LMFDB - Embedded newform 888.2.bu.a.643.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [888,2,Mod(547,888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(888, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 0, 7]))

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

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

chi := DirichletCharacter("888.547");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.bu (of order $12$, degree $4$, 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:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$4$
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:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			643.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	888.643
Dual form			888.2.bu.a.859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(0.866025 - 0.500000i) q^{3} -2.00000i q^{4} +(0.500000 - 1.86603i) q^{5} +(-0.366025 + 1.36603i) q^{6} +(0.633975 - 0.366025i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(0.866025 - 0.500000i) q^{3} -2.00000i q^{4} +(0.500000 - 1.86603i) q^{5} +(-0.366025 + 1.36603i) q^{6} +(0.633975 - 0.366025i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.500000 - 0.866025i) q^{9} +(1.36603 + 2.36603i) q^{10} -4.73205i q^{11} +(-1.00000 - 1.73205i) q^{12} +(0.0980762 - 0.366025i) q^{13} +(-0.267949 + 1.00000i) q^{14} +(-0.500000 - 1.86603i) q^{15} -4.00000 q^{16} +(-0.964102 - 3.59808i) q^{17} +(0.366025 + 1.36603i) q^{18} +(-4.09808 - 1.09808i) q^{19} +(-3.73205 - 1.00000i) q^{20} +(0.366025 - 0.633975i) q^{21} +(4.73205 + 4.73205i) q^{22} +(2.73205 + 2.73205i) q^{23} +(2.73205 + 0.732051i) q^{24} +(1.09808 + 0.633975i) q^{25} +(0.267949 + 0.464102i) q^{26} -1.00000i q^{27} +(-0.732051 - 1.26795i) q^{28} +(-3.83013 + 3.83013i) q^{29} +(2.36603 + 1.36603i) q^{30} +(-7.19615 + 7.19615i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-2.36603 - 4.09808i) q^{33} +(4.56218 + 2.63397i) q^{34} +(-0.366025 - 1.36603i) q^{35} +(-1.73205 - 1.00000i) q^{36} +(-5.50000 - 2.59808i) q^{37} +(5.19615 - 3.00000i) q^{38} +(-0.0980762 - 0.366025i) q^{39} +(4.73205 - 2.73205i) q^{40} +(8.13397 - 4.69615i) q^{41} +(0.267949 + 1.00000i) q^{42} +(1.00000 - 1.00000i) q^{43} -9.46410 q^{44} +(-1.36603 - 1.36603i) q^{45} -5.46410 q^{46} -8.19615i q^{47} +(-3.46410 + 2.00000i) q^{48} +(-3.23205 + 5.59808i) q^{49} +(-1.73205 + 0.464102i) q^{50} +(-2.63397 - 2.63397i) q^{51} +(-0.732051 - 0.196152i) q^{52} +(-0.803848 - 0.464102i) q^{53} +(1.00000 + 1.00000i) q^{54} +(-8.83013 - 2.36603i) q^{55} +(2.00000 + 0.535898i) q^{56} +(-4.09808 + 1.09808i) q^{57} -7.66025i q^{58} +(-3.66025 - 13.6603i) q^{59} +(-3.73205 + 1.00000i) q^{60} +(3.86603 + 1.03590i) q^{61} -14.3923i q^{62} -0.732051i q^{63} +8.00000i q^{64} +(-0.633975 - 0.366025i) q^{65} +(6.46410 + 1.73205i) q^{66} +(9.63397 - 5.56218i) q^{67} +(-7.19615 + 1.92820i) q^{68} +(3.73205 + 1.00000i) q^{69} +(1.73205 + 1.00000i) q^{70} +(4.90192 - 2.83013i) q^{71} +(2.73205 - 0.732051i) q^{72} +(8.09808 - 2.90192i) q^{74} +1.26795 q^{75} +(-2.19615 + 8.19615i) q^{76} +(-1.73205 - 3.00000i) q^{77} +(0.464102 + 0.267949i) q^{78} +(-1.63397 + 6.09808i) q^{79} +(-2.00000 + 7.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.43782 + 12.8301i) q^{82} +(-5.46410 + 9.46410i) q^{83} +(-1.26795 - 0.732051i) q^{84} -7.19615 q^{85} +2.00000i q^{86} +(-1.40192 + 5.23205i) q^{87} +(9.46410 - 9.46410i) q^{88} +(9.69615 - 2.59808i) q^{89} +2.73205 q^{90} +(-0.0717968 - 0.267949i) q^{91} +(5.46410 - 5.46410i) q^{92} +(-2.63397 + 9.83013i) q^{93} +(8.19615 + 8.19615i) q^{94} +(-4.09808 + 7.09808i) q^{95} +(1.46410 - 5.46410i) q^{96} +(9.75833 - 9.75833i) q^{97} +(-2.36603 - 8.83013i) q^{98} +(-4.09808 - 2.36603i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 2 q^{5} + 2 q^{6} + 6 q^{7} + 8 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 2 * q^5 + 2 * q^6 + 6 * q^7 + 8 * q^8 + 2 * q^9	$ 4 q - 4 q^{2} + 2 q^{5} + 2 q^{6} + 6 q^{7} + 8 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{12} - 10 q^{13} - 8 q^{14} - 2 q^{15} - 16 q^{16} + 10 q^{17} - 2 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} + 12 q^{22} + 4 q^{23} + 4 q^{24} - 6 q^{25} + 8 q^{26} + 4 q^{28} + 2 q^{29} + 6 