LMFDB - Embedded newform 280.2.bj.d.131.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(131,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("280.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bj (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:	$2.23581125660$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	280.131
Dual form			280.2.bj.d.171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 1.36603i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.633975 - 2.36603i) q^{6} +(0.866025 - 2.50000i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(-0.366025 + 1.36603i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.633975 - 2.36603i) q^{6} +(0.866025 - 2.50000i) q^{7} +(2.00000 - 2.00000i) q^{8} +(1.00000 + 1.00000i) q^{10} +(-2.73205 - 4.73205i) q^{11} +3.46410 q^{12} +1.26795 q^{13} +(3.09808 + 2.09808i) q^{14} +1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} +(4.09808 - 2.36603i) q^{17} +(-1.90192 - 1.09808i) q^{19} +(-1.73205 + 1.00000i) q^{20} +(0.866025 + 4.50000i) q^{21} +(7.46410 - 2.00000i) q^{22} +(6.86603 + 3.96410i) q^{23} +(-1.26795 + 4.73205i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.464102 + 1.73205i) q^{26} -5.19615i q^{27} +(-4.00000 + 3.46410i) q^{28} +3.53590i q^{29} +(-2.36603 - 0.633975i) q^{30} +(-4.09808 - 7.09808i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(8.19615 + 4.73205i) q^{33} +(1.73205 + 6.46410i) q^{34} +(-1.73205 - 2.00000i) q^{35} +(-1.73205 - 1.00000i) q^{37} +(2.19615 - 2.19615i) q^{38} +(-1.90192 + 1.09808i) q^{39} +(-0.732051 - 2.73205i) q^{40} -5.19615i q^{41} +(-6.46410 - 0.464102i) q^{42} -9.92820 q^{43} +10.9282i q^{44} +(-7.92820 + 7.92820i) q^{46} +(4.73205 - 8.19615i) q^{47} +(-6.00000 - 3.46410i) q^{48} +(-5.50000 - 4.33013i) q^{49} +(1.36603 - 0.366025i) q^{50} +(-4.09808 + 7.09808i) q^{51} +(-2.19615 - 1.26795i) q^{52} +(8.83013 - 5.09808i) q^{53} +(7.09808 + 1.90192i) q^{54} -5.46410 q^{55} +(-3.26795 - 6.73205i) q^{56} +3.80385 q^{57} +(-4.83013 - 1.29423i) q^{58} +(-1.09808 + 0.633975i) q^{59} +(1.73205 - 3.00000i) q^{60} +(3.86603 - 6.69615i) q^{61} +(11.1962 - 3.00000i) q^{62} -8.00000i q^{64} +(0.633975 - 1.09808i) q^{65} +(-9.46410 + 9.46410i) q^{66} +(4.69615 + 8.13397i) q^{67} -9.46410 q^{68} -13.7321 q^{69} +(3.36603 - 1.63397i) q^{70} +8.73205i q^{71} +(-4.90192 + 2.83013i) q^{73} +(2.00000 - 2.00000i) q^{74} +(1.50000 + 0.866025i) q^{75} +(2.19615 + 3.80385i) q^{76} +(-14.1962 + 2.73205i) q^{77} +(-0.803848 - 3.00000i) q^{78} +(1.09808 + 0.633975i) q^{79} +4.00000 q^{80} +(4.50000 + 7.79423i) q^{81} +(7.09808 + 1.90192i) q^{82} +2.66025i q^{83} +(3.00000 - 8.66025i) q^{84} -4.73205i q^{85} +(3.63397 - 13.5622i) q^{86} +(-3.06218 - 5.30385i) q^{87} +(-14.9282 - 4.00000i) q^{88} +(2.30385 + 1.33013i) q^{89} +(1.09808 - 3.16987i) q^{91} +(-7.92820 - 13.7321i) q^{92} +(12.2942 + 7.09808i) q^{93} +(9.46410 + 9.46410i) q^{94} +(-1.90192 + 1.09808i) q^{95} +(6.92820 - 6.92820i) q^{96} +3.46410i q^{97} +(7.92820 - 5.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 6 q^{3} + 2 q^{5} - 6 q^{6} + 8 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 6 * q^3 + 2 * q^5 - 6 * q^6 + 8 * q^8	$ 4 q + 2 q^{2} - 6 q^{3} + 2 q^{5} - 6 q^{6} + 8 q^{8} + 4 q^{10} - 4 q^{11} + 12 q^{13} + 2 q^{14} + 8 q^{16} + 6 q^{17} - 18 q^{19} + 16 q^{22} + 24 q^{23} - 12 q^{24} - 2 q^{25} + 12 q^{26} - 16 q^{28} - 6 q^{30} - 6 q^{31} - 8 q^{32} + 12 q^{33} - 12 q^{38} - 18 q^{39} + 4 q^{40} - 12 q^{42} - 12 q^{43} - 4 q^{46} + 12 q^{47} - 24 q^{48} - 22 q^{49} + 2 q^{50} - 6 q^{51} + 12 q^{52} + 18 q^{53} + 18 q^{54} - 8 q^{55} - 20 q^{56} + 36 q^{57} - 2 q^{58} + 6 q^{59} + 12 q^{61} + 24 q^{62} + 6 q^{65} - 24 q^{66} - 2 q^{67} - 24 q^{68} - 48 q^{69} + 10 q^{70} - 30 q^{73} + 8 q^{74} + 6 q^{75} - 12 q^{76} - 36 q^{77} - 24 q^{78} - 6 q^{79} + 16 q^{80} + 18 q^{81} + 18 q^{82} + 12 q^{84} + 18 q^{86} + 12 q^{87} - 32 q^{88} + 30 q^{89} - 6 q^{91} - 4 q^{92} + 18 q^{93} + 24 q^{94} - 18 q^{95} + 4 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 6 * q^3 + 2 * q^5 - 6 * q^6 + 8 * q^8 + 4 * q^10 - 4 * q^11 + 12 * q^13 + 2 * q^14 + 8 * q^16 + 6 * q^17 - 18 * q^19 + 16 * q^22 + 24 * q^23 - 12 * q^24 - 2 * q^25 + 12 * q^26 - 16 * q^28 - 6 * q^30 - 6 * q^31 - 8 * q^32 + 12 * q^33 - 12 * q^38 - 18 * q^39 + 4 * q^40 - 12 * q^42 - 12 * q^43 - 4 * q^46 + 12 * q^47 - 24 * q^48 - 22 * q^49 + 2 * q^50 - 6 * q^51 + 12 * q^52 + 18 * q^53 + 18 * q^54 - 8 * q^55 - 20 * q^56 + 36 * q^57 - 2 * q^58 + 6 * q^59 + 12 * q^61 + 24 * q^62 + 6 * q^65 - 24 * q^66 - 2 * q^67 - 24 * q^68 - 48 * q^69 + 10 * q^70 - 30 * q^73 + 8 * q^74 + 6 * q^75 - 12 * q^76 - 36 * q^77 - 24 * q^78 - 6 * q^79 + 16 * q^80 + 18 * q^81 + 18 * q^82 + 12 * q^84 + 18 * q^86 + 12 * q^87 - 32 * q^88 + 30 * q^89 - 6 * q^91 - 4 * q^92 + 18 * q^93 + 24 * q^94 - 18 * q^95 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.366025	+	1.36603i	−0.258819	+	0.965926i
$2$	−0.366025	+	1.36603i	−0.258819	+	0.965926i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.633975	−	2.36603i	−0.258819	−	0.965926i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$		0			0
$10$	1.00000	+	1.00000i	0.316228	+	0.316228i
$11$	−2.73205	−	4.73205i	−0.823744	−	1.42677i	−0.902875	−	0.429903i	$-0.858548\pi$
$11$	−2.73205	−	4.73205i	−0.823744	−	1.42677i	0.0791309	−	0.996864i	$-0.474785\pi$
$12$	3.46410			1.00000
$13$	1.26795			0.351666			0.175833	−	0.984420i	$-0.443738\pi$
$13$	1.26795			0.351666			0.175833	+	0.984420i	$0.443738\pi$
$14$	3.09808	+	2.09808i	0.827996	+	0.560734i
$15$			1.73205i			0.447214i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	4.09808	−	2.36603i	0.993929	−	0.573845i	0.0874829	−	0.996166i	$-0.472118\pi$
$17$	4.09808	−	2.36603i	0.993929	−	0.573845i	0.906447	+	0.422321i	$0.138784\pi$
$18$		0			0
$19$	−1.90192	−	1.09808i	−0.436331	−	0.251916i	0.265709	−	0.964053i	$-0.414394\pi$
$19$	−1.90192	−	1.09808i	−0.436331	−	0.251916i	−0.702040	+	0.712137i	$0.747727\pi$
$20$	−1.73205	+	1.00000i	−0.387298	+	0.223607i
$21$	0.866025	+	4.50000i	0.188982	+	0.981981i
$22$	7.46410	−	2.00000i	1.59135	−	0.426401i
$23$	6.86603	+	3.96410i	1.43167	+	0.826572i	0.997248	−	0.0741394i	$-0.0236210\pi$
$23$	6.86603	+	3.96410i	1.43167	+	0.826572i	0.434417	+	0.900712i	$0.356954\pi$
$24$	−1.26795	+	4.73205i	−0.258819	+	0.965926i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.464102	+	1.73205i	−0.0910178	+	0.339683i
$27$		−	5.19615i		−	1.00000i
$28$	−4.00000	+	3.46410i	−0.755929	+	0.654654i
$29$			3.53590i			0.656600i	0.944574	+	0.328300i	$0.106476\pi$
$29$			3.53590i			0.656600i	−0.944574	+	0.328300i	$0.893524\pi$
$30$	−2.36603	−	0.633975i	−0.431975	−	0.115747i
$31$	−4.09808	−	7.09808i	−0.736036	−	1.27485i	−0.954267	−	0.298955i	$-0.903362\pi$
$31$	−4.09808	−	7.09808i	−0.736036	−	1.27485i	0.218231	−	0.975897i	$-0.429971\pi$
$32$	−5.46410	+	1.46410i	−0.965926	+	0.258819i
$33$	8.19615	+	4.73205i	1.42677	+	0.823744i
$34$	1.73205	+	6.46410i	0.297044	+	1.10858i
$35$	−1.73205	−	2.00000i	−0.292770	−	0.338062i
$36$		0			0
$37$	−1.73205	−	1.00000i	−0.284747	−	0.164399i	0.350823	−	0.936442i	$-0.385902\pi$
$37$	−1.73205	−	1.00000i	−0.284747	−	0.164399i	−0.635571	+	0.772043i	$0.719235\pi$
$38$	2.19615	−	2.19615i	0.356263	−	0.356263i
$39$	−1.90192	+	1.09808i	−0.304552	+	0.175833i
$40$	−0.732051	−	2.73205i	−0.115747	−	0.431975i
$41$		−	5.19615i		−	0.811503i	−0.913984	−	0.405751i	$-0.867010\pi$
$41$		−	5.19615i		−	0.811503i	0.913984	−	0.405751i	$-0.132990\pi$
$42$	−6.46410	−	0.464102i	−0.997433	−	0.0716124i
$43$	−9.92820			−1.51404			−0.757018	−	0.653394i	$-0.773345\pi$
$43$	−9.92820			−1.51404			−0.757018	+	0.653394i	$0.773345\pi$
$44$			10.9282i			1.64749i
$45$		0			0
$46$	−7.92820	+	7.92820i	−1.16895	+	1.16895i
$47$	4.73205	−	8.19615i	0.690241	−	1.19553i	−0.281518	−	0.959556i	$-0.590838\pi$
$47$	4.73205	−	8.19615i	0.690241	−	1.19553i	0.971759	−	0.235976i	$-0.0758286\pi$
$48$	−6.00000	−	3.46410i	−0.866025	−	0.500000i
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$	1.36603	−	0.366025i	0.193185	−	0.0517638i
$51$	−4.09808	+	7.09808i	−0.573845	+	0.993929i
$52$	−2.19615	−	1.26795i	−0.304552	−	0.175833i
$53$	8.83013	−	5.09808i	1.21291	−	0.700275i	0.249519	−	0.968370i	$-0.419728\pi$
$53$	8.83013	−	5.09808i	1.21291	−	0.700275i	0.963392	+	0.268095i	$0.0863942\pi$
$54$	7.09808	+	1.90192i	0.965926	+	0.258819i
$55$	−5.46410			−0.736779
$56$	−3.26795	−	6.73205i	−0.436698	−	0.899608i
$57$	3.80385			0.503832
$58$	−4.83013	−	1.29423i	−0.634227	−	0.169941i
$59$	−1.09808	+	0.633975i	−0.142957	+	0.0825365i	−0.569773	−	0.821802i	$-0.692969\pi$
$59$	−1.09808	+	0.633975i	−0.142957	+	0.0825365i	0.426815	+	0.904339i	$0.359635\pi$
$60$	1.73205	−	3.00000i	0.223607	−	0.387298i
