LMFDB - Embedded newform 504.2.bf.a.115.2

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			115.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	504.115
Dual form			504.2.bf.a.355.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} -1.73205i q^{3} +2.00000i q^{4} +(-0.866025 + 1.50000i) q^{5} +(1.73205 - 1.73205i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(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} +(-2.36603 + 0.633975i) q^{10} +(2.50000 + 4.33013i) q^{11} +3.46410 q^{12} +(-0.866025 - 1.50000i) q^{13} +(-3.73205 + 0.267949i) 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} +(-1.83013 + 6.83013i) q^{22} +(-6.06218 - 3.50000i) q^{23} +(3.46410 + 3.46410i) q^{24} +(1.00000 + 1.73205i) q^{25} +(0.633975 - 2.36603i) q^{26} +5.19615i q^{27} +(-4.00000 - 3.46410i) q^{28} +(6.06218 + 3.50000i) q^{29} +(1.09808 + 4.09808i) q^{30} +6.92820 q^{31} +(-4.00000 - 4.00000i) 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} +(-2.36603 - 0.633975i) q^{38} +(-2.59808 + 1.50000i) q^{39} +(-1.26795 - 4.73205i) q^{40} +(10.5000 - 6.06218i) q^{41} +(0.464102 + 6.46410i) q^{42} +(-4.50000 + 7.79423i) q^{43} +(-8.66025 + 5.00000i) q^{44} +(2.59808 - 4.50000i) q^{45} +(-2.56218 - 9.56218i) q^{46} -3.46410 q^{47} +6.92820i q^{48} +(-1.00000 - 6.92820i) q^{49} +(-0.732051 + 2.73205i) 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} +(-0.535898 - 7.46410i) q^{56} +(1.50000 + 2.59808i) q^{57} +(2.56218 + 9.56218i) 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} +(11.8301 + 3.16987i) q^{66} -8.00000 q^{67} +(-1.73205 + 3.00000i) q^{68} +(-6.06218 + 10.5000i) q^{69} +(2.83013 - 5.83013i) q^{70} -10.0000i q^{71} +(6.00000 - 6.00000i) q^{72} +(-7.50000 - 4.33013i) q^{73} +(-1.36603 - 0.366025i) q^{74} +(3.00000 - 1.73205i) q^{75} +(-1.73205 - 3.00000i) q^{76} +(-12.9904 - 2.50000i) q^{77} +(-4.09808 - 1.09808i) q^{78} -6.00000i q^{79} +(3.46410 - 6.00000i) q^{80} +9.00000 q^{81} +(16.5622 + 4.43782i) q^{82} +(13.5000 + 7.79423i) q^{83} +(-6.00000 + 6.92820i) q^{84} +(-2.59808 + 1.50000i) q^{85} +(-12.2942 + 3.29423i) q^{86} +(6.06218 - 10.5000i) q^{87} +(-13.6603 - 3.66025i) 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} -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} +(5.92820 - 7.92820i) 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	−0.992085	−	0.125567i	$-0.959925\pi$
$5$	−0.866025	+	1.50000i	−0.387298	+	0.670820i	0.604787	+	0.796387i	$0.293258\pi$
$6$	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
$10$	−2.36603	+	0.633975i	−0.748203	+	0.200480i
$11$	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	0.720577	−	0.693375i	$-0.243877\pi$
$13$	−0.866025	−	1.50000i	−0.240192	−	0.416025i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	−3.73205	+	0.267949i	−0.997433	+	0.0716124i
$15$	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
$22$	−1.83013	+	6.83013i	−0.390184	+	1.45619i
$23$	−6.06218	−	3.50000i	−1.26405	−	0.729800i	−0.290196	−	0.956967i	$-0.593720\pi$
$23$	−6.06218	−	3.50000i	−1.26405	−	0.729800i	−0.973856	+	0.227167i	$0.927054\pi$
$24$	3.46410	+	3.46410i	0.707107	+	0.707107i
$25$	1.00000	+	1.73205i	0.200000	+	0.346410i
$26$	0.633975	−	2.36603i	0.124333	−	0.464016i
$27$			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	$0.441463\pi$
$30$	1.09808	+	4.09808i	0.200480	+	0.748203i
$31$	6.92820			1.24434			0.622171	−	0.782881i	$-0.286251\pi$
$31$	6.92820			1.24434			0.622171	+	0.782881i	$0.286251\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	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	$-0.692861\pi$
$37$	−0.866025	+	0.500000i	−0.142374	+	0.0821995i	0.427121	+	0.904194i	$0.359528\pi$
$38$	−2.36603	−	0.633975i	−0.383820	−	0.102844i
$39$	−2.59808	+	1.50000i	−0.416025	+	0.240192i
$40$	−1.26795	−	4.73205i	−0.200480	−	0.748203i
$41$	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	$-0.0623249\pi$
$42$	0.464102	+	6.46410i	0.0716124	+	0.997433i
$43$	−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
$46$	−2.56218	−	9.56218i	−0.377773	−	1.40987i
$47$	−3.46410			−0.505291			−0.252646	−	0.967559i	$-0.581301\pi$
$47$	−3.46410			−0.505291			−0.252646	+	0.967559i	$0.581301\pi$
$48$			6.92820i			1.00000i
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$	−0.732051	+	2.73205i	−0.103528	+	0.386370i
$51$	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	0.981852	−	0.189651i	$-0.0607356\pi$
$53$	9.52628	+	5.50000i	1.30854	+	0.755483i	0.326683	+	0.945134i	$0.394069\pi$
$54$	−5.19615	+	5.19615i	−0.707107	+	0.707107i
$55$	−8.66025			−1.16775
$56$	−0.535898	−	7.46410i	−0.0716124	−	0.997433i
$57$	1.50000	+	2.59808i	0.198680	+	0.344124i
$58$	2.56218	+	9.56218i	0.336430	+	1.25558i
$59$		−	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	$-0.571182\pi$
$61$	−3.46410			−0.443533			−0.221766	+	0.975100i	$0.571182\pi$
$62$	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
$66$	11.8301	+	3.16987i	1.45619	+	0.390184i
$67$	−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
$70$	2.83013	−	5.83013i	0.338265	−	0.696833i
$71$		−	10.0000i		−	1.18678i	−0.804914	−	0.593391i	$-0.797789\pi$
$71$		−	10.0000i		−	1.18678i	0.804914	−	0.593391i	$-0.202211\pi$