q^{30} - 8 q^{31} + 16 q^{32} - 6 q^{33} - 6 q^{34} + 2 q^{35} - 22 q^{37} + 10 q^{39} + 12 q^{40} + 36 q^{41} + 8 q^{42} + 4 q^{43} - 24 q^{44} - 2 q^{45} - 8 q^{46} - 6 q^{49} - 14 q^{51} + 4 q^{52} - 24 q^{53} + 4 q^{54} - 18 q^{55} + 8 q^{56} - 6 q^{57} + 20 q^{59} - 8 q^{60} + 12 q^{61} - 6 q^{65} + 12 q^{66} + 42 q^{67} - 8 q^{68} + 8 q^{69} + 30 q^{71} + 4 q^{72} + 22 q^{74} + 12 q^{75} + 12 q^{76} - 12 q^{78} - 10 q^{79} - 8 q^{80} - 2 q^{81} - 38 q^{82} - 8 q^{83} - 12 q^{84} - 8 q^{85} - 16 q^{87} + 24 q^{88} + 18 q^{89} + 4 q^{90} - 28 q^{91} + 8 q^{92} - 14 q^{93} + 12 q^{94} - 6 q^{95} - 8 q^{96} - 6 q^{97} - 6 q^{98} - 6 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 2 * q^5 + 2 * q^6 + 6 * q^7 + 8 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^12 - 10 * q^13 - 8 * q^14 - 2 * q^15 - 16 * q^16 + 10 * q^17 - 2 * q^18 - 6 * q^19 - 8 * q^20 - 2 * q^21 + 12 * q^22 + 4 * q^23 + 4 * q^24 - 6 * q^25 + 8 * q^26 + 4 * q^28 + 2 * q^29 + 6 * q^30 - 8 * q^31 + 16 * q^32 - 6 * q^33 - 6 * q^34 + 2 * q^35 - 22 * q^37 + 10 * q^39 + 12 * q^40 + 36 * q^41 + 8 * q^42 + 4 * q^43 - 24 * q^44 - 2 * q^45 - 8 * q^46 - 6 * q^49 - 14 * q^51 + 4 * q^52 - 24 * q^53 + 4 * q^54 - 18 * q^55 + 8 * q^56 - 6 * q^57 + 20 * q^59 - 8 * q^60 + 12 * q^61 - 6 * q^65 + 12 * q^66 + 42 * q^67 - 8 * q^68 + 8 * q^69 + 30 * q^71 + 4 * q^72 + 22 * q^74 + 12 * q^75 + 12 * q^76 - 12 * q^78 - 10 * q^79 - 8 * q^80 - 2 * q^81 - 38 * q^82 - 8 * q^83 - 12 * q^84 - 8 * q^85 - 16 * q^87 + 24 * q^88 + 18 * q^89 + 4 * q^90 - 28 * q^91 + 8 * q^92 - 14 * q^93 + 12 * q^94 - 6 * q^95 - 8 * q^96 - 6 * q^97 - 6 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$	$-1$	$1$

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
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		−	2.00000i		−	1.00000i
$5$	0.500000	−	1.86603i	0.223607	−	0.834512i	−0.759351	−	0.650681i	$-0.774483\pi$
$5$	0.500000	−	1.86603i	0.223607	−	0.834512i	0.982958	−	0.183831i	$-0.0588499\pi$
$6$	−0.366025	+	1.36603i	−0.149429	+	0.557678i
$7$	0.633975	−	0.366025i	0.239620	−	0.138345i	−0.375382	−	0.926870i	$-0.622489\pi$
$7$	0.633975	−	0.366025i	0.239620	−	0.138345i	0.615002	+	0.788526i	$0.289155\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.36603	+	2.36603i	0.431975	+	0.748203i
$11$		−	4.73205i		−	1.42677i	−0.700774	−	0.713384i	$-0.747162\pi$
$11$		−	4.73205i		−	1.42677i	0.700774	−	0.713384i	$-0.252838\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	0.0980762	−	0.366025i	0.0272014	−	0.101517i	−0.950991	−	0.309220i	$-0.899932\pi$
$13$	0.0980762	−	0.366025i	0.0272014	−	0.101517i	0.978192	+	0.207703i	$0.0665987\pi$
$14$	−0.267949	+	1.00000i	−0.0716124	+	0.267261i
$15$	−0.500000	−	1.86603i	−0.129099	−	0.481806i
$16$	−4.00000			−1.00000
$17$	−0.964102	−	3.59808i	−0.233829	−	0.872662i	−0.978673	−	0.205423i	$-0.934143\pi$
$17$	−0.964102	−	3.59808i	−0.233829	−	0.872662i	0.744844	−	0.667238i	$-0.232524\pi$
$18$	0.366025	+	1.36603i	0.0862730	+	0.321975i
$19$	−4.09808	−	1.09808i	−0.940163	−	0.251916i	−0.243980	−	0.969780i	$-0.578453\pi$
$19$	−4.09808	−	1.09808i	−0.940163	−	0.251916i	−0.696183	+	0.717864i	$0.745120\pi$
$20$	−3.73205	−	1.00000i	−0.834512	−	0.223607i
$21$	0.366025	−	0.633975i	0.0798733	−	0.138345i
$22$	4.73205	+	4.73205i	1.00888	+	1.00888i
$23$	2.73205	+	2.73205i	0.569672	+	0.569672i	0.932036	−	0.362364i	$-0.118030\pi$
$23$	2.73205	+	2.73205i	0.569672	+	0.569672i	−0.362364	+	0.932036i	$0.618030\pi$
$24$	2.73205	+	0.732051i	0.557678	+	0.149429i
$25$	1.09808	+	0.633975i	0.219615	+	0.126795i
$26$	0.267949	+	0.464102i	0.0525492	+	0.0910178i
$27$		−	1.00000i		−	0.192450i
$28$	−0.732051	−	1.26795i	−0.138345	−	0.239620i
$29$	−3.83013	+	3.83013i	−0.711237	+	0.711237i	−0.966794	−	0.255557i	$-0.917741\pi$
$29$	−3.83013	+	3.83013i	−0.711237	+	0.711237i	0.255557	+	0.966794i	$0.417741\pi$
$30$	2.36603	+	1.36603i	0.431975	+	0.249401i
$31$	−7.19615	+	7.19615i	−1.29247	+	1.29247i	−0.359211	+	0.933257i	$0.616954\pi$
$31$	−7.19615	+	7.19615i	−1.29247	+	1.29247i	−0.933257	+	0.359211i	$0.883046\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	−2.36603	−	4.09808i	−0.411872	−	0.713384i
$34$	4.56218	+	2.63397i	0.782407	+	0.451723i
$35$	−0.366025	−	1.36603i	−0.0618696	−	0.230900i