$61$	3.86603	−	6.69615i	0.494994	−	0.857354i	−0.504990	−	0.863125i	$-0.668504\pi$
$61$	3.86603	−	6.69615i	0.494994	−	0.857354i	0.999983	+	0.00577101i	$0.00183698\pi$
$62$	11.1962	−	3.00000i	1.42191	−	0.381000i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	0.633975	−	1.09808i	0.0786349	−	0.136200i
$66$	−9.46410	+	9.46410i	−1.16495	+	1.16495i
$67$	4.69615	+	8.13397i	0.573726	+	0.993723i	0.996179	+	0.0873380i	$0.0278360\pi$
$67$	4.69615	+	8.13397i	0.573726	+	0.993723i	−0.422452	+	0.906385i	$0.638831\pi$
$68$	−9.46410			−1.14769
$69$	−13.7321			−1.65314
$70$	3.36603	−	1.63397i	0.402317	−	0.195297i
$71$			8.73205i			1.03630i	0.855289	+	0.518152i	$0.173380\pi$
$71$			8.73205i			1.03630i	−0.855289	+	0.518152i	$0.826620\pi$
$72$		0			0
$73$	−4.90192	+	2.83013i	−0.573727	+	0.331241i	−0.758636	−	0.651514i	$-0.774134\pi$
$73$	−4.90192	+	2.83013i	−0.573727	+	0.331241i	0.184910	+	0.982756i	$0.440801\pi$
$74$	2.00000	−	2.00000i	0.232495	−	0.232495i
$75$	1.50000	+	0.866025i	0.173205	+	0.100000i
$76$	2.19615	+	3.80385i	0.251916	+	0.436331i
$77$	−14.1962	+	2.73205i	−1.61780	+	0.311346i
$78$	−0.803848	−	3.00000i	−0.0910178	−	0.339683i
$79$	1.09808	+	0.633975i	0.123543	+	0.0713277i	0.560498	−	0.828156i	$-0.310610\pi$
$79$	1.09808	+	0.633975i	0.123543	+	0.0713277i	−0.436955	+	0.899483i	$0.643943\pi$
$80$	4.00000			0.447214
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	7.09808	+	1.90192i	0.783851	+	0.210032i
$83$			2.66025i			0.292001i	0.989285	+	0.146000i	$0.0466401\pi$
$83$			2.66025i			0.292001i	−0.989285	+	0.146000i	$0.953360\pi$
$84$	3.00000	−	8.66025i	0.327327	−	0.944911i
$85$		−	4.73205i		−	0.513263i
$86$	3.63397	−	13.5622i	0.391862	−	1.46245i
$87$	−3.06218	−	5.30385i	−0.328300	−	0.568632i
$88$	−14.9282	−	4.00000i	−1.59135	−	0.426401i
$89$	2.30385	+	1.33013i	0.244207	+	0.140993i	0.617109	−	0.786878i	$-0.288304\pi$
$89$	2.30385	+	1.33013i	0.244207	+	0.140993i	−0.372902	+	0.927871i	$0.621637\pi$
$90$		0			0
$91$	1.09808	−	3.16987i	0.115110	−	0.332293i
$92$	−7.92820	−	13.7321i	−0.826572	−	1.43167i
$93$	12.2942	+	7.09808i	1.27485	+	0.736036i
$94$	9.46410	+	9.46410i	0.976148	+	0.976148i
$95$	−1.90192	+	1.09808i	−0.195133	+	0.112660i
$96$	6.92820	−	6.92820i	0.707107	−	0.707107i
$97$			3.46410i			0.351726i	0.984415	+	0.175863i	$0.0562716\pi$
$97$			3.46410i			0.351726i	−0.984415	+	0.175863i	$0.943728\pi$
$98$	7.92820	−	5.92820i	0.800869	−	0.598839i
$99$		0			0
$100$			2.00000i			0.200000i
$101$	0.401924	+	0.696152i	0.0399929	+	0.0692698i	0.885329	−	0.464965i	$-0.153933\pi$
$101$	0.401924	+	0.696152i	0.0399929	+	0.0692698i	−0.845336	+	0.534235i	$0.820600\pi$
$102$	−8.19615	−	8.19615i	−0.811540	−	0.811540i
$103$	−7.33013	+	12.6962i	−0.722259	+	1.25099i	0.237833	+	0.971306i	$0.423563\pi$
$103$	−7.33013	+	12.6962i	−0.722259	+	1.25099i	−0.960092	+	0.279683i	$0.909771\pi$
$104$	2.53590	−	2.53590i	0.248665	−	0.248665i
$105$	4.33013	+	1.50000i	0.422577	+	0.146385i
$106$	3.73205	+	13.9282i	0.362489	+	1.35283i
$107$	−3.50000	+	6.06218i	−0.338358	+	0.586053i	−0.984124	−	0.177482i	$-0.943205\pi$
$107$	−3.50000	+	6.06218i	−0.338358	+	0.586053i	0.645766	+	0.763535i	$0.276538\pi$
$108$	−5.19615	+	9.00000i	−0.500000	+	0.866025i
$109$	−2.93782	+	1.69615i	−0.281392	+	0.162462i	−0.634054	−	0.773289i	$-0.718610\pi$
$109$	−2.93782	+	1.69615i	−0.281392	+	0.162462i	0.352661	+	0.935751i	$0.385277\pi$
$110$	2.00000	−	7.46410i	0.190693	−	0.711674i
$111$	3.46410			0.328798
$112$	10.3923	−	2.00000i	0.981981	−	0.188982i
$113$	−6.73205			−0.633298			−0.316649	−	0.948543i	$-0.602558\pi$
$113$	−6.73205			−0.633298			−0.316649	+	0.948543i	$0.602558\pi$
$114$	−1.39230	+	5.19615i	−0.130401	+	0.486664i
$115$	6.86603	−	3.96410i	0.640260	−	0.369654i
$116$	3.53590	−	6.12436i	0.328300	−	0.568632i
$117$		0			0
$118$	−0.464102	−	1.73205i	−0.0427240	−	0.159448i
$119$	−2.36603	−	12.2942i	−0.216893	−	1.12701i
$120$	3.46410	+	3.46410i	0.316228	+	0.316228i
$121$	−9.42820	+	16.3301i	−0.857109	+	1.48456i
$122$	7.73205	+	7.73205i	0.700027	+	0.700027i
$123$	4.50000	+	7.79423i	0.405751	+	0.702782i
$124$			16.3923i			1.47207i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$			8.53590i			0.757438i	0.925512	+	0.378719i	$0.123635\pi$
$127$			8.53590i			0.757438i	−0.925512	+	0.378719i	$0.876365\pi$
$128$	10.9282	+	2.92820i	0.965926	+	0.258819i
$129$	14.8923	−	8.59808i	1.31119	−	0.757018i
$130$	1.26795	+	1.26795i	0.111207	+	0.111207i
$131$	10.3923	+	6.00000i	0.907980	+	0.524222i	0.879781	−	0.475380i	$-0.157689\pi$
$131$	10.3923	+	6.00000i	0.907980	+	0.524222i	0.0281993	+	0.999602i	$0.491023\pi$
$132$	−9.46410	−	16.3923i	−0.823744	−	1.42677i
$133$	−4.39230	+	3.80385i	−0.380861	+	0.329835i
$134$	−12.8301	+	3.43782i	−1.10835	+	0.296983i
$135$	−4.50000	−	2.59808i	−0.387298	−	0.223607i
$136$	3.46410	−	12.9282i	0.297044	−	1.10858i
$137$	−4.19615	−	7.26795i	−0.358501	−	0.620943i	0.629209	−	0.777236i	$-0.283379\pi$
$137$	−4.19615	−	7.26795i	−0.358501	−	0.620943i	−0.987711	+	0.156293i	$0.950046\pi$
$138$	5.02628	−	18.7583i	0.427865	−	1.59682i
$139$		−	2.53590i		−	0.215092i	−0.994200	−	0.107546i	$-0.965701\pi$
$139$		−	2.53590i		−	0.215092i	0.994200	−	0.107546i	$-0.0342993\pi$
$140$	1.00000	+	5.19615i	0.0845154	+	0.439155i
$141$			16.3923i			1.38048i
$142$	−11.9282	−	3.19615i	−1.00099	−	0.268215i
$143$	−3.46410	−	6.00000i	−0.289683	−	0.501745i
$144$		0			0
$145$	3.06218	+	1.76795i	0.254300	+	0.146820i
$146$	−2.07180	−	7.73205i	−0.171463	−	0.639909i
$147$	12.0000	+	1.73205i	0.989743	+	0.142857i
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$	3.86603	+	2.23205i	0.316717	+	0.182857i	0.649928	−	0.759995i	$-0.274799\pi$
$149$	3.86603	+	2.23205i	0.316717	+	0.182857i	−0.333211	+	0.942852i	$0.608132\pi$
$150$	−1.73205	+	1.73205i	−0.141421	+	0.141421i
$151$	14.0263	−	8.09808i	1.14144	−	0.659012i	0.194655	−	0.980872i	$-0.437641\pi$
$151$	14.0263	−	8.09808i	1.14144	−	0.659012i	0.946787	+	0.321860i	$0.104308\pi$
$152$	−6.00000	+	1.60770i	−0.486664	+	0.130401i
$153$		0			0
$154$	1.46410	−	20.3923i	0.117981	−	1.64326i
$155$	−8.19615			−0.658331
$156$	4.39230			0.351666
$157$	4.73205	+	8.19615i	0.377659	+	0.654124i	0.990721	−	0.135910i	$-0.0433959\pi$
$157$	4.73205	+	8.19615i	0.377659	+	0.654124i	−0.613062	+	0.790035i	$0.710063\pi$
$158$	−1.26795	+	1.26795i	−0.100873	+	0.100873i
$159$	−8.83013	+	15.2942i	−0.700275	+	1.21291i
$160$	−1.46410	+	5.46410i	−0.115747	+	0.431975i
$161$	15.8564	−	13.7321i	1.24966	−	1.08224i
$162$	−12.2942	+	3.29423i	−0.965926	+	0.258819i
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	−0.601035	−	0.799223i	$-0.705245\pi$
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	0.992665	+	0.120900i	$0.0385779\pi$
$164$	−5.19615	+	9.00000i	−0.405751	+	0.702782i
$165$	8.19615	−	4.73205i	0.638070	−	0.368390i
$166$	−3.63397	−	0.973721i	−0.282051	−	0.0755754i
$167$	20.6603			1.59874			0.799369	−	0.600840i	$-0.205167\pi$
$167$	20.6603			1.59874			0.799369	+	0.600840i	$0.205167\pi$
$168$	10.7321	+	7.26795i	0.827996	+	0.560734i
$169$	−11.3923			−0.876331
$170$	6.46410	+	1.73205i	0.495774	+	0.132842i
$171$		0			0
$172$	17.1962	+	9.92820i	1.31119	+	0.757018i
$173$	11.1962	−	19.3923i	0.851228	−	1.47437i	−0.0288733	−	0.999583i	$-0.509192\pi$
$173$	11.1962	−	19.3923i	0.851228	−	1.47437i	0.880101	−	0.474787i	$-0.157475\pi$
$174$	8.36603	−	2.24167i	0.634227	−	0.169941i
$175$	−2.59808	+	0.500000i	−0.196396	+	0.0377964i
$176$	10.9282	−	18.9282i	0.823744	−	1.42677i
$177$	1.09808	−	1.90192i	0.0825365	−	0.142957i
$178$	−2.66025	+	2.66025i	−0.199394	+	0.199394i
$179$	−3.90192	−	6.75833i	−0.291643	−	0.505141i	0.682555	−	0.730834i	$-0.260869\pi$
$179$	−3.90192	−	6.75833i	−0.291643	−	0.505141i	−0.974199	+	0.225693i	$0.927535\pi$
$180$		0			0
$181$	−1.73205			−0.128742			−0.0643712	−	0.997926i	$-0.520504\pi$
$181$	−1.73205			−0.128742			−0.0643712	+	0.997926i	$0.520504\pi$
$182$	3.92820	+	2.66025i	0.291178	+	0.197191i
$183$			13.3923i			0.989988i
$184$	21.6603	−	5.80385i	1.59682	−	0.427865i
$185$	−1.73205	+	1.00000i	−0.127343	+	0.0735215i
$186$	−14.1962	+	14.1962i	−1.04091	+	1.04091i
$187$	−22.3923	−	12.9282i	−1.63749	−	0.945404i
$188$	−16.3923	+	9.46410i	−1.19553	+	0.690241i
$189$	−12.9904	−	4.50000i	−0.944911	−	0.327327i
$190$	−0.803848	−	3.00000i	−0.0583172	−	0.217643i
$191$	−3.12436	−	1.80385i	−0.226070	−	0.130522i	0.382687	−	0.923878i	$-0.374999\pi$
$191$	−3.12436	−	1.80385i	−0.226070	−	0.130522i	−0.608758	+	0.793356i	$0.708332\pi$
$192$	6.92820	+	12.0000i	0.500000	+	0.866025i
$193$	6.92820	+	12.0000i	0.498703	+	0.863779i	0.999999	−	0.00149702i	$-0.000476517\pi$
$193$	6.92820	+	12.0000i	0.498703	+	0.863779i	−0.501296	+	0.865276i	$0.667143\pi$
$194$	−4.73205	−	1.26795i	−0.339741	−	0.0910334i
$195$			2.19615i			0.157270i
$196$	5.19615	+	13.0000i	0.371154	+	0.928571i