$72$	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	$0.835840\pi$
$74$	−1.36603	−	0.366025i	−0.158797	−	0.0425496i
$75$	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
$78$	−4.09808	−	1.09808i	−0.464016	−	0.124333i
$79$		−	6.00000i		−	0.675053i	−0.941316	−	0.337526i	$-0.890410\pi$
$79$		−	6.00000i		−	0.675053i	0.941316	−	0.337526i	$-0.109590\pi$
$80$	3.46410	−	6.00000i	0.387298	−	0.670820i
$81$	9.00000			1.00000
$82$	16.5622	+	4.43782i	1.82899	+	0.490075i
$83$	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
$86$	−12.2942	+	3.29423i	−1.32572	+	0.355226i
$87$	6.06218	−	10.5000i	0.649934	−	1.12572i
$88$	−13.6603	−	3.66025i	−1.45619	−	0.390184i
$89$	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	$0.181544\pi$
$90$	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
$93$		−	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	$0.638641\pi$
$98$	5.92820	−	7.92820i	0.598839	−	0.800869i
$99$	−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	0.905890	−	0.423512i	$-0.139203\pi$
$101$	0.866025	+	1.50000i	0.0861727	+	0.149256i	−0.819718	+	0.572768i	$0.805870\pi$
$102$	4.09808	−	1.09808i	0.405770	−	0.108726i
$103$	−2.59808	+	4.50000i	−0.255996	+	0.443398i	−0.965166	−	0.261640i	$-0.915737\pi$
$103$	−2.59808	+	4.50000i	−0.255996	+	0.443398i	0.709170	+	0.705038i	$0.249070\pi$
$104$	4.73205	+	1.26795i	0.464016	+	0.124333i
$105$	−7.50000	+	2.59808i	−0.731925	+	0.253546i
$106$	4.02628	+	15.0263i	0.391067	+	1.45948i
$107$	−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	0.692829	−	0.721102i	$-0.256364\pi$
$109$	4.33013	+	2.50000i	0.414751	+	0.239457i	−0.278078	+	0.960558i	$0.589697\pi$
$110$	−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	$0.818356\pi$
$114$	−1.09808	+	4.09808i	−0.102844	+	0.383820i
$115$	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
$120$	−8.19615	+	2.19615i	−0.748203	+	0.200480i
$121$	−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
$126$	11.1962	−	0.803848i	0.997433	−	0.0716124i
$127$			18.0000i			1.59724i	0.601834	+	0.798621i	$0.294437\pi$
$127$			18.0000i			1.59724i	−0.601834	+	0.798621i	$0.705563\pi$
$128$	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
$136$	−4.73205	+	1.26795i	−0.405770	+	0.108726i
$137$	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	$0.645924\pi$
$138$	−16.5622	+	4.43782i	−1.40987	+	0.377773i
$139$	−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
$146$	−3.16987	−	11.8301i	−0.262341	−	0.979068i
$147$	−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	0.836580	−	0.547844i	$-0.184551\pi$
$149$	9.52628	+	5.50000i	0.780423	+	0.450578i	−0.0561570	+	0.998422i	$0.517885\pi$
$150$	4.73205	+	1.26795i	0.386370	+	0.103528i
$151$	4.33013	−	2.50000i	0.352381	−	0.203447i	−0.313353	−	0.949637i	$-0.601452\pi$
$151$	4.33013	−	2.50000i	0.352381	−	0.203447i	0.665733	+	0.746190i	$0.268119\pi$
$152$	1.26795	−	4.73205i	0.102844	−	0.383820i
$153$	−4.50000	−	2.59808i	−0.363803	−	0.210042i
$154$	−10.4904	−	15.4904i	−0.845339	−	1.24825i
$155$	−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	$-0.188685\pi$
$157$	20.7846			1.65879			0.829396	+	0.558661i	$0.188685\pi$
$158$	6.00000	−	6.00000i	0.477334	−	0.477334i
$159$	9.52628	−	16.5000i	0.755483	−	1.30854i
$160$	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	0.969918	−	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
$166$	5.70577	+	21.2942i	0.442854	+	1.65275i
$167$	4.33013	+	7.50000i	0.335075	+	0.580367i	0.983499	−	0.180912i	$-0.0579049\pi$
$167$	4.33013	+	7.50000i	0.335075	+	0.580367i	−0.648424	+	0.761279i	$0.724572\pi$
$168$	−12.9282	+	0.928203i	−0.997433	+	0.0716124i
$169$	5.00000	−	8.66025i	0.384615	−	0.666173i
$170$	−4.09808	−	1.09808i	−0.314308	−	0.0842186i
$171$	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	$-0.457961\pi$
$173$	3.46410			0.263371			0.131685	+	0.991292i	$0.457961\pi$
$174$	16.5622	−	4.43782i	1.25558	−	0.336430i
$175$	−5.19615	−	1.00000i	−0.392792	−	0.0755929i
$176$	−10.0000	−	17.3205i	−0.753778	−	1.30558i
$177$	−12.0000			−0.901975
$178$	11.8301	+	3.16987i	0.886706	+	0.237592i
$179$	−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	$-0.541094\pi$
$181$	−3.46410			−0.257485			−0.128742	+	0.991678i	$0.541094\pi$
$182$	3.63397	+	5.36603i	0.269368	+	0.397756i
$183$			6.00000i			0.443533i
$184$	19.1244	−	5.12436i	1.40987	−	0.377773i
$185$		−	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	$-0.830938\pi$
$191$		−	14.0000i		−	1.01300i	0.862239	−	0.506502i	$-0.169062\pi$
$192$	−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	$0.569283\pi$
$194$	0.633975	+	2.36603i	0.0455167	+	0.169871i
$195$		−	5.19615i		−	0.372104i
$196$	13.8564	−	2.00000i	0.989743	−	0.142857i
$197$		−	8.00000i		−	0.569976i	−0.958531	−	0.284988i	$-0.908010\pi$
$197$		−	8.00000i		−	0.569976i	0.958531	−	0.284988i	$-0.0919897\pi$
$198$	5.49038	−	20.4904i	0.390184	−	1.45619i
$199$	−4.33013	+	7.50000i	−0.306955	+	0.531661i	−0.977695	−	0.210032i	$-0.932643\pi$
$199$	−4.33013	+	7.50000i	−0.306955	+	0.531661i	0.670740	+	0.741693i	$0.265977\pi$
$200$	−5.46410	−	1.46410i	−0.386370	−	0.103528i
$201$			13.8564i			0.977356i
$202$	−0.633975	+	2.36603i	−0.0446063	+	0.166473i
$203$	−17.5000	+	6.06218i	−1.22826	+	0.425481i
$204$	5.19615	+	3.00000i	0.363803	+	0.210042i