$36$	−1.73205	−	1.00000i	−0.288675	−	0.166667i
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$38$	5.19615	−	3.00000i	0.842927	−	0.486664i
$39$	−0.0980762	−	0.366025i	−0.0157048	−	0.0586110i
$40$	4.73205	−	2.73205i	0.748203	−	0.431975i
$41$	8.13397	−	4.69615i	1.27031	−	0.733416i	0.295267	−	0.955415i	$-0.404592\pi$
$41$	8.13397	−	4.69615i	1.27031	−	0.733416i	0.975047	+	0.221999i	$0.0712582\pi$
$42$	0.267949	+	1.00000i	0.0413455	+	0.154303i
$43$	1.00000	−	1.00000i	0.152499	−	0.152499i	−0.626734	−	0.779233i	$-0.715609\pi$
$43$	1.00000	−	1.00000i	0.152499	−	0.152499i	0.779233	+	0.626734i	$0.215609\pi$
$44$	−9.46410			−1.42677
$45$	−1.36603	−	1.36603i	−0.203635	−	0.203635i
$46$	−5.46410			−0.805638
$47$		−	8.19615i		−	1.19553i	−0.801671	−	0.597766i	$-0.796055\pi$
$47$		−	8.19615i		−	1.19553i	0.801671	−	0.597766i	$-0.203945\pi$
$48$	−3.46410	+	2.00000i	−0.500000	+	0.288675i
$49$	−3.23205	+	5.59808i	−0.461722	+	0.799725i
$50$	−1.73205	+	0.464102i	−0.244949	+	0.0656339i
$51$	−2.63397	−	2.63397i	−0.368830	−	0.368830i
$52$	−0.732051	−	0.196152i	−0.101517	−	0.0272014i
$53$	−0.803848	−	0.464102i	−0.110417	−	0.0637493i	0.443774	−	0.896138i	$-0.353639\pi$
$53$	−0.803848	−	0.464102i	−0.110417	−	0.0637493i	−0.554191	+	0.832389i	$0.686972\pi$
$54$	1.00000	+	1.00000i	0.136083	+	0.136083i
$55$	−8.83013	−	2.36603i	−1.19065	−	0.319035i
$56$	2.00000	+	0.535898i	0.267261	+	0.0716124i
$57$	−4.09808	+	1.09808i	−0.542803	+	0.145444i
$58$		−	7.66025i		−	1.00584i
$59$	−3.66025	−	13.6603i	−0.476524	−	1.77841i	−0.615521	−	0.788121i	$-0.711054\pi$
$59$	−3.66025	−	13.6603i	−0.476524	−	1.77841i	0.138996	−	0.990293i	$-0.455612\pi$
$60$	−3.73205	+	1.00000i	−0.481806	+	0.129099i
$61$	3.86603	+	1.03590i	0.494994	+	0.132633i	0.497676	−	0.867363i	$-0.334187\pi$
$61$	3.86603	+	1.03590i	0.494994	+	0.132633i	−0.00268183	+	0.999996i	$0.500854\pi$
$62$		−	14.3923i		−	1.82782i
$63$		−	0.732051i		−	0.0922297i
$64$			8.00000i			1.00000i
$65$	−0.633975	−	0.366025i	−0.0786349	−	0.0453999i
$66$	6.46410	+	1.73205i	0.795676	+	0.213201i
$67$	9.63397	−	5.56218i	1.17698	−	0.679528i	0.221664	−	0.975123i	$-0.428851\pi$
$67$	9.63397	−	5.56218i	1.17698	−	0.679528i	0.955313	+	0.295595i	$0.0955179\pi$
$68$	−7.19615	+	1.92820i	−0.872662	+	0.233829i
$69$	3.73205	+	1.00000i	0.449286	+	0.120386i
$70$	1.73205	+	1.00000i	0.207020	+	0.119523i
$71$	4.90192	−	2.83013i	0.581751	−	0.335874i	−0.180078	−	0.983652i	$-0.557635\pi$
$71$	4.90192	−	2.83013i	0.581751	−	0.335874i	0.761829	+	0.647778i	$0.224302\pi$
$72$	2.73205	−	0.732051i	0.321975	−	0.0862730i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	8.09808	−	2.90192i	0.941382	−	0.337342i
$75$	1.26795			0.146410
$76$	−2.19615	+	8.19615i	−0.251916	+	0.940163i
$77$	−1.73205	−	3.00000i	−0.197386	−	0.341882i
$78$	0.464102	+	0.267949i	0.0525492	+	0.0303393i
$79$	−1.63397	+	6.09808i	−0.183837	+	0.686087i	0.811040	+	0.584991i	$0.198902\pi$
$79$	−1.63397	+	6.09808i	−0.183837	+	0.686087i	−0.994877	+	0.101097i	$0.967765\pi$
$80$	−2.00000	+	7.46410i	−0.223607	+	0.834512i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.43782	+	12.8301i	−0.379644	+	1.41685i
$83$	−5.46410	+	9.46410i	−0.599763	+	1.03882i	0.393093	+	0.919499i	$0.371405\pi$
$83$	−5.46410	+	9.46410i	−0.599763	+	1.03882i	−0.992856	+	0.119321i	$0.961928\pi$
$84$	−1.26795	−	0.732051i	−0.138345	−	0.0798733i
$85$	−7.19615			−0.780532
$86$			2.00000i			0.215666i
$87$	−1.40192	+	5.23205i	−0.150302	+	0.560935i
$88$	9.46410	−	9.46410i	1.00888	−	1.00888i
$89$	9.69615	−	2.59808i	1.02779	−	0.275396i	0.294745	−	0.955576i	$-0.404765\pi$
$89$	9.69615	−	2.59808i	1.02779	−	0.275396i	0.733045	+	0.680180i	$0.238099\pi$
$90$	2.73205			0.287983
$91$	−0.0717968	−	0.267949i	−0.00752635	−	0.0280887i
$92$	5.46410	−	5.46410i	0.569672	−	0.569672i
$93$	−2.63397	+	9.83013i	−0.273130	+	1.01934i
$94$	8.19615	+	8.19615i	0.845369	+	0.845369i
$95$	−4.09808	+	7.09808i	−0.420454	+	0.728247i
$96$	1.46410	−	5.46410i	0.149429	−	0.557678i
$97$	9.75833	−	9.75833i	0.990808	−	0.990808i	−0.00914982	−	0.999958i	$-0.502913\pi$
$97$	9.75833	−	9.75833i	0.990808	−	0.990808i	0.999958	+	0.00914982i	$0.00291252\pi$
$98$	−2.36603	−	8.83013i	−0.239005	−	0.891978i
$99$	−4.09808	−	2.36603i	−0.411872	−	0.237795i
$100$	1.26795	−	2.19615i	0.126795	−	0.219615i