$197$			8.92820i			0.636108i	0.948073	+	0.318054i	$0.103029\pi$
$197$			8.92820i			0.636108i	−0.948073	+	0.318054i	$0.896971\pi$
$198$		0			0
$199$	−9.00000	−	15.5885i	−0.637993	−	1.10504i	−0.985873	−	0.167497i	$-0.946431\pi$
$199$	−9.00000	−	15.5885i	−0.637993	−	1.10504i	0.347879	−	0.937539i	$-0.386902\pi$
$200$	−2.73205	−	0.732051i	−0.193185	−	0.0517638i
$201$	−14.0885	−	8.13397i	−0.993723	−	0.573726i
$202$	−1.09808	+	0.294229i	−0.0772604	+	0.0207019i
$203$	8.83975	+	3.06218i	0.620429	+	0.214923i
$204$	14.1962	−	8.19615i	0.993929	−	0.573845i
$205$	−4.50000	−	2.59808i	−0.314294	−	0.181458i
$206$	−14.6603	−	14.6603i	−1.02143	−	1.02143i
$207$		0			0
$208$	2.53590	+	4.39230i	0.175833	+	0.304552i
$209$			12.0000i			0.830057i
$210$	−3.63397	+	5.36603i	−0.250768	+	0.370291i
$211$	12.5885			0.866625			0.433313	−	0.901244i	$-0.357345\pi$
$211$	12.5885			0.866625			0.433313	+	0.901244i	$0.357345\pi$
$212$	−20.3923			−1.40055
$213$	−7.56218	−	13.0981i	−0.518152	−	0.897465i
$214$	−7.00000	−	7.00000i	−0.478510	−	0.478510i
$215$	−4.96410	+	8.59808i	−0.338549	+	0.586384i
$216$	−10.3923	−	10.3923i	−0.707107	−	0.707107i
$217$	−21.2942	+	4.09808i	−1.44555	+	0.278196i
$218$	−1.24167	−	4.63397i	−0.0840965	−	0.313852i
$219$	4.90192	−	8.49038i	0.331241	−	0.573727i
$220$	9.46410	+	5.46410i	0.638070	+	0.368390i
$221$	5.19615	−	3.00000i	0.349531	−	0.201802i
$222$	−1.26795	+	4.73205i	−0.0850992	+	0.317594i
$223$	13.8564			0.927894			0.463947	−	0.885863i	$-0.346433\pi$
$223$	13.8564			0.927894			0.463947	+	0.885863i	$0.346433\pi$
$224$	−1.07180	+	14.9282i	−0.0716124	+	0.997433i
$225$		0			0
$226$	2.46410	−	9.19615i	0.163910	−	0.611719i
$227$	16.3923	−	9.46410i	1.08800	−	0.628154i	0.154953	−	0.987922i	$-0.450477\pi$
$227$	16.3923	−	9.46410i	1.08800	−	0.628154i	0.933042	+	0.359767i	$0.117144\pi$
$228$	−6.58846	−	3.80385i	−0.436331	−	0.251916i
$229$	−4.26795	+	7.39230i	−0.282034	+	0.488497i	−0.971886	−	0.235454i	$-0.924342\pi$
$229$	−4.26795	+	7.39230i	−0.282034	+	0.488497i	0.689852	+	0.723951i	$0.257676\pi$
$230$	2.90192	+	10.8301i	0.191347	+	0.714117i
$231$	18.9282	−	16.3923i	1.24538	−	1.07853i
$232$	7.07180	+	7.07180i	0.464286	+	0.464286i
$233$	4.36603	−	7.56218i	0.286028	−	0.495415i	−0.686830	−	0.726818i	$-0.740998\pi$
$233$	4.36603	−	7.56218i	0.286028	−	0.495415i	0.972858	+	0.231403i	$0.0743317\pi$
$234$		0			0
$235$	−4.73205	−	8.19615i	−0.308685	−	0.534658i
$236$	2.53590			0.165073
$237$	−2.19615			−0.142655
$238$	17.6603	+	1.26795i	1.14474	+	0.0821889i
$239$			12.1962i			0.788904i	0.918917	+	0.394452i	$0.129065\pi$
$239$			12.1962i			0.788904i	−0.918917	+	0.394452i	$0.870935\pi$
$240$	−6.00000	+	3.46410i	−0.387298	+	0.223607i
$241$	−17.1962	+	9.92820i	−1.10770	+	0.639532i	−0.938233	−	0.346004i	$-0.887538\pi$
$241$	−17.1962	+	9.92820i	−1.10770	+	0.639532i	−0.169468	+	0.985536i	$0.554205\pi$
$242$	−18.8564	−	18.8564i	−1.21214	−	1.21214i
$243$		0			0
$244$	−13.3923	+	7.73205i	−0.857354	+	0.494994i
$245$	−6.50000	+	2.59808i	−0.415270	+	0.165985i
$246$	−12.2942	+	3.29423i	−0.783851	+	0.210032i
$247$	−2.41154	−	1.39230i	−0.153443	−	0.0885902i
$248$	−22.3923	−	6.00000i	−1.42191	−	0.381000i
$249$	−2.30385	−	3.99038i	−0.146000	−	0.252880i
$250$	0.366025	−	1.36603i	0.0231495	−	0.0863950i
$251$			26.1962i			1.65349i	0.562579	+	0.826743i	$0.309809\pi$
$251$			26.1962i			1.65349i	−0.562579	+	0.826743i	$0.690191\pi$
$252$		0			0
$253$		−	43.3205i		−	2.72354i
$254$	−11.6603	−	3.12436i	−0.731629	−	0.196040i
$255$	4.09808	+	7.09808i	0.256631	+	0.444499i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−5.19615	−	3.00000i	−0.324127	−	0.187135i	0.329104	−	0.944294i	$-0.393253\pi$
$257$	−5.19615	−	3.00000i	−0.324127	−	0.187135i	−0.653231	+	0.757159i	$0.726587\pi$
$258$	6.29423	+	23.4904i	0.391862	+	1.46245i
$259$	−4.00000	+	3.46410i	−0.248548	+	0.215249i
$260$	−2.19615	+	1.26795i	−0.136200	+	0.0786349i
$261$		0			0
$262$	−12.0000	+	12.0000i	−0.741362	+	0.741362i
$263$	−25.9186	+	14.9641i	−1.59821	+	0.922726i	−0.606376	+	0.795178i	$0.707377\pi$
$263$	−25.9186	+	14.9641i	−1.59821	+	0.922726i	−0.991832	+	0.127548i	$0.959289\pi$
$264$	25.8564	−	6.92820i	1.59135	−	0.426401i
$265$		−	10.1962i		−	0.626345i
$266$	−3.58846	−	7.39230i	−0.220022	−	0.453251i
$267$	−4.60770			−0.281986
$268$		−	18.7846i		−	1.14745i
$269$	4.33013	+	7.50000i	0.264013	+	0.457283i	0.967304	−	0.253618i	$-0.0816206\pi$
$269$	4.33013	+	7.50000i	0.264013	+	0.457283i	−0.703292	+	0.710901i	$0.748287\pi$
$270$	5.19615	−	5.19615i	0.316228	−	0.316228i
$271$	1.90192	−	3.29423i	0.115534	−	0.200110i	−0.802459	−	0.596707i	$-0.796476\pi$
$271$	1.90192	−	3.29423i	0.115534	−	0.200110i	0.917993	+	0.396597i	$0.129809\pi$
$272$	16.3923	+	9.46410i	0.993929	+	0.573845i
$273$	1.09808	+	5.70577i	0.0664586	+	0.345329i
$274$	11.4641	−	3.07180i	0.692572	−	0.185574i
$275$	−2.73205	+	4.73205i	−0.164749	+	0.285353i
$276$	23.7846	+	13.7321i	1.43167	+	0.826572i
$277$	7.09808	−	4.09808i	0.426482	−	0.246230i	−0.271365	−	0.962477i	$-0.587475\pi$
$277$	7.09808	−	4.09808i	0.426482	−	0.246230i	0.697847	+	0.716247i	$0.254142\pi$
$278$	3.46410	+	0.928203i	0.207763	+	0.0556699i
$279$		0			0
$280$	−7.46410	−	0.535898i	−0.446065	−	0.0320261i
$281$	−5.85641			−0.349364			−0.174682	−	0.984625i	$-0.555890\pi$
$281$	−5.85641			−0.349364			−0.174682	+	0.984625i	$0.555890\pi$
$282$	−22.3923	−	6.00000i	−1.33344	−	0.357295i
$283$	3.00000	−	1.73205i	0.178331	−	0.102960i	−0.408177	−	0.912903i	$-0.633835\pi$
$283$	3.00000	−	1.73205i	0.178331	−	0.102960i	0.586509	+	0.809943i	$0.300502\pi$
$284$	8.73205	−	15.1244i	0.518152	−	0.897465i
$285$	1.90192	−	3.29423i	0.112660	−	0.195133i
$286$	9.46410	−	2.53590i	0.559624	−	0.149951i
$287$	−12.9904	−	4.50000i	−0.766798	−	0.265627i
$288$		0			0
$289$	2.69615	−	4.66987i	0.158597	−	0.274698i
$290$	−3.53590	+	3.53590i	−0.207635	+	0.207635i
$291$	−3.00000	−	5.19615i	−0.175863	−	0.304604i
$292$	11.3205			0.662483
$293$	13.8564			0.809500			0.404750	−	0.914427i	$-0.367359\pi$
$293$	13.8564			0.809500			0.404750	+	0.914427i	$0.367359\pi$
$294$	−6.75833	+	15.7583i	−0.394154	+	0.919044i
$295$			1.26795i			0.0738229i
$296$	−5.46410	+	1.46410i	−0.317594	+	0.0850992i
$297$	−24.5885	+	14.1962i	−1.42677	+	0.823744i
$298$	−4.46410	+	4.46410i	−0.258598	+	0.258598i
$299$	8.70577	+	5.02628i	0.503468	+	0.290677i
$300$	−1.73205	−	3.00000i	−0.100000	−	0.173205i
$301$	−8.59808	+	24.8205i	−0.495585	+	1.43063i
$302$	5.92820	+	22.1244i	0.341130	+	1.27311i
$303$	−1.20577	−	0.696152i	−0.0692698	−	0.0399929i
$304$		−	8.78461i		−	0.503832i
$305$	−3.86603	−	6.69615i	−0.221368	−	0.383421i
$306$		0			0
$307$			18.1244i			1.03441i	0.855861	+	0.517206i	$0.173028\pi$
$307$			18.1244i			1.03441i	−0.855861	+	0.517206i	$0.826972\pi$
$308$	27.3205	+	9.46410i	1.55673	+	0.539267i
$309$		−	25.3923i		−	1.44452i
$310$	3.00000	−	11.1962i	0.170389	−	0.635899i
$311$	−7.09808	−	12.2942i	−0.402495	−	0.697142i	0.591531	−	0.806282i	$-0.298524\pi$
$311$	−7.09808	−	12.2942i	−0.402495	−	0.697142i	−0.994026	+	0.109140i	$0.965190\pi$
$312$	−1.60770	+	6.00000i	−0.0910178	+	0.339683i
$313$	−15.0000	−	8.66025i	−0.847850	−	0.489506i	0.0120748	−	0.999927i	$-0.496156\pi$
$313$	−15.0000	−	8.66025i	−0.847850	−	0.489506i	−0.859925	+	0.510421i	$0.829490\pi$
$314$	−12.9282	+	3.46410i	−0.729581	+	0.195491i
$315$		0			0
$316$	−1.26795	−	2.19615i	−0.0713277	−	0.123543i
$317$	11.0263	+	6.36603i	0.619298	+	0.357552i	0.776595	−	0.630000i	$-0.216945\pi$
$317$	11.0263	+	6.36603i	0.619298	+	0.357552i	−0.157298	+	0.987551i	$0.550278\pi$
$318$	−17.6603	−	17.6603i	−0.990338	−	0.990338i
$319$	16.7321	−	9.66025i	0.936815	−	0.540870i
$320$	−6.92820	−	4.00000i	−0.387298	−	0.223607i
$321$		−	12.1244i		−	0.676716i
$322$	12.9545	+	26.6865i	0.721925	+	1.48718i
$323$	−10.3923			−0.578243
$324$		−	18.0000i		−	1.00000i
$325$	−0.633975	−	1.09808i	−0.0351666	−	0.0609103i
$326$	10.0000	+	10.0000i	0.553849	+	0.553849i
$327$	2.93782	−	5.08846i	0.162462	−	0.281392i
$328$	−10.3923	−	10.3923i	−0.573819	−	0.573819i
$329$	−16.3923	−	18.9282i	−0.903737	−	1.04355i
$330$	3.46410	+	12.9282i	0.190693	+	0.711674i
$331$	9.63397	−	16.6865i	0.529531	−	0.917175i	−0.469876	−	0.882733i	$-0.655701\pi$
$331$	9.63397	−	16.6865i	0.529531	−	0.917175i	0.999407	−	0.0344422i	$-0.0109654\pi$
$332$	2.66025	−	4.60770i	0.146000	−	0.252880i
$333$		0			0
$334$	−7.56218	+	28.2224i	−0.413784	+	1.54426i
$335$	9.39230			0.513156
$336$	−13.8564	+	12.0000i	−0.755929	+	0.654654i
$337$	22.9808			1.25184			0.625921	−	0.779887i	$-0.284723\pi$
$337$	22.9808			1.25184			0.625921	+	0.779887i	$0.284723\pi$
$338$	4.16987	−	15.5622i	0.226811	−	0.846471i
$339$	10.0981	−	5.83013i	0.548452	−	0.316649i
$340$	−4.73205	+	8.19615i	−0.256631	+	0.444499i
$341$	−22.3923	+	38.7846i	−1.21261	+	2.10030i
$342$		0			0
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	−19.8564	+	19.8564i	−1.07059	+	1.07059i