$205$			21.0000i			1.46670i
$206$	−7.09808	+	1.90192i	−0.494546	+	0.132513i
$207$	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
$210$	−10.0981	−	4.90192i	−0.696833	−	0.338265i
$211$	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
$214$	1.83013	−	6.83013i	0.125105	−	0.466898i
$215$	−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
$219$	−7.50000	+	12.9904i	−0.506803	+	0.877809i
$220$		−	17.3205i		−	1.16775i
$221$		−	3.00000i		−	0.201802i
$222$	−0.633975	+	2.36603i	−0.0425496	+	0.158797i
$223$	6.06218	−	10.5000i	0.405953	−	0.703132i	−0.588478	−	0.808513i	$-0.700273\pi$
$223$	6.06218	−	10.5000i	0.405953	−	0.703132i	0.994432	+	0.105381i	$0.0336062\pi$
$224$	14.9282	−	1.07180i	0.997433	−	0.0716124i
$225$	−3.00000	−	5.19615i	−0.200000	−	0.346410i
$226$	−0.366025	+	1.36603i	−0.0243476	+	0.0908667i
$227$	−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	−0.993798	−	0.111197i	$-0.964532\pi$
$229$	−6.06218	+	10.5000i	−0.400600	+	0.693860i	0.593198	+	0.805056i	$0.297865\pi$
$230$	16.5622	+	4.43782i	1.09208	+	0.292621i
$231$	−4.33013	+	22.5000i	−0.284901	+	1.48039i
$232$	−19.1244	+	5.12436i	−1.25558	+	0.336430i
$233$	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	$0.716002\pi$
$234$	−1.90192	+	7.09808i	−0.124333	+	0.464016i
$235$	3.00000	−	5.19615i	0.195698	−	0.338960i
$236$	13.8564			0.901975
$237$	−10.3923			−0.675053
$238$	−5.83013	−	2.83013i	−0.377911	−	0.183450i
$239$	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	$0.281632\pi$
$240$	−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	$0.386857\pi$
$242$	−19.1244	+	5.12436i	−1.22936	+	0.329406i
$243$		−	15.5885i		−	1.00000i
$244$		−	6.92820i		−	0.443533i
$245$	11.2583	+	4.50000i	0.719268	+	0.287494i
$246$	7.68653	−	28.6865i	0.490075	−	1.82899i
$247$	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	$0.914499\pi$
$258$	5.70577	+	21.2942i	0.355226	+	1.32572i
$259$	0.500000	−	2.59808i	0.0310685	−	0.161437i
$260$			6.00000i			0.372104i
$261$	−18.1865	−	10.5000i	−1.12572	−	0.649934i
$262$	3.16987	+	11.8301i	0.195835	+	0.730868i
$263$	−11.2583	+	6.50000i	−0.694218	+	0.400807i	−0.805190	−	0.593016i	$-0.797937\pi$
$263$	−11.2583	+	6.50000i	−0.694218	+	0.400807i	0.110972	+	0.993824i	$0.464604\pi$
$264$	−6.33975	+	23.6603i	−0.390184	+	1.45619i
$265$	−16.5000	+	9.52628i	−1.01359	+	0.585195i
$266$	5.36603	−	3.63397i	0.329012	−	0.222813i
$267$	−7.50000	−	12.9904i	−0.458993	−	0.794998i
$268$		−	16.0000i		−	0.977356i
$269$	0.866025	−	1.50000i	0.0528025	−	0.0914566i	−0.838416	−	0.545031i	$-0.816518\pi$
$269$	0.866025	−	1.50000i	0.0528025	−	0.0914566i	0.891219	+	0.453574i	$0.149851\pi$
$270$	−3.29423	−	12.2942i	−0.200480	−	0.748203i
$271$	−7.79423	−	13.5000i	−0.473466	−	0.820067i	0.526073	−	0.850439i	$-0.323664\pi$
$271$	−7.79423	−	13.5000i	−0.473466	−	0.820067i	−0.999539	+	0.0303728i	$0.990331\pi$
$272$	−6.00000	−	3.46410i	−0.363803	−	0.210042i
$273$	1.50000	−	7.79423i	0.0907841	−	0.471728i
$274$	−4.75833	+	17.7583i	−0.287461	+	1.07282i
$275$	−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	0.158423	−	0.987371i	$-0.449359\pi$
$277$	18.1865	−	10.5000i	1.09272	−	0.630884i	0.934300	+	0.356488i	$0.116026\pi$
$278$	−21.2942	−	5.70577i	−1.27714	−	0.342209i
$279$	−20.7846			−1.24434
$280$	11.6603	+	5.66025i	0.696833	+	0.338265i
$281$	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
$286$	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
$290$	−16.5622	−	4.43782i	−0.972565	−	0.260598i
$291$	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	0.839619	−	0.543175i	$-0.182778\pi$
$293$	−0.866025	−	1.50000i	−0.0505937	−	0.0876309i	−0.890213	+	0.455544i	$0.849445\pi$
$294$	−13.7321	−	10.2679i	−0.800869	−	0.598839i
$295$	10.3923	+	6.00000i	0.605063	+	0.349334i
$296$	0.732051	−	2.73205i	0.0425496	−	0.158797i
$297$	−22.5000	+	12.9904i	−1.30558	+	0.753778i
$298$	4.02628	+	15.0263i	0.233236	+	0.870449i
$299$			12.1244i			0.701170i
$300$	3.46410	+	6.00000i	0.200000	+	0.346410i
$301$	−7.79423	−	22.5000i	−0.449252	−	1.29688i
$302$	6.83013	+	1.83013i	0.393030	+	0.105312i
$303$	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
$306$	−1.90192	−	7.09808i	−0.108726	−	0.405770i
$307$		−	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
$310$	−16.3923	+	4.39230i	−0.931020	+	0.249466i
$311$	20.7846			1.17859			0.589294	−	0.807919i	$-0.299406\pi$
$311$	20.7846			1.17859			0.589294	+	0.807919i	$0.299406\pi$
$312$	2.19615	−	8.19615i	0.124333	−	0.464016i
$313$			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	$0.128618\pi$
$317$			14.0000i			0.786318i	−0.919470	+	0.393159i	$0.871382\pi$
$318$	26.0263	−	6.97372i	1.45948	−	0.391067i
$319$			35.0000i			1.95962i
$320$	12.0000	+	6.92820i	0.670820	+	0.387298i
$321$	−7.50000	+	4.33013i	−0.418609	+	0.241684i
$322$	23.5622	+	11.4378i	1.31307	+	0.637405i
$323$	−3.00000			−0.166924
$324$			18.0000i			1.00000i
$325$	1.73205	−	3.00000i	0.0960769	−	0.166410i
$326$	−2.56218	+	9.56218i	−0.141906	+	0.529600i
$327$	4.33013	−	7.50000i	0.239457	−	0.414751i
$328$	−8.87564	+	33.1244i	−0.490075	+	1.82899i
$329$	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
$334$	−3.16987	+	11.8301i	−0.173448	+	0.647316i
$335$	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	$0.754502\pi$