$101$	12.8564			1.27926			0.639630	−	0.768683i	$-0.279088\pi$
$101$	12.8564			1.27926			0.639630	+	0.768683i	$0.279088\pi$
$102$	5.26795			0.521605
$103$	−2.46410	+	2.46410i	−0.242795	+	0.242795i	−0.818006	−	0.575210i	$-0.804920\pi$
$103$	−2.46410	+	2.46410i	−0.242795	+	0.242795i	0.575210	+	0.818006i	$0.304920\pi$
$104$	0.928203	−	0.535898i	0.0910178	−	0.0525492i
$105$	−1.00000	−	1.00000i	−0.0975900	−	0.0975900i
$106$	1.26795	−	0.339746i	0.123154	−	0.0329990i
$107$	−2.83013	−	4.90192i	−0.273599	−	0.473887i	0.696182	−	0.717865i	$-0.254881\pi$
$107$	−2.83013	−	4.90192i	−0.273599	−	0.473887i	−0.969781	+	0.243979i	$0.921547\pi$
$108$	−2.00000			−0.192450
$109$	19.1603	−	5.13397i	1.83522	−	0.491746i	0.836777	−	0.547543i	$-0.184437\pi$
$109$	19.1603	−	5.13397i	1.83522	−	0.491746i	0.998442	+	0.0557976i	$0.0177702\pi$
$110$	11.1962	−	6.46410i	1.06751	−	0.616328i
$111$	−6.06218	+	0.500000i	−0.575396	+	0.0474579i
$112$	−2.53590	+	1.46410i	−0.239620	+	0.138345i
$113$	−12.5622	+	3.36603i	−1.18175	+	0.316649i	−0.795620	−	0.605795i	$-0.792855\pi$
$113$	−12.5622	+	3.36603i	−1.18175	+	0.316649i	−0.386130	+	0.922444i	$0.626188\pi$
$114$	3.00000	−	5.19615i	0.280976	−	0.486664i
$115$	6.46410	−	3.73205i	0.602781	−	0.348016i
$116$	7.66025	+	7.66025i	0.711237	+	0.711237i
$117$	−0.267949	−	0.267949i	−0.0247719	−	0.0247719i
$118$	17.3205	+	10.0000i	1.59448	+	0.920575i
$119$	−1.92820	−	1.92820i	−0.176758	−	0.176758i
$120$	2.73205	−	4.73205i	0.249401	−	0.431975i
$121$	−11.3923			−1.03566
$122$	−4.90192	+	2.83013i	−0.443799	+	0.256228i
$123$	4.69615	−	8.13397i	0.423438	−	0.733416i
$124$	14.3923	+	14.3923i	1.29247	+	1.29247i
$125$	8.56218	−	8.56218i	0.765824	−	0.765824i
$126$	0.732051	+	0.732051i	0.0652163	+	0.0652163i
$127$	−5.66025	−	3.26795i	−0.502266	−	0.289984i	0.227383	−	0.973805i	$-0.426983\pi$
$127$	−5.66025	−	3.26795i	−0.502266	−	0.289984i	−0.729649	+	0.683822i	$0.760317\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$	0.366025	−	1.36603i	0.0322267	−	0.120272i
$130$	1.00000	−	0.267949i	0.0877058	−	0.0235007i
$131$	1.26795	−	0.339746i	0.110781	−	0.0296837i	−0.203003	−	0.979178i	$-0.565070\pi$
$131$	1.26795	−	0.339746i	0.110781	−	0.0296837i	0.313784	+	0.949494i	$0.398403\pi$
$132$	−8.19615	+	4.73205i	−0.713384	+	0.411872i
$133$	−3.00000	+	0.803848i	−0.260133	+	0.0697024i
$134$	−4.07180	+	15.1962i	−0.351750	+	1.31275i
$135$	−1.86603	−	0.500000i	−0.160602	−	0.0430331i
$136$	5.26795	−	9.12436i	0.451723	−	0.782407i
$137$	10.2679			0.877250			0.438625	−	0.898670i	$-0.355466\pi$
$137$	10.2679			0.877250			0.438625	+	0.898670i	$0.355466\pi$
$138$	−4.73205	+	2.73205i	−0.402819	+	0.232568i
$139$	−2.19615	−	1.26795i	−0.186275	−	0.107546i	0.403962	−	0.914776i	$-0.367633\pi$
$139$	−2.19615	−	1.26795i	−0.186275	−	0.107546i	−0.590238	+	0.807230i	$0.700966\pi$
$140$	−2.73205	+	0.732051i	−0.230900	+	0.0618696i
$141$	−4.09808	−	7.09808i	−0.345120	−	0.597766i
$142$	−2.07180	+	7.73205i	−0.173861	+	0.648859i
$143$	−1.73205	−	0.464102i	−0.144841	−	0.0388101i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$	5.23205	+	9.06218i	0.434498	+	0.752573i
$146$		0			0
$147$			6.46410i			0.533150i
$148$	−5.19615	+	11.0000i	−0.427121	+	0.904194i
$149$			12.4641i			1.02110i	0.859848	+	0.510549i	$0.170558\pi$
$149$			12.4641i			1.02110i	−0.859848	+	0.510549i	$0.829442\pi$
$150$	−1.26795	+	1.26795i	−0.103528	+	0.103528i
$151$	5.92820	+	10.2679i	0.482430	+	0.835594i	0.999797	−	0.0201702i	$-0.00642082\pi$
$151$	5.92820	+	10.2679i	0.482430	+	0.835594i	−0.517366	+	0.855764i	$0.673087\pi$
$152$	−6.00000	−	10.3923i	−0.486664	−	0.842927i
$153$	−3.59808	−	0.964102i	−0.290887	−	0.0779430i
$154$	4.73205	+	1.26795i	0.381320	+	0.102174i
$155$	9.83013	+	17.0263i	0.789575	+	1.36758i
$156$	−0.732051	+	0.196152i	−0.0586110	+	0.0157048i
$157$	4.66987	+	2.69615i	0.372696	+	0.215176i	0.674636	−	0.738151i	$-0.264301\pi$
$157$	4.66987	+	2.69615i	0.372696	+	0.215176i	−0.301939	+	0.953327i	$0.597634\pi$
$158$	−4.46410	−	7.73205i	−0.355145	−	0.615129i
$159$	−0.928203			−0.0736113
$160$	−5.46410	−	9.46410i	−0.431975	−	0.748203i
$161$	2.73205	+	0.732051i	0.215316	+	0.0576937i
$162$	1.36603	+	0.366025i	0.107325	+	0.0287577i
$163$	−11.8301	+	3.16987i	−0.926607	+	0.248284i	−0.690407	−	0.723421i	$-0.742569\pi$