$345$	−6.86603	+	11.8923i	−0.369654	+	0.640260i
$346$	22.3923	+	22.3923i	1.20382	+	1.20382i
$347$	15.6244	+	27.0622i	0.838759	+	1.45277i	0.890932	+	0.454136i	$0.150052\pi$
$347$	15.6244	+	27.0622i	0.838759	+	1.45277i	−0.0521731	+	0.998638i	$0.516615\pi$
$348$			12.2487i			0.656600i
$349$	−10.5167			−0.562944			−0.281472	−	0.959569i	$-0.590823\pi$
$349$	−10.5167			−0.562944			−0.281472	+	0.959569i	$0.590823\pi$
$350$	0.267949	−	3.73205i	0.0143225	−	0.199487i
$351$		−	6.58846i		−	0.351666i
$352$	21.8564	+	21.8564i	1.16495	+	1.16495i
$353$	27.0788	−	15.6340i	1.44126	−	0.832113i	0.443327	−	0.896360i	$-0.353798\pi$
$353$	27.0788	−	15.6340i	1.44126	−	0.832113i	0.997934	+	0.0642474i	$0.0204647\pi$
$354$	2.19615	+	2.19615i	0.116724	+	0.116724i
$355$	7.56218	+	4.36603i	0.401359	+	0.231725i
$356$	−2.66025	−	4.60770i	−0.140993	−	0.244207i
$357$	14.1962	+	16.3923i	0.751340	+	0.867573i
$358$	10.6603	−	2.85641i	0.563412	−	0.150966i
$359$	−8.95448	−	5.16987i	−0.472600	−	0.272855i	0.244728	−	0.969592i	$-0.421301\pi$
$359$	−8.95448	−	5.16987i	−0.472600	−	0.272855i	−0.717327	+	0.696736i	$0.754635\pi$
$360$		0			0
$361$	−7.08846	−	12.2776i	−0.373077	−	0.646188i
$362$	0.633975	−	2.36603i	0.0333210	−	0.124356i
$363$		−	32.6603i		−	1.71422i
$364$	−5.07180	+	4.39230i	−0.265834	+	0.230219i
$365$			5.66025i			0.296271i
$366$	−18.2942	−	4.90192i	−0.956255	−	0.256228i
$367$	8.13397	+	14.0885i	0.424590	+	0.735411i	0.996382	−	0.0849871i	$-0.0270849\pi$
$367$	8.13397	+	14.0885i	0.424590	+	0.735411i	−0.571792	+	0.820399i	$0.693752\pi$
$368$			31.7128i			1.65314i
$369$		0			0
$370$	−0.732051	−	2.73205i	−0.0380575	−	0.142033i
$371$	−5.09808	−	26.4904i	−0.264679	−	1.37531i
$372$	−14.1962	−	24.5885i	−0.736036	−	1.27485i
$373$	11.1962	+	6.46410i	0.579715	+	0.334698i	0.761020	−	0.648728i	$-0.224699\pi$
$373$	11.1962	+	6.46410i	0.579715	+	0.334698i	−0.181305	+	0.983427i	$0.558032\pi$
$374$	25.8564	−	25.8564i	1.33700	−	1.33700i
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$	−6.92820	−	25.8564i	−0.357295	−	1.33344i
$377$			4.48334i			0.230904i
$378$	10.9019	−	16.0981i	0.560734	−	0.827996i
$379$	32.4449			1.66658			0.833290	−	0.552836i	$-0.186454\pi$
$379$	32.4449			1.66658			0.833290	+	0.552836i	$0.186454\pi$
$380$	4.39230			0.225320
$381$	−7.39230	−	12.8038i	−0.378719	−	0.655961i
$382$	3.60770	−	3.60770i	0.184586	−	0.184586i
$383$	−3.40192	+	5.89230i	−0.173830	+	0.301083i	−0.939756	−	0.341846i	$-0.888948\pi$
$383$	−3.40192	+	5.89230i	−0.173830	+	0.301083i	0.765926	+	0.642929i	$0.222281\pi$
$384$	−18.9282	+	5.07180i	−0.965926	+	0.258819i
$385$	−4.73205	+	13.6603i	−0.241168	+	0.696191i
$386$	−18.9282	+	5.07180i	−0.963420	+	0.258148i
$387$		0			0
$388$	3.46410	−	6.00000i	0.175863	−	0.304604i
$389$	33.7128	−	19.4641i	1.70931	−	0.986869i	0.773893	−	0.633317i	$-0.218307\pi$
$389$	33.7128	−	19.4641i	1.70931	−	0.986869i	0.935415	−	0.353552i	$-0.115026\pi$
$390$	−3.00000	−	0.803848i	−0.151911	−	0.0407044i
$391$	37.5167			1.89730
$392$	−19.6603	+	2.33975i	−0.992993	+	0.118175i
$393$	−20.7846			−1.04844
$394$	−12.1962	−	3.26795i	−0.614433	−	0.164637i
$395$	1.09808	−	0.633975i	0.0552502	−	0.0318987i
$396$		0			0
$397$	7.39230	−	12.8038i	0.371009	−	0.642607i	−0.618712	−	0.785618i	$-0.712345\pi$
$397$	7.39230	−	12.8038i	0.371009	−	0.642607i	0.989721	+	0.143011i	$0.0456785\pi$
$398$	24.5885	−	6.58846i	1.23251	−	0.330250i
$399$	3.29423	−	9.50962i	0.164918	−	0.476076i
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	−0.767949	+	1.33013i	−0.0383496	+	0.0664234i	−0.884563	−	0.466421i	$-0.845543\pi$
$401$	−0.767949	+	1.33013i	−0.0383496	+	0.0664234i	0.846214	+	0.532844i	$0.178877\pi$
$402$	16.2679	−	16.2679i	0.811372	−	0.811372i
$403$	−5.19615	−	9.00000i	−0.258839	−	0.448322i
$404$		−	1.60770i		−	0.0799858i
$405$	9.00000			0.447214
$406$	−7.41858	+	10.9545i	−0.368178	+	0.543662i
$407$			10.9282i			0.541691i
$408$	6.00000	+	22.3923i	0.297044	+	1.10858i
$409$	−2.89230	+	1.66987i	−0.143015	+	0.0825699i	−0.569800	−	0.821783i	$-0.692979\pi$
$409$	−2.89230	+	1.66987i	−0.143015	+	0.0825699i	0.426785	+	0.904353i	$0.359646\pi$
$410$	5.19615	−	5.19615i	0.256620	−	0.256620i
$411$	12.5885	+	7.26795i	0.620943	+	0.358501i
$412$	25.3923	−	14.6603i	1.25099	−	0.722259i
$413$	0.633975	+	3.29423i	0.0311959	+	0.162098i
$414$		0			0
$415$	2.30385	+	1.33013i	0.113091	+	0.0652934i
$416$	−6.92820	+	1.85641i	−0.339683	+	0.0910178i
$417$	2.19615	+	3.80385i	0.107546	+	0.186275i
$418$	−16.3923	−	4.39230i	−0.801774	−	0.214835i
$419$			23.3205i			1.13928i	0.821894	+	0.569641i	$0.192918\pi$
$419$			23.3205i			1.13928i	−0.821894	+	0.569641i	$0.807082\pi$
$420$	−6.00000	−	6.92820i	−0.292770	−	0.338062i
$421$		−	27.2487i		−	1.32802i	−0.747723	−	0.664010i	$-0.768853\pi$
$421$		−	27.2487i		−	1.32802i	0.747723	−	0.664010i	$-0.231147\pi$
$422$	−4.60770	+	17.1962i	−0.224299	+	0.837096i
$423$		0			0
$424$	7.46410	−	27.8564i	0.362489	−	1.35283i
$425$	−4.09808	−	2.36603i	−0.198786	−	0.114769i
$426$	20.6603	−	5.53590i	1.00099	−	0.268215i
$427$	−13.3923	−	15.4641i	−0.648099	−	0.748360i
$428$	12.1244	−	7.00000i	0.586053	−	0.338358i
$429$	10.3923	+	6.00000i	0.501745	+	0.289683i
$430$	−9.92820	−	9.92820i	−0.478780	−	0.478780i
$431$	−6.92820	+	4.00000i	−0.333720	+	0.192673i	−0.657491	−	0.753462i	$-0.728382\pi$
$431$	−6.92820	+	4.00000i	−0.333720	+	0.192673i	0.323772	+	0.946135i	$0.395049\pi$
$432$	18.0000	−	10.3923i	0.866025	−	0.500000i
$433$		−	22.9808i		−	1.10438i	−0.833717	−	0.552192i	$-0.813791\pi$
$433$		−	22.9808i		−	1.10438i	0.833717	−	0.552192i	$-0.186209\pi$
$434$	2.19615	−	30.5885i	0.105419	−	1.46829i
$435$	−6.12436			−0.293640
$436$	6.78461			0.324924
$437$	−8.70577	−	15.0788i	−0.416454	−	0.721319i
$438$	9.80385	+	9.80385i	0.468446	+	0.468446i
$439$	6.92820	−	12.0000i	0.330665	−	0.572729i	−0.651977	−	0.758238i	$-0.726060\pi$
$439$	6.92820	−	12.0000i	0.330665	−	0.572729i	0.982642	+	0.185510i	$0.0593936\pi$
$440$	−10.9282	+	10.9282i	−0.520982	+	0.520982i
$441$		0			0
$442$	2.19615	+	8.19615i	0.104460	+	0.389851i
$443$	−3.50000	+	6.06218i	−0.166290	+	0.288023i	−0.937113	−	0.349027i	$-0.886512\pi$
$443$	−3.50000	+	6.06218i	−0.166290	+	0.288023i	0.770823	+	0.637050i	$0.219845\pi$
$444$	−6.00000	−	3.46410i	−0.284747	−	0.164399i
$445$	2.30385	−	1.33013i	0.109213	−	0.0630541i
$446$	−5.07180	+	18.9282i	−0.240157	+	0.896276i
$447$	−7.73205			−0.365713
$448$	−20.0000	−	6.92820i	−0.944911	−	0.327327i
$449$	26.4641			1.24892			0.624459	−	0.781058i	$-0.285319\pi$
$449$	26.4641			1.24892			0.624459	+	0.781058i	$0.285319\pi$
$450$		0			0
$451$	−24.5885	+	14.1962i	−1.15783	+	0.668471i
$452$	11.6603	+	6.73205i	0.548452	+	0.316649i
$453$	−14.0263	+	24.2942i	−0.659012	+	1.14144i
$454$	6.92820	+	25.8564i	0.325157	+	1.21350i
$455$	−2.19615	−	2.53590i	−0.102957	−	0.118885i
$456$	7.60770	−	7.60770i	0.356263	−	0.356263i
$457$	14.3205	−	24.8038i	0.669885	−	1.16028i	−0.308051	−	0.951370i	$-0.599677\pi$
$457$	14.3205	−	24.8038i	0.669885	−	1.16028i	0.977936	−	0.208905i	$-0.0669900\pi$
$458$	−8.53590	−	8.53590i	−0.398856	−	0.398856i
$459$	−12.2942	−	21.2942i	−0.573845	−	0.993929i
$460$	−15.8564			−0.739309
$461$	−37.8564			−1.76315			−0.881574	−	0.472045i	$-0.843516\pi$
$461$	−37.8564			−1.76315			−0.881574	+	0.472045i	$0.843516\pi$
$462$	15.4641	+	31.8564i	0.719455	+	1.48209i
$463$			1.39230i			0.0647059i	0.999477	+	0.0323529i	$0.0103001\pi$
$463$			1.39230i			0.0647059i	−0.999477	+	0.0323529i	$0.989700\pi$
$464$	−12.2487	+	7.07180i	−0.568632	+	0.328300i
$465$	12.2942	−	7.09808i	0.570131	−	0.329165i
$466$	8.73205	+	8.73205i	0.404504	+	0.404504i
$467$	−27.4808	−	15.8660i	−1.27166	−	0.734192i	−0.296358	−	0.955077i	$-0.595772\pi$
$467$	−27.4808	−	15.8660i	−1.27166	−	0.734192i	−0.975300	+	0.220885i	$0.929106\pi$
$468$		0			0
$469$	24.4019	−	4.69615i	1.12678	−	0.216848i
$470$	12.9282	−	3.46410i	0.596334	−	0.159787i
$471$	−14.1962	−	8.19615i	−0.654124	−	0.377659i
$472$	−0.928203	+	3.46410i	−0.0427240	+	0.159448i
$473$	27.1244	+	46.9808i	1.24718	+	2.16018i
$474$	0.803848	−	3.00000i	0.0369219	−	0.137795i
$475$			2.19615i			0.100766i
$476$	−8.19615	+	23.6603i	−0.375670	+	1.08447i
$477$		0			0
$478$	−16.6603	−	4.46410i	−0.762022	−	0.204183i
$479$	5.83013	+	10.0981i	0.266385	+	0.461393i	0.967926	−	0.251237i	$-0.0808373\pi$
$479$	5.83013	+	10.0981i	0.266385	+	0.461393i	−0.701540	+	0.712630i	$0.747504\pi$
$480$	−2.53590	−	9.46410i	−0.115747	−	0.431975i
$481$	−2.19615	−	1.26795i	−0.100136	−	0.0578135i
$482$	−7.26795	−	27.1244i	−0.331046	−	1.23548i
$483$	−11.8923	+	34.3301i	−0.541119	+	1.56207i
$484$	32.6603	−	18.8564i	1.48456	−	0.857109i
$485$	3.00000	+	1.73205i	0.136223	+	0.0786484i
$486$		0			0
$487$	−14.5359	+	8.39230i	−0.658684	+	0.380292i	−0.791776	−	0.610812i	$-0.790843\pi$