$338$	13.6603	−	3.66025i	0.743020	−	0.199092i
$339$	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
$342$	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
$346$	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	−0.656910	−	0.753969i	$-0.728137\pi$
$349$	6.06218	−	10.5000i	0.324501	−	0.562052i	0.981411	+	0.191917i	$0.0614703\pi$
$350$	−4.19615	−	6.19615i	−0.224294	−	0.331198i
$351$	7.79423	−	4.50000i	0.416025	−	0.240192i
$352$	7.32051	−	27.3205i	0.390184	−	1.45619i
$353$	−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
$358$	−15.0263	+	4.02628i	−0.794164	+	0.212795i
$359$	−6.06218	+	3.50000i	−0.319950	+	0.184723i	−0.651370	−	0.758760i	$-0.725805\pi$
$359$	−6.06218	+	3.50000i	−0.319950	+	0.184723i	0.331421	+	0.943483i	$0.392472\pi$
$360$	3.80385	+	14.1962i	0.200480	+	0.748203i
$361$	−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	$-0.768431\pi$
$367$	−18.1865	−	31.5000i	−0.949329	−	1.64429i	−0.202488	−	0.979285i	$-0.564903\pi$
$368$	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	0.431228	−	0.902243i	$-0.358080\pi$
$373$	−2.59808	−	1.50000i	−0.134523	−	0.0776671i	−0.565751	+	0.824576i	$0.691414\pi$
$374$	−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
$378$	−1.39230	−	19.3923i	−0.0716124	−	0.997433i
$379$	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	$0.546245\pi$
$383$	−18.1865	+	31.5000i	−0.929288	+	1.60957i	−0.784515	+	0.620110i	$0.787088\pi$
$384$	−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	−0.477885	−	0.878423i	$-0.658596\pi$
$389$	0.866025	−	0.500000i	0.0439092	−	0.0253510i	0.521794	+	0.853072i	$0.325263\pi$
$390$	5.19615	−	5.19615i	0.263117	−	0.263117i
$391$	−6.06218	−	10.5000i	−0.306578	−	0.531008i
$392$	15.8564	+	11.8564i	0.800869	+	0.598839i
$393$	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	$-0.857376\pi$
$397$	−16.4545	−	28.5000i	−0.825827	−	1.43037i	0.0754589	−	0.997149i	$-0.475958\pi$
$398$	−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
$401$	−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
$406$	−23.5622	−	11.4378i	−1.16937	−	0.567650i
$407$	−4.33013	−	2.50000i	−0.214636	−	0.123920i
$408$	2.19615	+	8.19615i	0.108726	+	0.405770i
$409$		−	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
$414$	7.68653	+	28.6865i	0.377773	+	1.40987i
$415$	−23.3827	+	13.5000i	−1.14781	+	0.662689i
$416$	−2.53590	+	9.46410i	−0.124333	+	0.464016i
$417$	13.5000	+	23.3827i	0.661098	+	1.14506i
$418$	−3.16987	−	11.8301i	−0.155044	−	0.578630i
$419$	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	0.148844	−	0.988861i	$-0.452445\pi$
$421$	−12.9904	−	7.50000i	−0.633112	−	0.365528i	−0.781956	+	0.623333i	$0.785778\pi$
$422$	−3.29423	+	12.2942i	−0.160361	+	0.598474i
$423$	10.3923			0.505291
$424$	−30.0526	+	8.05256i	−1.45948	+	0.391067i
$425$			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
$430$	5.70577	−	21.2942i	0.275157	−	1.02690i
$431$	−4.33013	−	2.50000i	−0.208575	−	0.120421i	0.392074	−	0.919934i	$-0.371758\pi$
$431$	−4.33013	−	2.50000i	−0.208575	−	0.120421i	−0.600649	+	0.799513i	$0.705091\pi$
$432$		−	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	$-0.269530\pi$
$434$	−25.8564	+	1.85641i	−1.24115	+	0.0891104i
$435$	10.5000	+	18.1865i	0.503436	+	0.871978i
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$	12.1244			0.579987
$438$	−20.4904	+	5.49038i	−0.979068	+	0.262341i
$439$	−27.7128			−1.32266			−0.661330	−	0.750095i	$-0.730008\pi$
$439$	−27.7128			−1.32266			−0.661330	+	0.750095i	$0.730008\pi$
$440$	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
$446$	16.5622	−	4.43782i	0.784242	−	0.210137i
$447$	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	$0.326259\pi$
$450$	2.19615	−	8.19615i	0.103528	−	0.386370i
$451$	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
$454$	−26.0263	−	6.97372i	−1.22147	−	0.327293i
$455$	−5.19615	+	6.00000i	−0.243599	+	0.281284i
$456$	−8.19615	−	2.19615i	−0.383820	−	0.102844i
$457$	24.0000			1.12267			0.561336	−	0.827588i	$-0.310287\pi$
$457$	24.0000			1.12267			0.561336	+	0.827588i	$0.310287\pi$
$458$	−16.5622	+	4.43782i	−0.773900	+	0.207366i
$459$	−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	−0.920164	−	0.391533i	$-0.871945\pi$
$461$	−2.59808	+	4.50000i	−0.121004	+	0.209586i	0.799160	+	0.601119i	$0.205278\pi$
$462$	−26.8301	+	18.1699i	−1.24825	+	0.845339i
$463$	−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	$0.400397\pi$
$464$	−24.2487	−	14.0000i	−1.12572	−	0.649934i
$465$	18.0000	+	10.3923i	0.834730	+	0.481932i
$466$	−4.02628	+	15.0263i	−0.186514	+	0.696079i
$467$	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
$470$	8.19615	−	2.19615i	0.378060	−	0.101301i
$471$		−	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
$478$	6.83013	+	1.83013i	0.312403	+	0.0837081i
$479$	−0.866025	−	1.50000i	−0.0395697	−	0.0685367i	0.845562	−	0.533877i	$-0.179265\pi$
$479$	−0.866025	−	1.50000i	−0.0395697	−	0.0685367i	−0.885132	+	0.465340i	$0.845932\pi$
$480$	−4.39230	−	16.3923i	−0.200480	−	0.748203i
$481$	1.50000	+	0.866025i	0.0683941	+	0.0394874i
$482$	−7.09808	−	1.90192i	−0.323309	−	0.0866303i
$483$	−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	0.878042	−	0.478584i	$-0.158850\pi$