$163$	−11.8301	+	3.16987i	−0.926607	+	0.248284i	−0.236200	+	0.971705i	$0.575902\pi$
$164$	−9.39230	−	16.2679i	−0.733416	−	1.27031i
$165$	−8.83013	+	2.36603i	−0.687424	+	0.184195i
$166$	−4.00000	−	14.9282i	−0.310460	−	1.15865i
$167$	−2.00000	+	7.46410i	−0.154765	+	0.577590i	0.844361	+	0.535775i	$0.179981\pi$
$167$	−2.00000	+	7.46410i	−0.154765	+	0.577590i	−0.999125	+	0.0418145i	$0.986686\pi$
$168$	2.00000	−	0.535898i	0.154303	−	0.0413455i
$169$	11.1340	+	6.42820i	0.856460	+	0.494477i
$170$	7.19615	−	7.19615i	0.551920	−	0.551920i
$171$	−3.00000	+	3.00000i	−0.229416	+	0.229416i
$172$	−2.00000	−	2.00000i	−0.152499	−	0.152499i
$173$	6.33013	−	10.9641i	0.481271	−	0.833585i	−0.518498	−	0.855079i	$-0.673509\pi$
$173$	6.33013	−	10.9641i	0.481271	−	0.833585i	0.999769	+	0.0214934i	$0.00684210\pi$
$174$	−3.83013	−	6.63397i	−0.290361	−	0.502920i
$175$	0.928203			0.0701656
$176$			18.9282i			1.42677i
$177$	−10.0000	−	10.0000i	−0.751646	−	0.751646i
$178$	−7.09808	+	12.2942i	−0.532023	+	0.921491i
$179$	−11.2679	−	11.2679i	−0.842206	−	0.842206i	0.146939	−	0.989145i	$-0.453058\pi$
$179$	−11.2679	−	11.2679i	−0.842206	−	0.842206i	−0.989145	+	0.146939i	$0.953058\pi$
$180$	−2.73205	+	2.73205i	−0.203635	+	0.203635i
$181$	16.9641	−	9.79423i	1.26093	−	0.727999i	0.287677	−	0.957728i	$-0.407117\pi$
$181$	16.9641	−	9.79423i	1.26093	−	0.727999i	0.973255	+	0.229728i	$0.0737837\pi$
$182$	0.339746	+	0.196152i	0.0251836	+	0.0145398i
$183$	3.86603	−	1.03590i	0.285785	−	0.0765758i
$184$			10.9282i			0.805638i
$185$	−7.59808	+	8.96410i	−0.558622	+	0.659054i
$186$	−7.19615	−	12.4641i	−0.527647	−	0.913912i
$187$	−17.0263	+	4.56218i	−1.24508	+	0.333619i
$188$	−16.3923			−1.19553
$189$	−0.366025	−	0.633975i	−0.0266244	−	0.0461149i
$190$	−3.00000	−	11.1962i	−0.217643	−	0.812254i
$191$	−12.0000	−	12.0000i	−0.868290	−	0.868290i	0.123994	−	0.992283i	$-0.460430\pi$
$191$	−12.0000	−	12.0000i	−0.868290	−	0.868290i	−0.992283	+	0.123994i	$0.960430\pi$
$192$	4.00000	+	6.92820i	0.288675	+	0.500000i
$193$	−6.90192	+	6.90192i	−0.496811	+	0.496811i	−0.910444	−	0.413633i	$-0.864260\pi$
$193$	−6.90192	+	6.90192i	−0.496811	+	0.496811i	0.413633	+	0.910444i	$0.364260\pi$
$194$			19.5167i			1.40121i
$195$	−0.732051			−0.0524232
$196$	11.1962	+	6.46410i	0.799725	+	0.461722i
$197$	−0.866025	−	0.500000i	−0.0617018	−	0.0356235i	0.468832	−	0.883287i	$-0.344675\pi$
$197$	−0.866025	−	0.500000i	−0.0617018	−	0.0356235i	−0.530534	+	0.847664i	$0.678008\pi$
$198$	6.46410	−	1.73205i	0.459384	−	0.123091i
$199$	−19.0526	+	19.0526i	−1.35060	+	1.35060i	−0.465610	+	0.884990i	$0.654165\pi$
$199$	−19.0526	+	19.0526i	−1.35060	+	1.35060i	−0.884990	+	0.465610i	$0.845835\pi$
$200$	0.928203	+	3.46410i	0.0656339	+	0.244949i
$201$	5.56218	−	9.63397i	0.392326	−	0.679528i
$202$	−12.8564	+	12.8564i	−0.904574	+	0.904574i
$203$	−1.02628	+	3.83013i	−0.0720307	+	0.268822i
$204$	−5.26795	+	5.26795i	−0.368830	+	0.368830i
$205$	−4.69615	−	17.5263i	−0.327994	−	1.22409i
$206$		−	4.92820i		−	0.343364i
$207$	3.73205	−	1.00000i	0.259395	−	0.0695048i
$208$	−0.392305	+	1.46410i	−0.0272014	+	0.101517i
$209$	−5.19615	+	19.3923i	−0.359425	+	1.34139i
$210$	2.00000			0.138013
$211$	5.12436			0.352775			0.176388	−	0.984321i	$-0.443559\pi$
$211$	5.12436			0.352775			0.176388	+	0.984321i	$0.443559\pi$
$212$	−0.928203	+	1.60770i	−0.0637493	+	0.110417i
$213$	2.83013	−	4.90192i	0.193917	−	0.335874i
$214$	7.73205	+	2.07180i	0.528552	+	0.141625i
$215$	−1.36603	−	2.36603i	−0.0931622	−	0.161362i
$216$	2.00000	−	2.00000i	0.136083	−	0.136083i
$217$	−1.92820	+	7.19615i	−0.130895	+	0.488507i
$218$	−14.0263	+	24.2942i	−0.949980	+	1.64541i
$219$		0			0
$220$	−4.73205	+	17.6603i	−0.319035	+	1.19065i
$221$	−1.41154			−0.0949506
$222$	5.56218	−	6.56218i	0.373309	−	0.440425i
$223$		−	2.39230i		−	0.160201i	−0.996787	−	0.0801003i	$-0.974476\pi$
$223$		−	2.39230i		−	0.160201i	0.996787	−	0.0801003i	$-0.0255241\pi$
$224$	1.07180	−	4.00000i	0.0716124	−	0.267261i
$225$	1.09808	−	0.633975i	0.0732051	−	0.0422650i
$226$	9.19615	−	15.9282i	0.611719	−	1.05953i
$227$	25.0263	+	6.70577i	1.66105	+	0.445078i	0.962677	−	0.270654i	$-0.0872398\pi$
$227$	25.0263	+	6.70577i	1.66105	+	0.445078i	0.698376	+	0.715731i	$0.253906\pi$
