.50000i) q^{15} -4.00000 q^{16} +(1.50000 + 0.866025i) q^{17} +(-3.00000 + 3.00000i) q^{18} +(-1.50000 + 0.866025i) q^{19} +(-3.00000 - 1.73205i) q^{20} +(-3.46410 - 3.00000i) q^{21} +(6.83013 + 1.83013i) q^{22} +(6.06218 + 3.50000i) q^{23} +(-3.46410 + 3.46410i) q^{24} +(1.00000 + 1.73205i) q^{25} +(2.36603 + 0.633975i) q^{26} +5.19615i q^{27} +(-4.00000 - 3.46410i) q^{28} +(-6.06218 - 3.50000i) q^{29} +(-4.09808 + 1.09808i) q^{30} -6.92820 q^{31} +(-4.00000 + 4.00000i) q^{32} +(7.50000 - 4.33013i) q^{33} +(2.36603 - 0.633975i) q^{34} +(-1.50000 - 4.33013i) q^{35} +6.00000i q^{36} +(0.866025 - 0.500000i) q^{37} +(-0.633975 + 2.36603i) q^{38} +(2.59808 - 1.50000i) q^{39} +(-4.73205 + 1.26795i) q^{40} +(10.5000 - 6.06218i) q^{41} +(-6.46410 + 0.464102i) 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} +3.46410 q^{47} +6.92820i q^{48} +(-1.00000 - 6.92820i) q^{49} +(2.73205 + 0.732051i) q^{50} +(1.50000 - 2.59808i) q^{51} +(3.00000 - 1.73205i) q^{52} +(-9.52628 - 5.50000i) q^{53} +(5.19615 + 5.19615i) q^{54} +8.66025 q^{55} +(-7.46410 + 0.535898i) q^{56} +(1.50000 + 2.59808i) q^{57} +(-9.56218 + 2.56218i) q^{58} -6.92820i q^{59} +(-3.00000 + 5.19615i) q^{60} +3.46410 q^{61} +(-6.92820 + 6.92820i) q^{62} +(-5.19615 + 6.00000i) q^{63} +8.00000i q^{64} +3.00000 q^{65} +(3.16987 - 11.8301i) q^{66} -8.00000 q^{67} +(1.73205 - 3.00000i) q^{68} +(6.06218 - 10.5000i) q^{69} +(-5.83013 - 2.83013i) q^{70} +10.0000i q^{71} +(6.00000 + 6.00000i) q^{72} +(-7.50000 - 4.33013i) q^{73} +(0.366025 - 1.36603i) q^{74} +(3.00000 - 1.73205i) q^{75} +(1.73205 + 3.00000i) q^{76} +(12.9904 + 2.50000i) q^{77} +(1.09808 - 4.09808i) q^{78} +6.00000i q^{79} +(-3.46410 + 6.00000i) q^{80} +9.00000 q^{81} +(4.43782 - 16.5622i) q^{82} +(13.5000 + 7.79423i) q^{83} +(-6.00000 + 6.92820i) q^{84} +(2.59808 - 1.50000i) q^{85} +(3.29423 + 12.2942i) q^{86} +(-6.06218 + 10.5000i) q^{87} +(3.66025 - 13.6603i) q^{88} +(7.50000 - 4.33013i) q^{89} +(1.90192 + 7.09808i) q^{90} +(4.50000 + 0.866025i) q^{91} +(7.00000 - 12.1244i) q^{92} +12.0000i q^{93} +(3.46410 - 3.46410i) q^{94} +3.00000i q^{95} +(6.92820 + 6.92820i) q^{96} +(1.50000 + 0.866025i) q^{97} +(-7.92820 - 5.92820i) q^{98} +(-7.50000 - 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{8} - 12 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^8 - 12 * q^9	\( 4 q + 4 q^{2} - 8 q^{8} - 12 q^{9} - 6 q^{10} + 10 q^{11} - 8 q^{14} - 16 q^{16} + 6 q^{17} - 12 q^{18} - 6 q^{19} - 12 q^{20} + 10 q^{22} + 4 q^{25} + 6 q^{26} - 16 q^{28} - 6 q^{30} - 16 q^{32} + 30 q^{33} + 6 q^{34} - 6 q^{35} - 6 q^{38} - 12 q^{40} + 42 q^{41} - 12 q^{42} - 18 q^{43} + 14 q^{46} - 4 q^{49} + 4 q^{50} + 6 q^{51} + 12 q^{52} - 16 q^{56} + 6 q^{57} - 14 q^{58} - 12 q^{60} + 12 q^{65} + 30 q^{66} - 32 q^{67} - 6 q^{70} + 24 q^{72} - 30 q^{73} - 2 q^{74} + 12 q^{75} - 6 q^{78} + 36 q^{81} + 42 q^{82} + 54 q^{83} - 24 q^{84} - 18 q^{86} - 20 q^{88} + 30 q^{89} + 18 q^{90} + 18 q^{91} + 28 q^{92} + 6 q^{97} - 4 q^{98} - 30 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^8 - 12 * q^9 - 6 * q^10 + 10 * q^11 - 8 * q^14 - 16 * q^16 + 6 * q^17 - 12 * q^18 - 6 * q^19 - 12 * q^20 + 10 * q^22 + 4 * q^25 + 6 * q^26 - 16 * q^28 - 6 * q^30 - 16 * q^32 + 30 * q^33 + 6 * q^34 - 6 * q^35 - 6 * q^38 - 12 * q^40 + 42 * q^41 - 12 * q^42 - 18 * q^43 + 14 * q^46 - 4 * q^49 + 4 * q^50 + 6 * q^51 + 12 * q^52 - 16 * q^56 + 6 * q^57 - 14 * q^58 - 12 * q^60 + 12 * q^65 + 30 * q^66 - 32 * q^67 - 6 * q^70 + 24 * q^72 - 30 * q^73 - 2 * q^74 + 12 * q^75 - 6 * q^78 + 36 * q^81 + 42 * q^82 + 54 * q^83 - 24 * q^84 - 18 * q^86 - 20 * q^88 + 30 * q^89 + 18 * q^90 + 18 * q^91 + 28 * q^92 + 6 * q^97 - 4 * q^98 - 30 * q^99

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