$487$	19.9186	+	11.5000i	0.902597	+	0.521115i	0.0245553	+	0.999698i	$0.492183\pi$
$488$	6.92820	−	6.92820i	0.313625	−	0.313625i
$489$	10.5000	−	6.06218i	0.474826	−	0.274141i
$490$	6.75833	+	15.7583i	0.305310	+	0.711889i
$491$	−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
$494$	1.09808	+	4.09808i	0.0494048	+	0.184381i
$495$	25.9808			1.16775
$496$	−27.7128			−1.24434
$497$	20.0000	+	17.3205i	0.897123	+	0.776931i
$498$	36.8827	−	9.88269i	1.65275	−	0.442854i
$499$	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	$-0.450637\pi$
$503$	6.92820			0.308913			0.154457	+	0.988000i	$0.450637\pi$
$504$	1.60770	+	22.3923i	0.0716124	+	0.997433i
$505$	−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	$-0.573164\pi$
$509$	16.4545	−	28.5000i	0.729332	−	1.26324i	0.957166	−	0.289540i	$-0.0935024\pi$
$510$	−1.90192	+	7.09808i	−0.0842186	+	0.314308i
$511$	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
$514$	−8.24167	−	30.7583i	−0.363524	−	1.35669i
$515$	−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
$518$	3.09808	−	2.09808i	0.136122	−	0.0921842i
$519$		−	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	$0.702977\pi$
$522$	−7.68653	−	28.6865i	−0.336430	−	1.25558i
$523$	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
$526$	−17.7583	−	4.75833i	−0.774300	−	0.207473i
$527$	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
$530$	−26.0263	−	6.97372i	−1.13051	−	0.302919i
$531$			20.7846i			0.901975i
$532$	9.00000	+	1.73205i	0.390199	+	0.0750939i
$533$	−18.1865	−	10.5000i	−0.787746	−	0.454805i
$534$	5.49038	−	20.4904i	0.237592	−	0.886706i
$535$	8.66025			0.374415
$536$	16.0000	−	16.0000i	0.691095	−	0.691095i
$537$	16.5000	+	9.52628i	0.712028	+	0.411089i
$538$	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	$-0.646125\pi$
$541$	2.59808	−	1.50000i	0.111700	−	0.0644900i	0.554809	+	0.831978i	$0.312791\pi$
$542$	5.70577	−	21.2942i	0.245084	−	0.914665i
$543$			6.00000i			0.257485i
$544$	−2.53590	−	9.46410i	−0.108726	−	0.405770i
$545$	−7.50000	+	4.33013i	−0.321265	+	0.185482i
$546$	9.29423	−	6.29423i	0.397756	−	0.269368i
$547$	−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
$550$	−13.6603	+	3.66025i	−0.582475	+	0.156074i
$551$	−12.1244			−0.516515
$552$	−8.87564	−	33.1244i	−0.377773	−	1.40987i
$553$	12.0000	+	10.3923i	0.510292	+	0.441926i
$554$	28.6865	+	7.68653i	1.21877	+	0.326570i
$555$	−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	$-0.862770\pi$
$557$	−40.7032	−	23.5000i	−1.72465	−	0.995727i	−0.816152	−	0.577838i	$-0.803897\pi$
$558$	−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
$562$	15.0263	−	4.02628i	0.633845	−	0.169838i
$563$			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
$574$	−37.5622	+	25.4378i	−1.56782	+	1.06175i
$575$		−	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	$0.906868\pi$
$578$	5.12436	−	19.1244i	0.213145	−	0.795468i
$579$			10.3923i			0.431889i
$580$	−12.1244	−	21.0000i	−0.503436	−	0.871978i
$581$	−38.9711	+	13.5000i	−1.61680	+	0.560074i
$582$	4.09808	−	1.09808i	0.169871	−	0.0455167i
$583$			55.0000i			2.27787i
$584$	23.6603	−	6.33975i	0.979068	−	0.262341i
$585$	−9.00000			−0.372104
$586$	0.633975	−	2.36603i	0.0261892	−	0.0977396i
$587$	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
$590$	4.39230	+	16.3923i	0.180828	+	0.674861i
$591$	−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	$0.539991\pi$
$594$	−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
$597$	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	$-0.644371\pi$
$599$		−	44.0000i		−	1.79779i	0.438163	−	0.898896i	$-0.355629\pi$
$600$	−2.53590	+	9.46410i	−0.103528	+	0.386370i
$601$	−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	$0.723186\pi$
$602$	14.7058	−	30.2942i	0.599362	−	1.23470i
$603$	24.0000			0.977356
$604$	5.00000	+	8.66025i	0.203447	+	0.352381i
$605$	−12.1244	−	21.0000i	−0.492925	−	0.853771i
$606$	4.09808	+	1.09808i	0.166473	+	0.0446063i
$607$	18.1865	−	31.5000i	0.738169	−	1.27855i	−0.215150	−	0.976581i	$-0.569024\pi$
$607$	18.1865	−	31.5000i	0.738169	−	1.27855i	0.953319	−	0.301965i	$-0.0976425\pi$
$608$	9.46410	+	2.53590i	0.383820	+	0.102844i
$609$	10.5000	+	30.3109i	0.425481	+	1.22826i
$610$	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	$-0.193927\pi$
$613$	18.1865	+	10.5000i	0.734547	+	0.424091i	−0.0855362	+	0.996335i	$0.527260\pi$
$614$	6.92820	−	6.92820i	0.279600	−	0.279600i
$615$	36.3731			1.46670
$616$	30.9808	−	20.9808i	1.24825	−	0.845339i
$617$	−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	$0.986550\pi$
$618$	3.29423	+	12.2942i	0.132513	+	0.494546i
$619$	−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
$630$	−8.49038	+	17.4904i	−0.338265	+	0.696833i
$631$			42.0000i			1.67199i	0.548734	+	0.835997i	$0.315110\pi$
$631$			42.0000i			1.67199i	−0.548734	+	0.835997i	$0.684890\pi$
$632$	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
$640$	5.07180	+	18.9282i	0.200480	+	0.748203i
$641$	−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	$0.903038\pi$
$642$	−11.8301	−	3.16987i	−0.466898	−	0.125105i
$643$	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	$-0.609402\pi$
$647$	16.4545	−	28.5000i	0.646892	−	1.12045i	0.983861	−	0.178935i	$-0.0572651\pi$