$228$	2.19615	+	8.19615i	0.145444	+	0.542803i
$229$	0.526279	−	0.303848i	0.0347775	−	0.0200788i	−0.482510	−	0.875890i	$-0.660275\pi$
$229$	0.526279	−	0.303848i	0.0347775	−	0.0200788i	0.517288	+	0.855811i	$0.326942\pi$
$230$	−2.73205	+	10.1962i	−0.180146	+	0.672314i
$231$	−3.00000	−	1.73205i	−0.197386	−	0.113961i
$232$	−15.3205			−1.00584
$233$			10.4641i			0.685526i	0.939422	+	0.342763i	$0.111363\pi$
$233$			10.4641i			0.685526i	−0.939422	+	0.342763i	$0.888637\pi$
$234$	0.535898			0.0350328
$235$	−15.2942	−	4.09808i	−0.997685	−	0.267329i
$236$	−27.3205	+	7.32051i	−1.77841	+	0.476524i
$237$	1.63397	+	6.09808i	0.106138	+	0.396113i
$238$	3.85641			0.249974
$239$	3.09808	−	0.830127i	0.200398	−	0.0536965i	−0.157224	−	0.987563i	$-0.550254\pi$
$239$	3.09808	−	0.830127i	0.200398	−	0.0536965i	0.357622	+	0.933867i	$0.383588\pi$
$240$	2.00000	+	7.46410i	0.129099	+	0.481806i
$241$	−3.63397	−	0.973721i	−0.234085	−	0.0627229i	0.139870	−	0.990170i	$-0.455332\pi$
$241$	−3.63397	−	0.973721i	−0.234085	−	0.0627229i	−0.373954	+	0.927447i	$0.621998\pi$
$242$	11.3923	−	11.3923i	0.732325	−	0.732325i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	2.07180	−	7.73205i	0.132633	−	0.494994i
$245$	8.83013	+	8.83013i	0.564136	+	0.564136i
$246$	3.43782	+	12.8301i	0.219188	+	0.818019i
$247$	−0.803848	+	1.39230i	−0.0511476	+	0.0885902i
$248$	−28.7846			−1.82782
$249$			10.9282i			0.692547i
$250$			17.1244i			1.08304i
$251$	16.1244	+	16.1244i	1.01776	+	1.01776i	0.999839	+	0.0179209i	$0.00570470\pi$
$251$	16.1244	+	16.1244i	1.01776	+	1.01776i	0.0179209	+	0.999839i	$0.494295\pi$
$252$	−1.46410			−0.0922297
$253$	12.9282	−	12.9282i	0.812789	−	0.812789i
$254$	8.92820	−	2.39230i	0.560205	−	0.150107i
$255$	−6.23205	+	3.59808i	−0.390266	+	0.225320i
$256$	16.0000			1.00000
$257$	7.42820	+	27.7224i	0.463359	+	1.72928i	0.662275	+	0.749261i	$0.269591\pi$
$257$	7.42820	+	27.7224i	0.463359	+	1.72928i	−0.198916	+	0.980017i	$0.563742\pi$
$258$	1.00000	+	1.73205i	0.0622573	+	0.107833i
$259$	−4.43782	+	0.366025i	−0.275753	+	0.0227437i
$260$	−0.732051	+	1.26795i	−0.0453999	+	0.0786349i
$261$	1.40192	+	5.23205i	0.0867769	+	0.323856i
$262$	−0.928203	+	1.60770i	−0.0573446	+	0.0993237i
$263$	−3.46410	−	6.00000i	−0.213606	−	0.369976i	0.739235	−	0.673448i	$-0.235187\pi$
$263$	−3.46410	−	6.00000i	−0.213606	−	0.369976i	−0.952840	+	0.303472i	$0.901854\pi$
$264$	3.46410	−	12.9282i	0.213201	−	0.795676i
$265$	−1.26795	+	1.26795i	−0.0778895	+	0.0778895i
$266$	2.19615	−	3.80385i	0.134655	−	0.233229i
$267$	7.09808	−	7.09808i	0.434395	−	0.434395i
$268$	−11.1244	−	19.2679i	−0.679528	−	1.17698i
$269$		−	10.0000i		−	0.609711i	−0.952399	−	0.304855i	$-0.901392\pi$
$269$		−	10.0000i		−	0.609711i	0.952399	−	0.304855i	$-0.0986081\pi$
$270$	2.36603	−	1.36603i	0.143992	−	0.0831337i
$271$	−14.3660	−	8.29423i	−0.872674	−	0.503839i	−0.00443801	−	0.999990i	$-0.501413\pi$
$271$	−14.3660	−	8.29423i	−0.872674	−	0.503839i	−0.868236	+	0.496152i	$0.834746\pi$
$272$	3.85641	+	14.3923i	0.233829	+	0.872662i
$273$	−0.196152	−	0.196152i	−0.0118717	−	0.0118717i
$274$	−10.2679	+	10.2679i	−0.620309	+	0.620309i
$275$	3.00000	−	5.19615i	0.180907	−	0.313340i
$276$	2.00000	−	7.46410i	0.120386	−	0.449286i
$277$	24.3564	+	6.52628i	1.46343	+	0.392126i	0.900675	−	0.434494i	$-0.143073\pi$
$277$	24.3564	+	6.52628i	1.46343	+	0.392126i	0.562760	+	0.826620i	$0.309740\pi$
$278$	3.46410	−	0.928203i	0.207763	−	0.0556699i
$279$	2.63397	+	9.83013i	0.157692	+	0.588514i
$280$	2.00000	−	3.46410i	0.119523	−	0.207020i
$281$	3.25833	+	12.1603i	0.194376	+	0.725420i	0.992428	+	0.122831i	$0.0391974\pi$
$281$	3.25833	+	12.1603i	0.194376	+	0.725420i	−0.798052	+	0.602589i	$0.794136\pi$
$282$	11.1962	+	3.00000i	0.666721	+	0.178647i
$283$	−2.16987	+	8.09808i	−0.128986	+	0.481381i	−0.999950	−	0.00996477i	$-0.996828\pi$
$283$	−2.16987	+	8.09808i	−0.128986	+	0.481381i	0.870965	+	0.491345i	$0.163495\pi$
$284$	−5.66025	−	9.80385i	−0.335874	−	0.581751i
$285$			8.19615i			0.485498i
$286$	2.19615	−	1.26795i	0.129861	−	0.0749754i
$287$	3.43782	−	5.95448i	0.202928	−	0.351482i
$288$	−1.46410	−	5.46410i	−0.0862730	−	0.321975i
$289$	2.70577	−	1.56218i	0.159163	−	0.0918928i
$290$	−14.2942	−	3.83013i	−0.839386	−	0.224913i
$291$	3.57180	−	13.3301i	0.209382	−	0.781426i
$292$		0			0