$487$	−14.5359	+	8.39230i	−0.658684	+	0.380292i	0.133091	+	0.991104i	$0.457510\pi$
$488$	−5.66025	−	21.1244i	−0.256228	−	0.956255i
$489$			17.3205i			0.783260i
$490$	−1.16987	−	9.83013i	−0.0528495	−	0.444080i
$491$	−23.2679			−1.05007			−0.525034	−	0.851081i	$-0.675947\pi$
$491$	−23.2679			−1.05007			−0.525034	+	0.851081i	$0.675947\pi$
$492$		−	18.0000i		−	0.811503i
$493$	8.36603	+	14.4904i	0.376787	+	0.652614i
$494$	2.78461	−	2.78461i	0.125286	−	0.125286i
$495$		0			0
$496$	16.3923	−	28.3923i	0.736036	−	1.27485i
$497$	21.8301	+	7.56218i	0.979215	+	0.339210i
$498$	6.29423	−	1.68653i	0.282051	−	0.0755754i
$499$	−0.803848	+	1.39230i	−0.0359852	+	0.0623281i	−0.883457	−	0.468512i	$-0.844790\pi$
$499$	−0.803848	+	1.39230i	−0.0359852	+	0.0623281i	0.847472	+	0.530840i	$0.178124\pi$
$500$	1.73205	+	1.00000i	0.0774597	+	0.0447214i
$501$	−30.9904	+	17.8923i	−1.38455	+	0.799369i
$502$	−35.7846	−	9.58846i	−1.59715	−	0.427954i
$503$	14.6603			0.653668			0.326834	−	0.945082i	$-0.394018\pi$
$503$	14.6603			0.653668			0.326834	+	0.945082i	$0.394018\pi$
$504$		0			0
$505$	0.803848			0.0357707
$506$	59.1769	+	15.8564i	2.63073	+	0.704903i
$507$	17.0885	−	9.86603i	0.758925	−	0.438166i
$508$	8.53590	−	14.7846i	0.378719	−	0.655961i
$509$	−8.25833	+	14.3038i	−0.366044	+	0.634007i	−0.988943	−	0.148295i	$-0.952621\pi$
$509$	−8.25833	+	14.3038i	−0.366044	+	0.634007i	0.622899	+	0.782302i	$0.285955\pi$
$510$	−11.1962	+	3.00000i	−0.495774	+	0.132842i
$511$	2.83013	+	14.7058i	0.125197	+	0.650545i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	−5.70577	+	9.88269i	−0.251916	+	0.436331i
$514$	6.00000	−	6.00000i	0.264649	−	0.264649i
$515$	7.33013	+	12.6962i	0.323004	+	0.559459i
$516$	−34.3923			−1.51404
$517$	−51.7128			−2.27433
$518$	−3.26795	−	6.73205i	−0.143585	−	0.295789i
$519$			38.7846i			1.70246i
$520$	−0.928203	−	3.46410i	−0.0407044	−	0.151911i
$521$	31.3923	−	18.1244i	1.37532	−	0.794042i	0.383730	−	0.923445i	$-0.374639\pi$
$521$	31.3923	−	18.1244i	1.37532	−	0.794042i	0.991592	+	0.129403i	$0.0413061\pi$
$522$		0			0
$523$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$523$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$524$	−12.0000	−	20.7846i	−0.524222	−	0.907980i
$525$	3.46410	−	3.00000i	0.151186	−	0.130931i
$526$	−10.9545	−	40.8827i	−0.477638	−	1.78257i
$527$	−33.5885	−	19.3923i	−1.46314	−	0.844742i
$528$			37.8564i			1.64749i
$529$	19.9282	+	34.5167i	0.866444	+	1.50072i
$530$	13.9282	+	3.73205i	0.605002	+	0.162110i
$531$		0			0
$532$	11.4115	−	2.19615i	0.494753	−	0.0952153i
$533$		−	6.58846i		−	0.285378i
$534$	1.68653	−	6.29423i	0.0729834	−	0.272378i
$535$	3.50000	+	6.06218i	0.151318	+	0.262091i
$536$	25.6603	+	6.87564i	1.10835	+	0.296983i
$537$	11.7058	+	6.75833i	0.505141	+	0.291643i
$538$	−11.8301	+	3.16987i	−0.510033	+	0.136663i
$539$	−5.46410	+	37.8564i	−0.235356	+	1.63059i
$540$	5.19615	+	9.00000i	0.223607	+	0.387298i
$541$	−2.81347	−	1.62436i	−0.120960	−	0.0698365i	0.438299	−	0.898829i	$-0.355581\pi$
$541$	−2.81347	−	1.62436i	−0.120960	−	0.0698365i	−0.559259	+	0.828993i	$0.688914\pi$
$542$	3.80385	+	3.80385i	0.163389	+	0.163389i
$543$	2.59808	−	1.50000i	0.111494	−	0.0643712i
$544$	−18.9282	+	18.9282i	−0.811540	+	0.811540i
$545$			3.39230i			0.145310i
$546$	−8.19615	−	0.588457i	−0.350763	−	0.0251836i
$547$	1.00000			0.0427569			0.0213785	−	0.999771i	$-0.493195\pi$
$547$	1.00000			0.0427569			0.0213785	+	0.999771i	$0.493195\pi$
$548$			16.7846i			0.717003i
$549$		0			0
$550$	−5.46410	−	5.46410i	−0.232990	−	0.232990i
$551$	3.88269	−	6.72501i	0.165408	−	0.286495i
$552$	−27.4641	+	27.4641i	−1.16895	+	1.16895i
$553$	2.53590	−	2.19615i	0.107837	−	0.0933899i
$554$	3.00000	+	11.1962i	0.127458	+	0.475679i
$555$	1.73205	−	3.00000i	0.0735215	−	0.127343i
$556$	−2.53590	+	4.39230i	−0.107546	+	0.186275i
$557$	11.8756	−	6.85641i	0.503187	−	0.290515i	−0.226842	−	0.973932i	$-0.572840\pi$
$557$	11.8756	−	6.85641i	0.503187	−	0.290515i	0.730029	+	0.683416i	$0.239507\pi$
$558$		0			0
$559$	−12.5885			−0.532435
$560$	3.46410	−	10.0000i	0.146385	−	0.422577i
$561$	44.7846			1.89081
$562$	2.14359	−	8.00000i	0.0904220	−	0.337460i
$563$	−24.6962	+	14.2583i	−1.04082	+	0.600917i	−0.920065	−	0.391766i	$-0.871864\pi$
$563$	−24.6962	+	14.2583i	−1.04082	+	0.600917i	−0.120754	+	0.992683i	$0.538531\pi$
$564$	16.3923	−	28.3923i	0.690241	−	1.19553i
$565$	−3.36603	+	5.83013i	−0.141610	+	0.245275i
$566$	1.26795	+	4.73205i	0.0532959	+	0.198903i
$567$	23.3827	−	4.50000i	0.981981	−	0.188982i
$568$	17.4641	+	17.4641i	0.732777	+	0.732777i
$569$	−6.73205	+	11.6603i	−0.282222	+	0.488823i	−0.971932	−	0.235263i	$-0.924405\pi$
$569$	−6.73205	+	11.6603i	−0.282222	+	0.488823i	0.689710	+	0.724086i	$0.257738\pi$
$570$	3.80385	+	3.80385i	0.159326	+	0.159326i
$571$	14.2942	+	24.7583i	0.598195	+	1.03610i	0.993087	+	0.117377i	$0.0374485\pi$
$571$	14.2942	+	24.7583i	0.598195	+	1.03610i	−0.394893	+	0.918727i	$0.629218\pi$
$572$			13.8564i			0.579365i
$573$	6.24871			0.261044
$574$	10.9019	−	16.0981i	0.455038	−	0.671921i
$575$		−	7.92820i		−	0.330629i
$576$		0			0
$577$	−26.7846	+	15.4641i	−1.11506	+	0.643779i	−0.940135	−	0.340803i	$-0.889301\pi$
$577$	−26.7846	+	15.4641i	−1.11506	+	0.643779i	−0.174923	+	0.984582i	$0.555968\pi$
$578$	5.39230	+	5.39230i	0.224290	+	0.224290i
$579$	−20.7846	−	12.0000i	−0.863779	−	0.498703i
$580$	−3.53590	−	6.12436i	−0.146820	−	0.254300i
$581$	6.65064	+	2.30385i	0.275915	+	0.0955797i
$582$	8.19615	−	2.19615i	0.339741	−	0.0910334i
$583$	−48.2487	−	27.8564i	−1.99826	−	1.15369i
$584$	−4.14359	+	15.4641i	−0.171463	+	0.639909i
$585$		0			0
$586$	−5.07180	+	18.9282i	−0.209514	+	0.781917i
$587$		−	2.53590i		−	0.104668i	−0.998630	−	0.0523339i	$-0.983334\pi$
$587$		−	2.53590i		−	0.104668i	0.998630	−	0.0523339i	$-0.0166660\pi$
$588$	−19.0526	−	15.0000i	−0.785714	−	0.618590i
$589$			18.0000i			0.741677i
$590$	−1.73205	−	0.464102i	−0.0713074	−	0.0191068i
$591$	−7.73205	−	13.3923i	−0.318054	−	0.550886i
$592$		−	8.00000i		−	0.328798i
$593$	32.2750	+	18.6340i	1.32538	+	0.765206i	0.984580	−	0.174932i	$-0.0559706\pi$
$593$	32.2750	+	18.6340i	1.32538	+	0.765206i	0.340795	+	0.940138i	$0.389304\pi$
$594$	−10.3923	−	38.7846i	−0.426401	−	1.59135i
$595$	−11.8301	−	4.09808i	−0.484988	−	0.168005i
$596$	−4.46410	−	7.73205i	−0.182857	−	0.316717i
$597$	27.0000	+	15.5885i	1.10504	+	0.637993i
$598$	−10.0526	+	10.0526i	−0.411080	+	0.411080i
$599$	16.7321	−	9.66025i	0.683653	−	0.394707i	−0.117577	−	0.993064i	$-0.537513\pi$
$599$	16.7321	−	9.66025i	0.683653	−	0.394707i	0.801230	+	0.598356i	$0.204179\pi$
$600$	4.73205	−	1.26795i	0.193185	−	0.0517638i
$601$			22.3923i			0.913401i	0.889620	+	0.456701i	$0.150969\pi$
$601$			22.3923i			0.913401i	−0.889620	+	0.456701i	$0.849031\pi$
$602$	−30.7583	−	20.8301i	−1.25362	−	0.848973i
$603$		0			0
$604$	−32.3923			−1.31802
$605$	9.42820	+	16.3301i	0.383311	+	0.663914i
$606$	1.39230	−	1.39230i	0.0565585	−	0.0565585i
$607$	3.52628	−	6.10770i	0.143127	−	0.247904i	−0.785545	−	0.618804i	$-0.787618\pi$
$607$	3.52628	−	6.10770i	0.143127	−	0.247904i	0.928673	+	0.370900i	$0.120951\pi$
$608$	12.0000	+	3.21539i	0.486664	+	0.130401i
$609$	−15.9115	+	3.06218i	−0.644768	+	0.124086i
$610$	10.5622	−	2.83013i	0.427650	−	0.114588i
$611$	6.00000	−	10.3923i	0.242734	−	0.420428i
$612$		0			0
$613$	−24.8827	+	14.3660i	−1.00500	+	0.580238i	−0.909724	−	0.415212i	$-0.863707\pi$
$613$	−24.8827	+	14.3660i	−1.00500	+	0.580238i	−0.0952777	+	0.995451i	$0.530374\pi$
$614$	−24.7583	−	6.63397i	−0.999165	−	0.267725i
$615$	9.00000			0.362915
$616$	−22.9282	+	33.8564i	−0.923804	+	1.36411i
$617$	15.0718			0.606768			0.303384	−	0.952868i	$-0.401884\pi$
$617$	15.0718			0.606768			0.303384	+	0.952868i	$0.401884\pi$
$618$	34.6865	+	9.29423i	1.39530	+	0.373869i
$619$	−24.5885	+	14.1962i	−0.988294	+	0.570592i	−0.904764	−	0.425914i	$-0.859953\pi$
$619$	−24.5885	+	14.1962i	−0.988294	+	0.570592i	−0.0835298	+	0.996505i	$0.526619\pi$
$620$	14.1962	+	8.19615i	0.570131	+	0.329165i
$621$	20.5981	−	35.6769i	0.826572	−	1.43167i
$622$	19.3923	−	5.19615i	0.777561	−	0.208347i
$623$	5.32051	−	4.60770i	0.213162	−	0.184603i
$624$	−7.60770	−	4.39230i	−0.304552	−	0.175833i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	17.3205	−	17.3205i	0.692267	−	0.692267i
$627$	−10.3923	−	18.0000i	−0.415029	−	0.718851i
$628$		−	18.9282i		−	0.755318i
$629$	−9.46410			−0.377358
$630$		0			0
$631$		−	14.5359i		−	0.578665i	−0.957229	−	0.289332i	$-0.906567\pi$
$631$		−	14.5359i		−	0.578665i	0.957229	−	0.289332i	$-0.0934333\pi$
$632$	3.46410	−	0.928203i	0.137795	−	0.0369219i
$633$	−18.8827	+	10.9019i	−0.750519	+	0.433313i
$634$	−12.7321	+	12.7321i	−0.505654	+	0.505654i
$635$	7.39230	+	4.26795i	0.293355	+	0.169368i
$636$	30.5885	−	17.6603i	1.21291	−	0.700275i
$637$	−6.97372	−	5.49038i	−0.276309	−	0.217537i