$648$	−18.0000	+	18.0000i	−0.707107	+	0.707107i
$649$	30.0000	−	17.3205i	1.17760	−	0.679889i
$650$	4.73205	−	1.26795i	0.185606	−	0.0497331i
$651$	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	0.703840	−	0.710358i	$-0.251467\pi$
$653$	11.2583	+	6.50000i	0.440573	+	0.254365i	−0.263268	+	0.964723i	$0.584800\pi$
$654$	11.8301	−	3.16987i	0.462595	−	0.123952i
$655$	−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
$658$	12.9282	−	0.928203i	0.503994	−	0.0361851i
$659$	−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	$-0.478540\pi$
$661$	3.46410			0.134738			0.0673690	+	0.997728i	$0.478540\pi$
$662$	6.00000	+	6.00000i	0.233197	+	0.233197i
$663$	−5.19615			−0.201802
$664$	−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
$668$	−15.0000	+	8.66025i	−0.580367	+	0.335075i
$669$	−18.1865	−	10.5000i	−0.703132	−	0.405953i
$670$	18.9282	−	5.07180i	0.731260	−	0.195941i
$671$	−8.66025	−	15.0000i	−0.334325	−	0.579069i
$672$	−1.85641	−	25.8564i	−0.0716124	−	0.997433i
$673$	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	$0.0733094\pi$
$674$	−3.29423	+	12.2942i	−0.126889	+	0.473556i
$675$	−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	$-0.369215\pi$
$677$	20.7846			0.798817			0.399409	+	0.916773i	$0.369215\pi$
$678$	2.36603	+	0.633975i	0.0908667	+	0.0243476i
$679$	−4.33013	+	1.50000i	−0.166175	+	0.0575647i
$680$	2.19615	−	8.19615i	0.0842186	−	0.314308i
$681$	16.5000	+	28.5788i	0.632281	+	1.09514i
$682$	−12.6795	+	47.3205i	−0.485523	+	1.81200i
$683$	−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
$686$	5.58846	+	25.5885i	0.213368	+	0.976972i
$687$	18.1865	+	10.5000i	0.693860	+	0.400600i
$688$	18.0000	−	31.1769i	0.686244	−	1.18861i
$689$		−	19.0526i		−	0.725845i
$690$	7.68653	−	28.6865i	0.292621	−	1.09208i
$691$		−	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
$696$	8.87564	+	33.1244i	0.336430	+	1.25558i
$697$	21.0000			0.795432
$698$	16.5622	−	4.43782i	0.626888	−	0.167974i
$699$	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	$-0.687810\pi$
$701$		−	44.0000i		−	1.66186i	0.556379	−	0.830929i	$-0.312190\pi$
$702$	12.2942	+	3.29423i	0.464016	+	0.124333i
$703$	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
$706$	−7.09808	−	1.90192i	−0.267140	−	0.0715798i
$707$	−4.50000	−	0.866025i	−0.169240	−	0.0325702i
$708$		−	24.0000i		−	0.901975i
$709$			52.0000i			1.95290i	0.215742	+	0.976450i	$0.430783\pi$
$709$			52.0000i			1.95290i	−0.215742	+	0.976450i	$0.569217\pi$
$710$	6.33975	+	23.6603i	0.237926	+	0.887954i
$711$			18.0000i			0.675053i
$712$	−6.33975	+	23.6603i	−0.237592	+	0.886706i
$713$	−42.0000	−	24.2487i	−1.57291	−	0.908121i
$714$	−4.90192	+	10.0981i	−0.183450	+	0.377911i
$715$	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
$718$	−9.56218	−	2.56218i	−0.356857	−	0.0956196i
$719$	23.3827	+	40.5000i	0.872027	+	1.51040i	0.859896	+	0.510469i	$0.170528\pi$
$719$	23.3827	+	40.5000i	0.872027	+	1.51040i	0.0121307	+	0.999926i	$0.496139\pi$
$720$	−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
$724$		−	6.92820i		−	0.257485i
$725$			14.0000i			0.519947i
$726$	8.87564	+	33.1244i	0.329406	+	1.22936i
$727$	16.4545	−	28.5000i	0.610263	−	1.05701i	−0.380933	−	0.924603i	$-0.624397\pi$
$727$	16.4545	−	28.5000i	0.610263	−	1.05701i	0.991196	−	0.132404i	$-0.0422696\pi$
$728$	−10.7321	+	7.26795i	−0.397756	+	0.269368i
$729$	−27.0000			−1.00000
$730$	20.4904	+	5.49038i	0.758383	+	0.203208i
$731$	−13.5000	+	7.79423i	−0.499316	+	0.288280i
$732$	−12.0000			−0.443533
$733$	4.33013	−	7.50000i	0.159937	−	0.277019i	−0.774909	−	0.632073i	$-0.782204\pi$
$733$	4.33013	−	7.50000i	0.159937	−	0.277019i	0.934846	+	0.355054i	$0.115538\pi$
$734$	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
$738$	−49.6865	−	13.3135i	−1.82899	−	0.490075i
$739$	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
$742$	−37.0263	−	17.9737i	−1.35928	−	0.659836i
$743$	−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	$0.446649\pi$
$744$	24.0000	+	24.0000i	0.879883	+	0.879883i
$745$	−16.5000	+	9.52628i	−0.604513	+	0.349016i
$746$	−1.09808	−	4.09808i	−0.0402034	−	0.150041i
$747$	−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	0.999860	−	0.0167534i	$-0.00533301\pi$
$751$	40.7032	+	23.5000i	1.48528	+	0.857527i	0.485421	+	0.874281i	$0.338666\pi$
$752$	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	$0.156646\pi$
$757$			26.0000i			0.944986i	−0.881334	+	0.472493i	$0.843354\pi$
$758$	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
$766$	−49.6865	+	13.3135i	−1.79525	+	0.481035i
$767$	−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	$0.466405\pi$
$770$	32.3205	−	2.32051i	1.16475	−	0.0836253i
$771$	−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	$0.525540\pi$
$773$	−25.1147	+	43.5000i	−0.903314	+	1.56459i	−0.823164	+	0.567803i	$0.807793\pi$
$774$	36.8827	−	9.88269i	1.32572	−	0.355226i
$775$	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
$779$	−10.5000	+	18.1865i	−0.376202	+	0.651600i
$780$	10.3923			0.372104
$781$	43.3013	−	25.0000i	1.54944	−	0.894570i
$782$	4.43782	−	16.5622i	0.158696	−	0.592262i
$783$	−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
$786$	20.4904	−	5.49038i	0.730868	−	0.195835i
$787$		−	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