$293$	−17.8923	+	10.3301i	−1.04528	+	0.603492i	−0.921324	−	0.388795i	$-0.872891\pi$
$293$	−17.8923	+	10.3301i	−1.04528	+	0.603492i	−0.123955	+	0.992288i	$0.539558\pi$
$294$	−6.46410	−	6.46410i	−0.376994	−	0.376994i
$295$	−27.3205			−1.59066
$296$	−5.80385	−	16.1962i	−0.337342	−	0.941382i
$297$	−4.73205			−0.274581
$298$	−12.4641	−	12.4641i	−0.722026	−	0.722026i
$299$	1.26795	−	0.732051i	0.0733274	−	0.0423356i
$300$		−	2.53590i		−	0.146410i
$301$	0.267949	−	1.00000i	0.0154443	−	0.0576390i
$302$	−16.1962	−	4.33975i	−0.931984	−	0.249724i
$303$	11.1340	−	6.42820i	0.639630	−	0.369291i
$304$	16.3923	+	4.39230i	0.940163	+	0.251916i
$305$	3.86603	−	6.69615i	0.221368	−	0.383421i
$306$	4.56218	−	2.63397i	0.260802	−	0.150574i
$307$		−	13.8038i		−	0.787827i	−0.919147	−	0.393914i	$-0.871121\pi$
$307$		−	13.8038i		−	0.787827i	0.919147	−	0.393914i	$-0.128879\pi$
$308$	−6.00000	+	3.46410i	−0.341882	+	0.197386i
$309$	−0.901924	+	3.36603i	−0.0513087	+	0.191486i
$310$	−26.8564	−	7.19615i	−1.52534	−	0.408714i
$311$	−4.09808	−	15.2942i	−0.232381	−	0.867256i	−0.979312	−	0.202355i	$-0.935140\pi$
$311$	−4.09808	−	15.2942i	−0.232381	−	0.867256i	0.746932	−	0.664901i	$-0.231526\pi$
$312$	0.535898	−	0.928203i	0.0303393	−	0.0525492i
$313$	3.99038	+	14.8923i	0.225550	+	0.841763i	0.982184	+	0.187924i	$0.0601759\pi$
$313$	3.99038	+	14.8923i	0.225550	+	0.841763i	−0.756634	+	0.653839i	$0.773157\pi$
$314$	−7.36603	+	1.97372i	−0.415689	+	0.111383i
$315$	−1.36603	−	0.366025i	−0.0769668	−	0.0206232i
$316$	12.1962	+	3.26795i	0.686087	+	0.183837i
$317$	−3.33013	+	5.76795i	−0.187039	+	0.323960i	−0.944262	−	0.329196i	$-0.893222\pi$
$317$	−3.33013	+	5.76795i	−0.187039	+	0.323960i	0.757223	+	0.653156i	$0.226556\pi$
$318$	0.928203	−	0.928203i	0.0520511	−	0.0520511i
$319$	18.1244	+	18.1244i	1.01477	+	1.01477i
$320$	14.9282	+	4.00000i	0.834512	+	0.223607i
$321$	−4.90192	−	2.83013i	−0.273599	−	0.157962i
$322$	−3.46410	+	2.00000i	−0.193047	+	0.111456i
$323$			15.8038i			0.879350i
$324$	−1.73205	+	1.00000i	−0.0962250	+	0.0555556i
$325$	0.339746	−	0.339746i	0.0188457	−	0.0188457i
$326$	8.66025	−	15.0000i	0.479647	−	0.830773i
$327$	14.0263	−	14.0263i	0.775655	−	0.775655i
$328$	25.6603	+	6.87564i	1.41685	+	0.379644i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$	6.46410	−	11.1962i	0.355837	−	0.616328i
$331$	−2.07180	−	7.73205i	−0.113876	−	0.424992i	0.885324	−	0.464974i	$-0.153936\pi$
$331$	−2.07180	−	7.73205i	−0.113876	−	0.424992i	−0.999200	+	0.0399824i	$0.987270\pi$
$332$	18.9282	+	10.9282i	1.03882	+	0.599763i
$333$	−5.00000	+	3.46410i	−0.273998	+	0.189832i
$334$	−5.46410	−	9.46410i	−0.298982	−	0.517853i
$335$	−5.56218	−	20.7583i	−0.303894	−	1.13415i
$336$	−1.46410	+	2.53590i	−0.0798733	+	0.138345i
$337$	12.0622	−	6.96410i	0.657069	−	0.379359i	−0.134090	−	0.990969i	$-0.542811\pi$
$337$	12.0622	−	6.96410i	0.657069	−	0.379359i	0.791159	+	0.611610i	$0.209478\pi$
$338$	−17.5622	+	4.70577i	−0.955257	+	0.255960i
$339$	−9.19615	+	9.19615i	−0.499466	+	0.499466i
$340$			14.3923i			0.780532i
$341$	34.0526	+	34.0526i	1.84405	+	1.84405i
$342$		−	6.00000i		−	0.324443i
$343$			9.85641i			0.532196i
$344$	4.00000			0.215666
$345$	3.73205	−	6.46410i	0.200927	−	0.348016i
$346$	4.63397	+	17.2942i	0.249124	+	0.929743i
$347$	3.26795	+	3.26795i	0.175433	+	0.175433i	0.789361	−	0.613929i	$-0.210412\pi$
$347$	3.26795	+	3.26795i	0.175433	+	0.175433i	−0.613929	+	0.789361i	$0.710412\pi$
$348$	10.4641	+	2.80385i	0.560935	+	0.150302i
$349$	−9.23205	−	5.33013i	−0.494180	−	0.285315i	0.232127	−	0.972686i	$-0.425432\pi$
$349$	−9.23205	−	5.33013i	−0.494180	−	0.285315i	−0.726307	+	0.687370i	$0.758765\pi$
$350$	−0.928203	+	0.928203i	−0.0496145	+	0.0496145i
$351$	−0.366025	−	0.0980762i	−0.0195370	−	0.00523492i
$352$	−18.9282	−	18.9282i	−1.00888	−	1.00888i
$353$	−0.964102	+	0.258330i	−0.0513140	+	0.0137495i	−0.284385	−	0.958710i	$-0.591789\pi$
$353$	−0.964102	+	0.258330i	−0.0513140	+	0.0137495i	0.233071	+	0.972460i	$0.425123\pi$
$354$	20.0000			1.06299
$355$	−2.83013	−	10.5622i	−0.150208	−	0.560582i
$356$	−5.19615	−	19.3923i	−0.275396	−	1.02779i
$357$	−2.63397	−	0.705771i	−0.139405	−	0.0373534i
$358$	22.5359			1.19106
$359$			32.2487i			1.70202i	0.525148	+	0.851011i	$0.324010\pi$