$638$	7.07180	+	26.3923i	0.279975	+	1.04488i
$639$		0			0
$640$	8.00000	−	8.00000i	0.316228	−	0.316228i
$641$	−13.7679	−	23.8468i	−0.543801	−	0.941891i	−0.998681	−	0.0513387i	$-0.983651\pi$
$641$	−13.7679	−	23.8468i	−0.543801	−	0.941891i	0.454880	−	0.890553i	$-0.349682\pi$
$642$	16.5622	+	4.43782i	0.653657	+	0.175147i
$643$		−	40.3923i		−	1.59292i	−0.604693	−	0.796459i	$-0.706704\pi$
$643$		−	40.3923i		−	1.59292i	0.604693	−	0.796459i	$-0.293296\pi$
$644$	−41.1962	+	7.92820i	−1.62336	+	0.312415i
$645$		−	17.1962i		−	0.677098i
$646$	3.80385	−	14.1962i	0.149660	−	0.558540i
$647$	−1.79423	−	3.10770i	−0.0705384	−	0.122176i	0.828599	−	0.559843i	$-0.189138\pi$
$647$	−1.79423	−	3.10770i	−0.0705384	−	0.122176i	−0.899137	+	0.437666i	$0.855805\pi$
$648$	24.5885	+	6.58846i	0.965926	+	0.258819i
$649$	6.00000	+	3.46410i	0.235521	+	0.135978i
$650$	1.73205	−	0.464102i	0.0679366	−	0.0182036i
$651$	28.3923	−	24.5885i	1.11278	−	0.963698i
$652$	−17.3205	+	10.0000i	−0.678323	+	0.391630i
$653$	−28.5622	−	16.4904i	−1.11772	−	0.645318i	−0.176905	−	0.984228i	$-0.556609\pi$
$653$	−28.5622	−	16.4904i	−1.11772	−	0.645318i	−0.940819	+	0.338909i	$0.889942\pi$
$654$	5.87564	+	5.87564i	0.229756	+	0.229756i
$655$	10.3923	−	6.00000i	0.406061	−	0.234439i
$656$	18.0000	−	10.3923i	0.702782	−	0.405751i
$657$		0			0
$658$	31.8564	−	15.4641i	1.24189	−	0.602853i
$659$	−28.1962			−1.09837			−0.549183	−	0.835702i	$-0.685061\pi$
$659$	−28.1962			−1.09837			−0.549183	+	0.835702i	$0.685061\pi$
$660$	−18.9282			−0.736779
$661$	13.7942	+	23.8923i	0.536533	+	0.929303i	0.999087	+	0.0427119i	$0.0135998\pi$
$661$	13.7942	+	23.8923i	0.536533	+	0.929303i	−0.462554	+	0.886591i	$0.653067\pi$
$662$	19.2679	+	19.2679i	0.748870	+	0.748870i
$663$	−5.19615	+	9.00000i	−0.201802	+	0.349531i
$664$	5.32051	+	5.32051i	0.206476	+	0.206476i
$665$	1.09808	+	5.70577i	0.0425816	+	0.221260i
$666$		0			0
$667$	−14.0167	+	24.2776i	−0.542727	+	0.940031i
$668$	−35.7846	−	20.6603i	−1.38455	−	0.799369i
$669$	−20.7846	+	12.0000i	−0.803579	+	0.463947i
$670$	−3.43782	+	12.8301i	−0.132815	+	0.495671i
$671$	−42.2487			−1.63099
$672$	−11.3205	−	23.3205i	−0.436698	−	0.899608i
$673$	−2.78461			−0.107339			−0.0536694	−	0.998559i	$-0.517092\pi$
$673$	−2.78461			−0.107339			−0.0536694	+	0.998559i	$0.517092\pi$
$674$	−8.41154	+	31.3923i	−0.324001	+	1.20919i
$675$	−4.50000	+	2.59808i	−0.173205	+	0.100000i
$676$	19.7321	+	11.3923i	0.758925	+	0.438166i
$677$	−2.70577	+	4.68653i	−0.103991	+	0.180118i	−0.913326	−	0.407230i	$-0.866495\pi$
$677$	−2.70577	+	4.68653i	−0.103991	+	0.180118i	0.809334	+	0.587348i	$0.199828\pi$
$678$	4.26795	+	15.9282i	0.163910	+	0.611719i
$679$	8.66025	+	3.00000i	0.332350	+	0.115129i
$680$	−9.46410	−	9.46410i	−0.362932	−	0.362932i
$681$	−16.3923	+	28.3923i	−0.628154	+	1.08800i
$682$	−44.7846	−	44.7846i	−1.71489	−	1.71489i
$683$	1.42820	+	2.47372i	0.0546487	+	0.0946543i	0.892056	−	0.451926i	$-0.149263\pi$
$683$	1.42820	+	2.47372i	0.0546487	+	0.0946543i	−0.837407	+	0.546580i	$0.815929\pi$
$684$		0			0
$685$	−8.39230			−0.320653
$686$	−7.95448	−	24.9545i	−0.303704	−	0.952767i
$687$		−	14.7846i		−	0.564068i
$688$	−19.8564	−	34.3923i	−0.757018	−	1.31119i
$689$	11.1962	−	6.46410i	0.426539	−	0.246263i
$690$	−13.7321	−	13.7321i	−0.522770	−	0.522770i
$691$	−1.39230	−	0.803848i	−0.0529658	−	0.0305798i	0.473283	−	0.880910i	$-0.343069\pi$
$691$	−1.39230	−	0.803848i	−0.0529658	−	0.0305798i	−0.526249	+	0.850330i	$0.676402\pi$
$692$	−38.7846	+	22.3923i	−1.47437	+	0.851228i
$693$		0			0
$694$	−42.6865	+	11.4378i	−1.62036	+	0.434174i
$695$	−2.19615	−	1.26795i	−0.0833048	−	0.0480961i
$696$	−16.7321	−	4.48334i	−0.634227	−	0.169941i
$697$	−12.2942	−	21.2942i	−0.465677	−	0.806576i
$698$	3.84936	−	14.3660i	0.145701	−	0.543762i
$699$			15.1244i			0.572056i
$700$	5.00000	+	1.73205i	0.188982	+	0.0654654i
$701$			7.78461i			0.294021i	0.989135	+	0.147010i	$0.0469651\pi$
$701$			7.78461i			0.294021i	−0.989135	+	0.147010i	$0.953035\pi$
$702$	9.00000	+	2.41154i	0.339683	+	0.0910178i
$703$	2.19615	+	3.80385i	0.0828295	+	0.143465i
$704$	−37.8564	+	21.8564i	−1.42677	+	0.823744i
$705$	14.1962	+	8.19615i	0.534658	+	0.308685i
$706$	11.4449	+	42.7128i	0.430733	+	1.60752i
$707$	2.08846	−	0.401924i	0.0785445	−	0.0151159i
$708$	−3.80385	+	2.19615i	−0.142957	+	0.0825365i
$709$	31.3301	+	18.0885i	1.17663	+	0.679326i	0.955232	−	0.295858i	$-0.0956055\pi$
$709$	31.3301	+	18.0885i	1.17663	+	0.679326i	0.221396	+	0.975184i	$0.428939\pi$
$710$	−8.73205	+	8.73205i	−0.327708	+	0.327708i
$711$		0			0
$712$	7.26795	−	1.94744i	0.272378	−	0.0729834i
$713$		−	64.9808i		−	2.43355i
$714$	−27.5885	+	13.3923i	−1.03247	+	0.501194i
$715$	−6.92820			−0.259100
$716$			15.6077i			0.583287i
$717$	−10.5622	−	18.2942i	−0.394452	−	0.683210i
$718$	10.3397	−	10.3397i	0.385876	−	0.385876i
$719$	14.5359	−	25.1769i	0.542098	−	0.938940i	−0.456686	−	0.889628i	$-0.650964\pi$
$719$	14.5359	−	25.1769i	0.542098	−	0.938940i	0.998783	−	0.0493125i	$-0.0157030\pi$
$720$		0			0
$721$	25.3923	+	29.3205i	0.945659	+	1.09195i
$722$	19.3660	−	5.18911i	0.720729	−	0.193119i
$723$	17.1962	−	29.7846i	0.639532	−	1.10770i
$724$	3.00000	+	1.73205i	0.111494	+	0.0643712i
$725$	3.06218	−	1.76795i	0.113726	−	0.0656600i
$726$	44.6147	+	11.9545i	1.65581	+	0.443672i
$727$	−13.0526			−0.484093			−0.242046	−	0.970265i	$-0.577819\pi$
$727$	−13.0526			−0.484093			−0.242046	+	0.970265i	$0.577819\pi$
$728$	−4.14359	−	8.53590i	−0.153572	−	0.316361i
$729$	−27.0000			−1.00000
$730$	−7.73205	−	2.07180i	−0.286176	−	0.0766806i
$731$	−40.6865	+	23.4904i	−1.50485	+	0.868823i
$732$	13.3923	−	23.1962i	0.494994	−	0.857354i
$733$	5.19615	−	9.00000i	0.191924	−	0.332423i	−0.753964	−	0.656916i	$-0.771861\pi$
$733$	5.19615	−	9.00000i	0.191924	−	0.332423i	0.945888	+	0.324494i	$0.105194\pi$
$734$	−22.2224	+	5.95448i	−0.820245	+	0.219784i
$735$	7.50000	−	9.52628i	0.276642	−	0.351382i
$736$	−43.3205	−	11.6077i	−1.59682	−	0.427865i
$737$	25.6603	−	44.4449i	0.945208	−	1.63715i
$738$		0			0
$739$	−13.1962	−	22.8564i	−0.485428	−	0.840787i	0.514431	−	0.857531i	$-0.328003\pi$
$739$	−13.1962	−	22.8564i	−0.485428	−	0.840787i	−0.999860	+	0.0167450i	$0.994670\pi$
$740$	4.00000			0.147043
$741$	4.82309			0.177180
$742$	38.0526	+	2.73205i	1.39695	+	0.100297i
$743$			11.3923i			0.417943i	0.977922	+	0.208972i	$0.0670116\pi$
$743$			11.3923i			0.417943i	−0.977922	+	0.208972i	$0.932988\pi$
$744$	38.7846	−	10.3923i	1.42191	−	0.381000i
$745$	3.86603	−	2.23205i	0.141640	−	0.0817760i
$746$	−12.9282	+	12.9282i	−0.473335	+	0.473335i
$747$		0			0
$748$	25.8564	+	44.7846i	0.945404	+	1.63749i
$749$	12.1244	+	14.0000i	0.443014	+	0.511549i
$750$	0.633975	+	2.36603i	0.0231495	+	0.0863950i
$751$	13.1436	+	7.58846i	0.479617	+	0.276907i	0.720257	−	0.693708i	$-0.244024\pi$
$751$	13.1436	+	7.58846i	0.479617	+	0.276907i	−0.240640	+	0.970614i	$0.577357\pi$
$752$	37.8564			1.38048
$753$	−22.6865	−	39.2942i	−0.826743	−	1.43196i
$754$	−6.12436	−	1.64102i	−0.223036	−	0.0597623i
$755$		−	16.1962i		−	0.589438i
$756$	18.0000	+	20.7846i	0.654654	+	0.755929i
$757$		−	7.80385i		−	0.283636i	−0.989893	−	0.141818i	$-0.954705\pi$
$757$		−	7.80385i		−	0.283636i	0.989893	−	0.141818i	$-0.0452947\pi$
$758$	−11.8756	+	44.3205i	−0.431343	+	1.60979i
$759$	37.5167	+	64.9808i	1.36177	+	2.35865i
$760$	−1.60770	+	6.00000i	−0.0583172	+	0.217643i
$761$	−41.1962	−	23.7846i	−1.49336	−	0.862191i	−0.493388	−	0.869809i	$-0.664242\pi$
$761$	−41.1962	−	23.7846i	−1.49336	−	0.862191i	−0.999971	+	0.00761770i	$0.997575\pi$
$762$	20.1962	−	5.41154i	0.731629	−	0.196040i
$763$	1.69615	+	8.81347i	0.0614048	+	0.319069i
$764$	3.60770	+	6.24871i	0.130522	+	0.226070i
$765$		0			0
$766$	−6.80385	−	6.80385i	−0.245833	−	0.245833i
$767$	−1.39230	+	0.803848i	−0.0502732	+	0.0290253i
$768$		−	27.7128i		−	1.00000i
$769$		−	10.3923i		−	0.374756i	−0.982288	−	0.187378i	$-0.940001\pi$
$769$		−	10.3923i		−	0.374756i	0.982288	−	0.187378i	$-0.0599989\pi$
$770$	−16.9282	−	11.4641i	−0.610050	−	0.413138i
$771$	10.3923			0.374270
$772$		−	27.7128i		−	0.997406i
$773$	−8.70577	−	15.0788i	−0.313125	−	0.542348i	0.665912	−	0.746030i	$-0.268042\pi$
$773$	−8.70577	−	15.0788i	−0.313125	−	0.542348i	−0.979037	+	0.203682i	$0.934709\pi$
$774$		0			0
$775$	−4.09808	+	7.09808i	−0.147207	+	0.254970i
$776$	6.92820	+	6.92820i	0.248708	+	0.248708i
$777$	3.00000	−	8.66025i	0.107624	−	0.310685i
$778$	14.2487	+	53.1769i	0.510841	+	1.90648i
$779$	−5.70577	+	9.88269i	−0.204430	+	0.354084i
$780$	2.19615	−	3.80385i	0.0786349	−	0.136200i
$781$	41.3205	−	23.8564i	1.47856	−	0.853649i
$782$	−13.7321	+	51.2487i	−0.491057	+	1.83265i
$783$	18.3731			0.656600
$784$	4.00000	−	27.7128i	0.142857	−	0.989743i
$785$	9.46410			0.337788
$786$	7.60770	−	28.3923i	0.271357	−	1.01272i