$790$	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
$794$	12.0455	−	44.9545i	0.427479	−	1.59537i
$795$	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	0.998968	−	0.0454270i	$-0.0144648\pi$
$797$	12.9904	+	22.5000i	0.460143	+	0.796991i	−0.538825	+	0.842418i	$0.681132\pi$
$798$	−6.29423	−	9.29423i	−0.222813	−	0.329012i
$799$	−5.19615	−	3.00000i	−0.183827	−	0.106132i
$800$	2.92820	−	10.9282i	0.103528	−	0.386370i
$801$	−22.5000	+	12.9904i	−0.794998	+	0.458993i
$802$	−34.1506	+	9.15064i	−1.20590	+	0.323120i
$803$		−	43.3013i		−	1.52807i
$804$	−27.7128			−0.977356
$805$	−6.06218	+	31.5000i	−0.213664	+	1.11023i
$806$	4.39230	−	16.3923i	0.154712	−	0.577394i
$807$	−2.59808	−	1.50000i	−0.0914566	−	0.0528025i
$808$	−4.73205	−	1.26795i	−0.166473	−	0.0446063i
$809$	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	$0.138653\pi$
$810$	−21.2942	+	5.70577i	−0.748203	+	0.200480i
$811$			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
$814$	−1.83013	−	6.83013i	−0.0641459	−	0.239396i
$815$	−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	$0.0111113\pi$
$821$			2.00000i			0.0698005i	−0.999391	+	0.0349002i	$0.988889\pi$
$822$	30.7583	+	8.24167i	1.07282	+	0.287461i
$823$		−	54.0000i		−	1.88232i	−0.337959	−	0.941161i	$-0.609737\pi$
$823$		−	54.0000i		−	1.88232i	0.337959	−	0.941161i	$-0.390263\pi$
$824$	−3.80385	−	14.1962i	−0.132513	−	0.494546i
$825$	15.0000	+	8.66025i	0.522233	+	0.301511i
$826$	1.85641	+	25.8564i	0.0645926	+	0.899659i
$827$	−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	−0.992584	−	0.121560i	$-0.961210\pi$
$829$	−11.2583	+	19.5000i	−0.391018	+	0.677263i	0.601566	+	0.798823i	$0.294544\pi$
$830$	−36.8827	−	9.88269i	−1.28022	−	0.343033i
$831$	−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
$834$	−9.88269	+	36.8827i	−0.342209	+	1.27714i
$835$	−15.0000			−0.519096
$836$	8.66025	−	15.0000i	0.299521	−	0.518786i
$837$			36.0000i			1.24434i
$838$	2.36603	+	0.633975i	0.0817330	+	0.0219003i
$839$	7.79423	−	13.5000i	0.269087	−	0.466072i	−0.699540	−	0.714594i	$-0.746612\pi$
$839$	7.79423	−	13.5000i	0.269087	−	0.466072i	0.968626	+	0.248522i	$0.0799449\pi$
$840$	9.80385	−	20.1962i	0.338265	−	0.696833i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	−5.49038	−	20.4904i	−0.189211	−	0.706145i
$843$	−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	−0.981749	−	0.190180i	$-0.939093\pi$
$853$	−9.52628	+	16.5000i	−0.326174	+	0.564949i	0.655576	+	0.755130i	$0.272426\pi$
$854$	12.9282	−	0.928203i	0.442394	−	0.0317625i
$855$			9.00000i			0.307794i
$856$	13.6603	+	3.66025i	0.466898	+	0.125105i
$857$	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	$0.247550\pi$
$858$	−5.49038	−	20.4904i	−0.187439	−	0.699530i
$859$	−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
$862$	−1.83013	−	6.83013i	−0.0623344	−	0.232635i
$863$	19.9186	−	11.5000i	0.678036	−	0.391465i	−0.121078	−	0.992643i	$-0.538635\pi$
$863$	19.9186	−	11.5000i	0.678036	−	0.391465i	0.799115	+	0.601178i	$0.205302\pi$
$864$	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
$870$	−7.68653	+	28.6865i	−0.260598	+	0.972565i
$871$	6.92820	+	12.0000i	0.234753	+	0.406604i
$872$	−13.6603	+	3.66025i	−0.462595	+	0.123952i
$873$	−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	−0.332886	−	0.942967i	$-0.608022\pi$
$877$	−38.9711	−	22.5000i	−1.31596	−	0.759771i	−0.983076	+	0.183196i	$0.941356\pi$
$878$	−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	$0.943987\pi$
$882$	−17.7846	+	23.7846i	−0.598839	+	0.800869i
$883$	−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	−0.561216	−	0.827669i	$-0.689666\pi$
$887$	12.9904	−	22.5000i	0.436174	−	0.755476i	0.997391	+	0.0721931i	$0.0229998\pi$
$888$	−4.73205	−	1.26795i	−0.158797	−	0.0425496i
$889$	−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
$894$	26.0263	−	6.97372i	0.870449	−	0.233236i
$895$	−9.52628	−	16.5000i	−0.318428	−	0.551534i
$896$	2.14359	+	29.8564i	0.0716124	+	0.997433i
$897$	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
$902$	22.1891	+	82.8109i	0.738817	+	2.75730i
$903$	−38.9711	+	13.5000i	−1.29688	+	0.449252i
$904$	−2.73205	−	0.732051i	−0.0908667	−	0.0243476i
$905$	3.00000	−	5.19615i	0.0997234	−	0.172726i
$906$	3.16987	−	11.8301i	0.105312	−	0.393030i
$907$	−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
$910$	−11.1962	+	0.803848i	−0.371149	+	0.0266473i
$911$	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
$913$			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
$918$	−12.2942	+	3.29423i	−0.405770	+	0.108726i
$919$	−16.4545	+	9.50000i	−0.542783	+	0.313376i	−0.746206	−	0.665715i	$-0.768127\pi$
$919$	−16.4545	+	9.50000i	−0.542783	+	0.313376i	0.203423	+	0.979091i	$0.434793\pi$
$920$	−8.87564	+	33.1244i	−0.292621	+	1.09208i
$921$	−12.0000			−0.395413
$922$	−7.09808	+	1.90192i	−0.233763	+	0.0626365i
$923$	−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
$926$	−12.2942	−	3.29423i	−0.404013	−	0.108255i
$927$	7.79423	−	13.5000i	0.255996	−	0.443398i
$928$	−10.2487	−	38.2487i	−0.336430	−	1.25558i
$929$		−	17.3205i		−	0.568267i	−0.958785	−	0.284134i	$-0.908294\pi$
$929$		−	17.3205i		−	0.568267i	0.958785	−	0.284134i	$-0.0917060\pi$
$930$	7.60770	+	28.3923i	0.249466	+	0.931020i
$931$	7.50000	+	9.52628i	0.245803	+	0.312211i
$932$	−19.0526	+	11.0000i	−0.624087	+	0.360317i
$933$		−	36.0000i		−	1.17859i
$934$	11.8301	+	3.16987i	0.387094	+	0.103721i
$935$	−12.9904	−	7.50000i	−0.424831	−	0.245276i
$936$	−14.1962	−	3.80385i	−0.464016	−	0.124333i
$937$		−	17.3205i		−	0.565836i	−0.959144	−	0.282918i	$-0.908698\pi$
$937$		−	17.3205i		−	0.565836i	0.959144	−	0.282918i	$-0.0913025\pi$
$938$	29.8564	−	2.14359i	0.974846	−	0.0699908i
$939$	18.0000			0.587408
$940$	10.3923	+	6.00000i	0.338960	+	0.195698i
$941$	−45.0333			−1.46804			−0.734022	−	0.679126i	$-0.762359\pi$
$941$	−45.0333			−1.46804			−0.734022	+	0.679126i	$0.762359\pi$
$942$	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
$950$	−1.26795	−	4.73205i	−0.0411377	−	0.153528i
$951$	24.2487			0.786318
$952$	5.66025	−	11.6603i	0.183450	−	0.377911i
$953$	20.0000			0.647864			0.323932	−	0.946080i	$-0.394995\pi$
$953$	20.0000			0.647864			0.323932	+	0.946080i	$0.394995\pi$
$954$	−12.0788	−	45.0788i	−0.391067	−	1.45948i
$955$	21.0000	+	12.1244i	0.679544	+	0.392335i
$956$	5.00000	+	8.66025i	0.161712	+	0.280093i
$957$	60.6218			1.95962
$958$	0.633975	−	2.36603i	0.0204828	−	0.0764428i
$959$	−33.7750	−	6.50000i	−1.09065	−	0.209896i
$960$	12.0000	−	20.7846i	0.387298	−	0.670820i
$961$	17.0000			0.548387
$962$	0.633975	+	2.36603i	0.0204402	+	0.0762837i
$963$	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
$966$	19.8109	−	40.8109i	0.637405	−	1.31307i
$967$	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	$0.155298\pi$
$968$	−10.2487	−	38.2487i	−0.329406	−	1.22936i
$969$			5.19615i			0.166924i
$970$	−4.09808	−	1.09808i	−0.131581	−	0.0352571i
$971$	−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
$974$	8.41858	+	31.4186i	0.269749	+	1.00672i
$975$	−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	$0.603659\pi$
$978$	16.5622	+	4.43782i	0.529600	+	0.141906i
$979$	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
$982$	13.5429	−	50.5429i	0.432173	−	1.61289i
$983$	14.7224	+	25.5000i	0.469573	+	0.813324i	0.999395	−	0.0347851i	$-0.0110747\pi$
$983$	14.7224	+	25.5000i	0.469573	+	0.813324i	−0.529822	+	0.848109i	$0.677741\pi$
$984$	57.3731	+	15.3731i	1.82899	+	0.490075i
$985$	12.0000	+	6.92820i	0.382352	+	0.220751i
$986$	−4.43782	+	16.5622i	−0.141329	+	0.527447i
$987$	−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	$-0.995135\pi$
$991$	−47.6314	−	27.5000i	−1.51306	−	0.873566i	−0.513178	−	0.858282i	$-0.671532\pi$
$992$	−27.7128	−	27.7128i	−0.879883	−	0.879883i
$993$		−	10.3923i		−	0.329790i
$994$	2.67949	+	37.3205i	0.0849883	+	1.18373i
$995$	−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	$0.126068\pi$
$997$	25.1147	+	43.5000i	0.795392	+	1.37766i	−0.127198	+	0.991877i	$0.540599\pi$
$998$	20.4904	−	5.49038i	0.648612	−	0.173795i
$999$	−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.115.2	yes	4
7.5	odd	6		504.2.cz.a.187.2	yes	4
8.3	odd	2	inner	504.2.bf.a.115.1	✓	4
9.4	even	3		504.2.cz.a.283.1	yes	4
56.19	even	6		504.2.cz.a.187.1	yes	4
63.40	odd	6	inner	504.2.bf.a.355.2	yes	4
72.67	odd	6		504.2.cz.a.283.2	yes	4
504.355	even	6	inner	504.2.bf.a.355.1	yes	4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
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} +(-2.36603 + 0.633975i) q^{10} +(2.50000 + 4.33013i) q^{11} +3.46410 q^{12} +(-0.866025 - 1.50000i) q^{13} +(-3.73205 + 0.267949i) 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} +(-1.83013 + 6.83013i) q^{22} +(-6.06218 - 3.50000i) q^{23} +(3.46410 + 3.46410i) q^{24} +(1.00000 + 1.73205i) q^{25} +(0.633975 - 2.36603i) q^{26} +5.19615i q^{27} +(-4.00000 - 3.46410i) q^{28} +(6.06218 + 3.50000i) q^{29} +(1.09808 + 4.09808i) q^{30} +6.92820 q^{31} +(-4.00000 - 4.00000i) 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} +(-2.36603 - 0.633975i) q^{38} +(-2.59808 + 1.50000i) q^{39} +(-1.26795 - 4.73205i) q^{40} +(10.5000 - 6.06218i) q^{41} +(0.464102 + 6.46410i) q^{42} +(-4.50000 + 7.79423i) q^{43} +(-8.66025 + 5.00000i) q^{44} +(2.59808 - 4.50000i) q^{45} +(-2.56218 - 9.56218i) q^{46} -3.46410 q^{47} +6.92820i q^{48} +(-1.00000 - 6.92820i) q^{49} +(-0.732051 + 2.73205i) 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} +(-0.535898 - 7.46410i) q^{56} +(1.50000 + 2.59808i) q^{57} +(2.56218 + 9.56218i) 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} +(11.8301 + 3.16987i) q^{66} -8.00000 q^{67} +(-1.73205 + 3.00000i) q^{68} +(-6.06218 + 10.5000i) q^{69} +(2.83013 - 5.83013i) q^{70} -10.0000i q^{71} +(6.00000 - 6.00000i) q^{72} +(-7.50000 - 4.33013i) q^{73} +(-1.36603 - 0.366025i) q^{74} +(3.00000 - 1.73205i) q^{75} +(-1.73205 - 3.00000i) q^{76} +(-12.9904 - 2.50000i) q^{77} +(-4.09808 - 1.09808i) q^{78} -6.00000i q^{79} +(3.46410 - 6.00000i) q^{80} +9.00000 q^{81} +(16.5622 + 4.43782i) q^{82} +(13.5000 + 7.79423i) q^{83} +(-6.00000 + 6.92820i) q^{84} +(-2.59808 + 1.50000i) q^{85} +(-12.2942 + 3.29423i) q^{86} +(6.06218 - 10.5000i) q^{87} +(-13.6603 - 3.66025i) 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} -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} +(5.92820 - 7.92820i) 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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