$787$	39.6962	−	22.9186i	1.41502	−	0.816959i	0.419160	−	0.907912i	$-0.362325\pi$
$787$	39.6962	−	22.9186i	1.41502	−	0.816959i	0.995855	+	0.0909532i	$0.0289914\pi$
$788$	8.92820	−	15.4641i	0.318054	−	0.550886i
$789$	25.9186	−	44.8923i	0.922726	−	1.59821i
$790$	0.464102	+	1.73205i	0.0165120	+	0.0616236i
$791$	−5.83013	+	16.8301i	−0.207295	+	0.598410i
$792$		0			0
$793$	4.90192	−	8.49038i	0.174072	−	0.301502i
$794$	14.7846	+	14.7846i	0.524686	+	0.524686i
$795$	8.83013	+	15.2942i	0.313172	+	0.542430i
$796$			36.0000i			1.27599i
$797$	29.3205			1.03859			0.519293	−	0.854596i	$-0.326195\pi$
$797$	29.3205			1.03859			0.519293	+	0.854596i	$0.326195\pi$
$798$	11.7846	+	7.98076i	0.417171	+	0.282516i
$799$		−	44.7846i		−	1.58437i
$800$	4.00000	+	4.00000i	0.141421	+	0.141421i
$801$		0			0
$802$	−1.53590	−	1.53590i	−0.0542345	−	0.0542345i
$803$	26.7846	+	15.4641i	0.945208	+	0.545716i
$804$	16.2679	+	28.1769i	0.573726	+	0.993723i
$805$	−3.96410	−	20.5981i	−0.139716	−	0.725987i
$806$	14.1962	−	3.80385i	0.500038	−	0.133985i
$807$	−12.9904	−	7.50000i	−0.457283	−	0.264013i
$808$	2.19615	+	0.588457i	0.0772604	+	0.0207019i
$809$	−8.16025	−	14.1340i	−0.286899	−	0.496924i	0.686169	−	0.727442i	$-0.259291\pi$
$809$	−8.16025	−	14.1340i	−0.286899	−	0.496924i	−0.973068	+	0.230518i	$0.925958\pi$
$810$	−3.29423	+	12.2942i	−0.115747	+	0.431975i
$811$		−	0.339746i		−	0.0119301i	−0.999982	−	0.00596505i	$-0.998101\pi$
$811$		−	0.339746i		−	0.0119301i	0.999982	−	0.00596505i	$-0.00189874\pi$
$812$	−12.2487	−	14.1436i	−0.429845	−	0.496343i
$813$			6.58846i			0.231067i
$814$	−14.9282	−	4.00000i	−0.523233	−	0.140200i
$815$	−5.00000	−	8.66025i	−0.175142	−	0.303355i
$816$	−32.7846			−1.14769
$817$	18.8827	+	10.9019i	0.660622	+	0.381410i
$818$	−1.22243	−	4.56218i	−0.0427413	−	0.159513i
$819$		0			0
$820$	5.19615	+	9.00000i	0.181458	+	0.314294i
$821$	1.73205	+	1.00000i	0.0604490	+	0.0349002i	0.529920	−	0.848048i	$-0.322222\pi$
$821$	1.73205	+	1.00000i	0.0604490	+	0.0349002i	−0.469471	+	0.882948i	$0.655555\pi$
$822$	−14.5359	+	14.5359i	−0.506998	+	0.506998i
$823$	−26.3827	+	15.2321i	−0.919643	+	0.530956i	−0.883521	−	0.468391i	$-0.844834\pi$
$823$	−26.3827	+	15.2321i	−0.919643	+	0.530956i	−0.0361216	+	0.999347i	$0.511500\pi$
$824$	10.7321	+	40.0526i	0.373869	+	1.39530i
$825$		−	9.46410i		−	0.329498i
$826$	−4.73205	−	0.339746i	−0.164649	−	0.0118213i
$827$	18.8564			0.655701			0.327851	−	0.944730i	$-0.393676\pi$
$827$	18.8564			0.655701			0.327851	+	0.944730i	$0.393676\pi$
$828$		0			0
$829$	28.3923	+	49.1769i	0.986106	+	1.70798i	0.636917	+	0.770932i	$0.280209\pi$
$829$	28.3923	+	49.1769i	0.986106	+	1.70798i	0.349188	+	0.937053i	$0.386457\pi$
$830$	−2.66025	+	2.66025i	−0.0923388	+	0.0923388i
$831$	−7.09808	+	12.2942i	−0.246230	+	0.426482i
$832$		−	10.1436i		−	0.351666i
$833$	−32.7846	−	4.73205i	−1.13592	−	0.163956i
$834$	−6.00000	+	1.60770i	−0.207763	+	0.0556699i
$835$	10.3301	−	17.8923i	0.357489	−	0.619189i
$836$	12.0000	−	20.7846i	0.415029	−	0.718851i
$837$	−36.8827	+	21.2942i	−1.27485	+	0.736036i
$838$	−31.8564	−	8.53590i	−1.10046	−	0.294868i
$839$	51.4641			1.77674			0.888369	−	0.459130i	$-0.151839\pi$
$839$	51.4641			1.77674			0.888369	+	0.459130i	$0.151839\pi$
$840$	11.6603	−	5.66025i	0.402317	−	0.195297i
$841$	16.4974			0.568877
$842$	37.2224	+	9.97372i	1.28277	+	0.343717i
$843$	8.78461	−	5.07180i	0.302558	−	0.174682i
$844$	−21.8038	−	12.5885i	−0.750519	−	0.433313i
$845$	−5.69615	+	9.86603i	−0.195954	+	0.339402i
$846$		0			0
$847$	32.6603	+	37.7128i	1.12222	+	1.29583i
$848$	35.3205	+	20.3923i	1.21291	+	0.700275i
$849$	−3.00000	+	5.19615i	−0.102960	+	0.178331i
$850$	4.73205	−	4.73205i	0.162308	−	0.162308i
$851$	−7.92820	−	13.7321i	−0.271775	−	0.470729i
$852$			30.2487i			1.03630i
$853$	−43.5167			−1.48998			−0.744991	−	0.667074i	$-0.767546\pi$
$853$	−43.5167			−1.48998			−0.744991	+	0.667074i	$0.767546\pi$
$854$	26.0263	−	12.6340i	0.890601	−	0.432326i
$855$		0			0
$856$	5.12436	+	19.1244i	0.175147	+	0.653657i
$857$	−39.5885	+	22.8564i	−1.35232	+	0.780760i	−0.988574	−	0.150740i	$-0.951835\pi$
$857$	−39.5885	+	22.8564i	−1.35232	+	0.780760i	−0.363742	+	0.931500i	$0.618501\pi$
$858$	−12.0000	+	12.0000i	−0.409673	+	0.409673i
$859$	7.98076	+	4.60770i	0.272300	+	0.157213i	0.629932	−	0.776650i	$-0.283083\pi$
$859$	7.98076	+	4.60770i	0.272300	+	0.157213i	−0.357632	+	0.933862i	$0.616416\pi$
$860$	17.1962	−	9.92820i	0.586384	−	0.338549i
$861$	23.3827	−	4.50000i	0.796880	−	0.153360i
$862$	−2.92820	−	10.9282i	−0.0997350	−	0.372216i
$863$	47.7224	+	27.5526i	1.62449	+	0.937900i	0.985698	+	0.168521i	$0.0538991\pi$
$863$	47.7224	+	27.5526i	1.62449	+	0.937900i	0.638792	+	0.769379i	$0.279434\pi$
$864$	7.60770	+	28.3923i	0.258819	+	0.965926i
$865$	−11.1962	−	19.3923i	−0.380681	−	0.659358i
$866$	31.3923	+	8.41154i	1.06675	+	0.285836i
$867$			9.33975i			0.317194i
$868$	40.9808	+	14.1962i	1.39098	+	0.481849i
$869$		−	6.92820i		−	0.235023i
$870$	2.24167	−	8.36603i	0.0759997	−	0.283635i
$871$	5.95448	+	10.3135i	0.201760	+	0.349458i
$872$	−2.48334	+	9.26795i	−0.0840965	+	0.313852i
$873$		0			0
$874$	23.7846	−	6.37307i	0.804526	−	0.215572i
$875$	−0.866025	+	2.50000i	−0.0292770	+	0.0845154i
$876$	−16.9808	+	9.80385i	−0.573727	+	0.331241i
$877$	−9.88269	−	5.70577i	−0.333715	−	0.192670i	0.323774	−	0.946134i	$-0.395048\pi$
$877$	−9.88269	−	5.70577i	−0.333715	−	0.192670i	−0.657489	+	0.753464i	$0.728381\pi$
$878$	13.8564	+	13.8564i	0.467631	+	0.467631i
$879$	−20.7846	+	12.0000i	−0.701047	+	0.404750i
$880$	−10.9282	−	18.9282i	−0.368390	−	0.638070i
$881$			9.33975i			0.314664i	0.987546	+	0.157332i	$0.0502893\pi$
$881$			9.33975i			0.314664i	−0.987546	+	0.157332i	$0.949711\pi$
$882$		0			0
$883$	3.46410			0.116576			0.0582882	−	0.998300i	$-0.481436\pi$
$883$	3.46410			0.116576			0.0582882	+	0.998300i	$0.481436\pi$
$884$	−12.0000			−0.403604
$885$	−1.09808	−	1.90192i	−0.0369114	−	0.0639325i
$886$	−7.00000	−	7.00000i	−0.235170	−	0.235170i
$887$	21.8660	−	37.8731i	0.734189	−	1.27165i	−0.220889	−	0.975299i	$-0.570896\pi$
$887$	21.8660	−	37.8731i	0.734189	−	1.27165i	0.955078	−	0.296354i	$-0.0957709\pi$
$888$	6.92820	−	6.92820i	0.232495	−	0.232495i
$889$	21.3397	+	7.39230i	0.715712	+	0.247930i
$890$	0.973721	+	3.63397i	0.0326392	+	0.121811i
$891$	24.5885	−	42.5885i	0.823744	−	1.42677i
$892$	−24.0000	−	13.8564i	−0.803579	−	0.463947i
$893$	−18.0000	+	10.3923i	−0.602347	+	0.347765i
$894$	2.83013	−	10.5622i	0.0946536	−	0.353252i
$895$	−7.80385			−0.260854
$896$	16.7846	−	24.7846i	0.560734	−	0.827996i
$897$	−17.4115			−0.581354
$898$	−9.68653	+	36.1506i	−0.323244	+	1.20636i
$899$	25.0981	−	14.4904i	0.837068	−	0.483281i
$900$		0			0
$901$	24.1244	−	41.7846i	0.803699	−	1.39205i
$902$	−10.3923	−	38.7846i	−0.346026	−	1.29139i
$903$	−8.59808	−	44.6769i	−0.286126	−	1.48675i
$904$	−13.4641	+	13.4641i	−0.447809	+	0.447809i
$905$	−0.866025	+	1.50000i	−0.0287877	+	0.0498617i
$906$	−28.0526	−	28.0526i	−0.931984	−	0.931984i
$907$	−14.0885	−	24.4019i	−0.467800	−	0.810253i	0.531523	−	0.847044i	$-0.321620\pi$
$907$	−14.0885	−	24.4019i	−0.467800	−	0.810253i	−0.999323	+	0.0367910i	$0.988286\pi$
$908$	−37.8564			−1.25631
$909$		0			0
$910$	4.26795	−	2.07180i	0.141481	−	0.0686794i
$911$			53.7128i			1.77958i	0.456365	+	0.889792i	$0.349151\pi$
$911$			53.7128i			1.77958i	−0.456365	+	0.889792i	$0.650849\pi$
$912$	7.60770	+	13.1769i	0.251916	+	0.436331i
$913$	12.5885	−	7.26795i	0.416617	−	0.240534i
$914$	28.6410	+	28.6410i	0.947361	+	0.947361i
$915$	11.5981	+	6.69615i	0.383421	+	0.221368i
$916$	14.7846	−	8.53590i	0.488497	−	0.282034i
$917$	24.0000	−	20.7846i	0.792550	−	0.686368i
$918$	33.5885	−	9.00000i	1.10858	−	0.297044i
$919$	−16.4378	−	9.49038i	−0.542234	−	0.313059i	0.203750	−	0.979023i	$-0.434687\pi$
$919$	−16.4378	−	9.49038i	−0.542234	−	0.313059i	−0.745984	+	0.665964i	$0.768020\pi$
$920$	5.80385	−	21.6603i	0.191347	−	0.714117i
$921$	−15.6962	−	27.1865i	−0.517206	−	0.895827i
$922$	13.8564	−	51.7128i	0.456336	−	1.70307i
$923$			11.0718i			0.364433i
$924$	−49.1769	+	9.46410i	−1.61780	+	0.311346i
$925$			2.00000i			0.0657596i
$926$	−1.90192	−	0.509619i	−0.0625011	−	0.0167471i
$927$		0			0
$928$	−5.17691	−	19.3205i	−0.169941	−	0.634227i
$929$	−6.10770	−	3.52628i	−0.200387	−	0.115693i	0.396449	−	0.918057i	$-0.370242\pi$
$929$	−6.10770	−	3.52628i	−0.200387	−	0.115693i	−0.596836	+	0.802363i	$0.703576\pi$
$930$	5.19615	+	19.3923i	0.170389	+	0.635899i
$931$	5.70577	+	14.2750i	0.186999	+	0.467844i
$932$	−15.1244	+	8.73205i	−0.495415	+	0.286028i
$933$	21.2942	+	12.2942i	0.697142	+	0.402495i
$934$	31.7321	−	31.7321i	1.03830	−	1.03830i
$935$	−22.3923	+	12.9282i	−0.732307	+	0.422797i
$936$		0			0
$937$			13.8564i			0.452669i	0.974050	+	0.226335i	$0.0726743\pi$
$937$			13.8564i			0.452669i	−0.974050	+	0.226335i	$0.927326\pi$
$938$	−2.51666	+	35.0526i	−0.0821719	+	1.14451i
$939$	30.0000			0.979013
$940$			18.9282i			0.617370i
$941$	5.53590	+	9.58846i	0.180465	+	0.312575i	0.942039	−	0.335503i	$-0.108906\pi$
$941$	5.53590	+	9.58846i	0.180465	+	0.312575i	−0.761574	+	0.648078i	$0.775573\pi$
$942$	16.3923	−	16.3923i	0.534090	−	0.534090i
$943$	20.5981	−	35.6769i	0.670766	−	1.16180i
$944$	−4.39230	−	2.53590i	−0.142957	−	0.0825365i
$945$	−10.3923	+	9.00000i	−0.338062	+	0.292770i
$946$	−74.1051	+	19.8564i	−2.40937	+	0.645587i
$947$	−24.0885	+	41.7224i	−0.782770	+	1.35580i	0.147553	+	0.989054i	$0.452860\pi$
$947$	−24.0885	+	41.7224i	−0.782770	+	1.35580i	−0.930322	+	0.366743i	$0.880473\pi$
$948$	3.80385	+	2.19615i	0.123543	+	0.0713277i
$949$	−6.21539	+	3.58846i	−0.201760	+	0.116486i
$950$	−3.00000	−	0.803848i	−0.0973329	−	0.0260803i
$951$	−22.0526			−0.715103
$952$	−29.3205	−	19.8564i	−0.950283	−	0.643550i
$953$	−46.1051			−1.49349			−0.746746	−	0.665110i	$-0.768385\pi$
$953$	−46.1051			−1.49349			−0.746746	+	0.665110i	$0.768385\pi$
$954$		0			0
$955$	−3.12436	+	1.80385i	−0.101102	+	0.0583711i
$956$	12.1962	−	21.1244i	0.394452	−	0.683210i
$957$	−16.7321	+	28.9808i	−0.540870	+	0.936815i
$958$	−15.9282	+	4.26795i	−0.514617	+	0.137891i
$959$	−21.8038	+	4.19615i	−0.704083	+	0.135501i
$960$	13.8564			0.447214
$961$	−18.0885	+	31.3301i	−0.583499	+	1.01065i
$962$	2.53590	−	2.53590i	0.0817606	−	0.0817606i
$963$		0			0
$964$	39.7128			1.27906
$965$	13.8564			0.446054
$966$	−42.5429	−	28.8109i	−1.36880	−	0.926975i
$967$			28.1769i			0.906108i	0.891483	+	0.453054i	$0.149666\pi$
$967$			28.1769i			0.906108i	−0.891483	+	0.453054i	$0.850334\pi$
$968$	13.8038	+	51.5167i	0.443672	+	1.65581i
$969$	15.5885	−	9.00000i	0.500773	−	0.289122i
$970$	−3.46410	+	3.46410i	−0.111226	+	0.111226i
$971$	−22.1769	−	12.8038i	−0.711691	−	0.410895i	0.0999958	−	0.994988i	$-0.468117\pi$
$971$	−22.1769	−	12.8038i	−0.711691	−	0.410895i	−0.811687	+	0.584093i	$0.801450\pi$
$972$		0			0
$973$	−6.33975	−	2.19615i	−0.203243	−	0.0704054i
$974$	−6.14359	−	22.9282i	−0.196853	−	0.734667i
$975$	1.90192	+	1.09808i	0.0609103	+	0.0351666i
$976$	30.9282			0.989988
$977$	7.07180	+	12.2487i	0.226247	+	0.391871i	0.956693	−	0.291100i	$-0.0940211\pi$
$977$	7.07180	+	12.2487i	0.226247	+	0.391871i	−0.730446	+	0.682970i	$0.760688\pi$
$978$	−23.6603	−	6.33975i	−0.756571	−	0.202723i
$979$		−	14.5359i		−	0.464569i
$980$	13.8564	+	2.00000i	0.442627	+	0.0638877i
$981$		0			0
$982$	8.51666	−	31.7846i	0.271778	−	1.01429i
$983$	−13.6699	−	23.6769i	−0.436001	−	0.755176i	0.561376	−	0.827561i	$-0.310272\pi$
$983$	−13.6699	−	23.6769i	−0.436001	−	0.755176i	−0.997377	+	0.0723849i	$0.976939\pi$
$984$	24.5885	+	6.58846i	0.783851	+	0.210032i
$985$	7.73205	+	4.46410i	0.246364	+	0.142238i
$986$	−22.8564	+	6.12436i	−0.727896	+	0.195039i
$987$	40.9808	+	14.1962i	1.30443	+	0.451869i
$988$	2.78461	+	4.82309i	0.0885902	+	0.153443i
$989$	−68.1673	−	39.3564i	−2.16759	−	1.25146i
$990$		0			0
$991$	−51.4186	+	29.6865i	−1.63337	+	0.943024i	−0.650320	+	0.759660i	$0.725365\pi$
$991$	−51.4186	+	29.6865i	−1.63337	+	0.943024i	−0.983045	+	0.183363i	$0.941302\pi$
$992$	32.7846	+	32.7846i	1.04091	+	1.04091i
$993$			33.3731i			1.05906i
$994$	−18.3205	+	27.0526i	−0.581091	+	0.858055i
$995$	−18.0000			−0.570638
$996$			9.21539i			0.292001i
$997$	−10.4378	−	18.0788i	−0.330569	−	0.572563i	0.652054	−	0.758172i	$-0.273907\pi$
$997$	−10.4378	−	18.0788i	−0.330569	−	0.572563i	−0.982624	+	0.185610i	$0.940574\pi$
$998$	−1.60770	−	1.60770i	−0.0508907	−	0.0508907i
$999$	−5.19615	+	9.00000i	−0.164399	+	0.284747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bj.d.131.1	yes	4
4.3	odd	2		1120.2.bz.d.271.1		4
7.3	odd	6		280.2.bj.a.171.1	yes	4
8.3	odd	2		280.2.bj.a.131.2	✓	4
8.5	even	2		1120.2.bz.a.271.2		4
28.3	even	6		1120.2.bz.a.591.2		4
56.3	even	6	inner	280.2.bj.d.171.1	yes	4
56.45	odd	6		1120.2.bz.d.591.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.a.131.2	✓	4	8.3	odd	2
280.2.bj.a.171.1	yes	4	7.3	odd	6
280.2.bj.d.131.1	yes	4	1.1	even	1	trivial
280.2.bj.d.171.1	yes	4	56.3	even	6	inner
1120.2.bz.a.271.2		4	8.5	even	2
1120.2.bz.a.591.2		4	28.3	even	6
1120.2.bz.d.271.1		4	4.3	odd	2
1120.2.bz.d.591.1		4	56.45	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 1.36603i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.633975 - 2.36603i) q^{6} +(0.866025 - 2.50000i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(-0.366025 + 1.36603i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.633975 - 2.36603i) q^{6} +(0.866025 - 2.50000i) q^{7} +(2.00000 - 2.00000i) q^{8} +(1.00000 + 1.00000i) q^{10} +(-2.73205 - 4.73205i) q^{11} +3.46410 q^{12} +1.26795 q^{13} +(3.09808 + 2.09808i) q^{14} +1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} +(4.09808 - 2.36603i) q^{17} +(-1.90192 - 1.09808i) q^{19} +(-1.73205 + 1.00000i) q^{20} +(0.866025 + 4.50000i) q^{21} +(7.46410 - 2.00000i) q^{22} +(6.86603 + 3.96410i) q^{23} +(-1.26795 + 4.73205i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.464102 + 1.73205i) q^{26} -5.19615i q^{27} +(-4.00000 + 3.46410i) q^{28} +3.53590i q^{29} +(-2.36603 - 0.633975i) q^{30} +(-4.09808 - 7.09808i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(8.19615 + 4.73205i) q^{33} +(1.73205 + 6.46410i) q^{34} +(-1.73205 - 2.00000i) q^{35} +(-1.73205 - 1.00000i) q^{37} +(2.19615 - 2.19615i) q^{38} +(-1.90192 + 1.09808i) q^{39} +(-0.732051 - 2.73205i) q^{40} -5.19615i q^{41} +(-6.46410 - 0.464102i) q^{42} -9.92820 q^{43} +10.9282i q^{44} +(-7.92820 + 7.92820i) q^{46} +(4.73205 - 8.19615i) q^{47} +(-6.00000 - 3.46410i) q^{48} +(-5.50000 - 4.33013i) q^{49} +(1.36603 - 0.366025i) q^{50} +(-4.09808 + 7.09808i) q^{51} +(-2.19615 - 1.26795i) q^{52} +(8.83013 - 5.09808i) q^{53} +(7.09808 + 1.90192i) q^{54} -5.46410 q^{55} +(-3.26795 - 6.73205i) q^{56} +3.80385 q^{57} +(-4.83013 - 1.29423i) q^{58} +(-1.09808 + 0.633975i) q^{59} +(1.73205 - 3.00000i) q^{60} +(3.86603 - 6.69615i) q^{61} +(11.1962 - 3.00000i) q^{62} -8.00000i q^{64} +(0.633975 - 1.09808i) q^{65} +(-9.46410 + 9.46410i) q^{66} +(4.69615 + 8.13397i) q^{67} -9.46410 q^{68} -13.7321 q^{69} +(3.36603 - 1.63397i) q^{70} +8.73205i q^{71} +(-4.90192 + 2.83013i) q^{73} +(2.00000 - 2.00000i) q^{74} +(1.50000 + 0.866025i) q^{75} +(2.19615 + 3.80385i) q^{76} +(-14.1962 + 2.73205i) q^{77} +(-0.803848 - 3.00000i) q^{78} +(1.09808 + 0.633975i) q^{79} +4.00000 q^{80} +(4.50000 + 7.79423i) q^{81} +(7.09808 + 1.90192i) q^{82} +2.66025i q^{83} +(3.00000 - 8.66025i) q^{84} -4.73205i q^{85} +(3.63397 - 13.5622i) q^{86} +(-3.06218 - 5.30385i) q^{87} +(-14.9282 - 4.00000i) q^{88} +(2.30385 + 1.33013i) q^{89} +(1.09808 - 3.16987i) q^{91} +(-7.92820 - 13.7321i) q^{92} +(12.2942 + 7.09808i) q^{93} +(9.46410 + 9.46410i) q^{94} +(-1.90192 + 1.09808i) q^{95} +(6.92820 - 6.92820i) q^{96} +3.46410i q^{97} +(7.92820 - 5.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 6 q^{3} + 2 q^{5} - 6 q^{6} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 6 * q^3 + 2 * q^5 - 6 * q^6 + 8 * q^8	\( 4 q + 2 q^{2} - 6 q^{3} + 2 q^{5} - 6 q^{6} + 8 q^{8} + 4 q^{10} - 4 q^{11} + 12 q^{13} + 2 q^{14} + 8 q^{16} + 6 q^{17} - 18 q^{19} + 16 q^{22} + 24 q^{23} - 12 q^{24} - 2 q^{25} + 12 q^{26} - 16 q^{28} - 6 q^{30} - 6 q^{31} - 8 q^{32} + 12 q^{33} - 12 q^{38} - 18 q^{39} + 4 q^{40} - 12 q^{42} - 12 q^{43} - 4 q^{46} + 12 q^{47} - 24 q^{48} - 22 q^{49} + 2 q^{50} - 6 q^{51} + 12 q^{52} + 18 q^{53} + 18 q^{54} - 8 q^{55} - 20 q^{56} + 36 q^{57} - 2 q^{58} + 6 q^{59} + 12 q^{61} + 24 q^{62} + 6 q^{65} - 24 q^{66} - 2 q^{67} - 24 q^{68} - 48 q^{69} + 10 q^{70} - 30 q^{73} + 8 q^{74} + 6 q^{75} - 12 q^{76} - 36 q^{77} - 24 q^{78} - 6 q^{79} + 16 q^{80} + 18 q^{81} + 18 q^{82} + 12 q^{84} + 18 q^{86} + 12 q^{87} - 32 q^{88} + 30 q^{89} - 6 q^{91} - 4 q^{92} + 18 q^{93} + 24 q^{94} - 18 q^{95} + 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 6 * q^3 + 2 * q^5 - 6 * q^6 + 8 * q^8 + 4 * q^10 - 4 * q^11 + 12 * q^13 + 2 * q^14 + 8 * q^16 + 6 * q^17 - 18 * q^19 + 16 * q^22 + 24 * q^23 - 12 * q^24 - 2 * q^25 + 12 * q^26 - 16 * q^28 - 6 * q^30 - 6 * q^31 - 8 * q^32 + 12 * q^33 - 12 * q^38 - 18 * q^39 + 4 * q^40 - 12 * q^42 - 12 * q^43 - 4 * q^46 + 12 * q^47 - 24 * q^48 - 22 * q^49 + 2 * q^50 - 6 * q^51 + 12 * q^52 + 18 * q^53 + 18 * q^54 - 8 * q^55 - 20 * q^56 + 36 * q^57 - 2 * q^58 + 6 * q^59 + 12 * q^61 + 24 * q^62 + 6 * q^65 - 24 * q^66 - 2 * q^67 - 24 * q^68 - 48 * q^69 + 10 * q^70 - 30 * q^73 + 8 * q^74 + 6 * q^75 - 12 * q^76 - 36 * q^77 - 24 * q^78 - 6 * q^79 + 16 * q^80 + 18 * q^81 + 18 * q^82 + 12 * q^84 + 18 * q^86 + 12 * q^87 - 32 * q^88 + 30 * q^89 - 6 * q^91 - 4 * q^92 + 18 * q^93 + 24 * q^94 - 18 * q^95 + 4 * q^98

Introduction

L-functions

Modular forms

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