$359$			32.2487i			1.70202i	−0.525148	+	0.851011i	$0.675990\pi$
$360$		−	5.46410i		−	0.287983i
$361$	−0.866025	−	0.500000i	−0.0455803	−	0.0263158i
$362$	−7.16987	+	26.7583i	−0.376840	+	1.40639i
$363$	−9.86603	+	5.69615i	−0.517832	+	0.298970i
$364$	−0.535898	+	0.143594i	−0.0280887	+	0.00752635i
$365$		0			0
$366$	−2.83013	+	4.90192i	−0.147933	+	0.256228i
$367$	7.85641	−	4.53590i	0.410101	−	0.236772i	−0.280732	−	0.959786i	$-0.590577\pi$
$367$	7.85641	−	4.53590i	0.410101	−	0.236772i	0.690833	+	0.723014i	$0.257244\pi$
$368$	−10.9282	−	10.9282i	−0.569672	−	0.569672i
$369$		−	9.39230i		−	0.488944i
$370$	−1.36603	−	16.5622i	−0.0710163	−	0.861027i
$371$	−0.679492			−0.0352775
$372$	19.6603	+	5.26795i	1.01934	+	0.273130i
$373$	−8.86603	−	15.3564i	−0.459065	−	0.795125i	0.539846	−	0.841764i	$-0.318482\pi$
$373$	−8.86603	−	15.3564i	−0.459065	−	0.795125i	−0.998912	+	0.0466389i	$0.985149\pi$
$374$	12.4641	−	21.5885i	0.644503	−	1.11631i
$375$	3.13397	−	11.6962i	0.161838	−	0.603987i
$376$	16.3923	−	16.3923i	0.845369	−	0.845369i
$377$	1.02628	+	1.77757i	0.0528561	+	0.0915494i
$378$	1.00000	+	0.267949i	0.0514344	+	0.0137818i
$379$	6.36603	−	11.0263i	0.327001	−	0.566382i	−0.654914	−	0.755703i	$-0.727295\pi$
$379$	6.36603	−	11.0263i	0.327001	−	0.566382i	0.981915	+	0.189321i	$0.0606287\pi$
$380$	14.1962	+	8.19615i	0.728247	+	0.420454i
$381$	−6.53590			−0.334844
$382$	24.0000			1.22795
$383$	4.29423	−	16.0263i	0.219425	−	0.818905i	−0.765137	−	0.643868i	$-0.777329\pi$
$383$	4.29423	−	16.0263i	0.219425	−	0.818905i	0.984562	−	0.175037i	$-0.0560045\pi$
$384$	−10.9282	−	2.92820i	−0.557678	−	0.149429i
$385$	−6.46410	+	1.73205i	−0.329441	+	0.0882735i
$386$		−	13.8038i		−	0.702597i
$387$	−0.366025	−	1.36603i	−0.0186061	−	0.0694390i
$388$	−19.5167	−	19.5167i	−0.990808	−	0.990808i
$389$	2.47372	−	9.23205i	0.125423	−	0.468084i	−0.874432	−	0.485149i	$-0.838766\pi$
$389$	2.47372	−	9.23205i	0.125423	−	0.468084i	0.999854	+	0.0170650i	$0.00543221\pi$
$390$	0.732051	−	0.732051i	0.0370688	−	0.0370688i
$391$	7.19615	−	12.4641i	0.363925	−	0.630337i
$392$	−17.6603	+	4.73205i	−0.891978	+	0.239005i
$393$	0.928203	−	0.928203i	0.0468217	−	0.0468217i
$394$	1.36603	−	0.366025i	0.0688194	−	0.0184401i
$395$	10.5622	+	6.09808i	0.531441	+	0.306828i
$396$	−4.73205	+	8.19615i	−0.237795	+	0.411872i
$397$	21.3923			1.07365			0.536825	−	0.843694i	$-0.319624\pi$
$397$	21.3923			1.07365			0.536825	+	0.843694i	$0.319624\pi$
$398$		−	38.1051i		−	1.91004i
$399$	−2.19615	+	2.19615i	−0.109945	+	0.109945i
$400$	−4.39230	−	2.53590i	−0.219615	−	0.126795i
$401$	−9.19615	−	9.19615i	−0.459234	−	0.459234i	0.439170	−	0.898404i	$-0.355273\pi$
$401$	−9.19615	−	9.19615i	−0.459234	−	0.459234i	−0.898404	+	0.439170i	$0.855273\pi$
$402$	4.07180	+	15.1962i	0.203083	+	0.757915i
$403$	1.92820	+	3.33975i	0.0960506	+	0.166365i
$404$		−	25.7128i		−	1.27926i
$405$	−1.86603	+	0.500000i	−0.0927235	+	0.0248452i
$406$	−2.80385	−	4.85641i	−0.139153	−	0.241019i
$407$	−12.2942	+	26.0263i	−0.609402	+	1.29007i
$408$		−	10.5359i		−	0.521605i
$409$	30.6244	−	8.20577i	1.51428	−	0.405749i	0.596424	−	0.802670i	$-0.296588\pi$
$409$	30.6244	−	8.20577i	1.51428	−	0.405749i	0.917853	+	0.396920i	$0.129921\pi$
$410$	22.2224	+	12.8301i	1.09749	+	0.633635i
$411$	8.89230	−	5.13397i	0.438625	−	0.253240i
$412$	4.92820	+	4.92820i	0.242795	+	0.242795i
$413$	−7.32051	−	7.32051i	−0.360219	−	0.360219i
$414$	−2.73205	+	4.73205i	−0.134273	+	0.232568i
$415$	14.9282	+	14.9282i	0.732797	+	0.732797i
$416$	−1.07180	−	1.85641i	−0.0525492	−	0.0910178i
$417$	−2.53590			−0.124183
$418$	−14.1962	−	24.5885i	−0.694357	−	1.20266i
$419$	−7.56218	+	13.0981i	−0.369437	+	0.639883i	−0.989478	−	0.144687i	$-0.953783\pi$
$419$	−7.56218	+	13.0981i	−0.369437	+	0.639883i	0.620041	+	0.784569i	$0.287116\pi$
$420$	−2.00000	+	2.00000i	−0.0975900	+	0.0975900i
$421$	−24.8301	+	24.8301i	−1.21015	+	1.21015i	−0.239168	+	0.970978i	$0.576875\pi$
$421$	−24.8301	+	24.8301i	−1.21015	+	1.21015i	−0.970978	+	0.239168i	$0.923125\pi$
$422$	−5.12436	+	5.12436i	−0.249450	+	0.249450i
$423$	−7.09808	−	4.09808i	−0.345120	−	0.199255i
$424$	−0.679492	−	2.53590i	−0.0329990	−	0.123154i
$425$	1.22243	−	4.56218i	0.0592967	−	0.221298i
$426$	2.07180	+	7.73205i	0.100379	+	0.374619i
$427$	2.83013	−	0.758330i	0.136959	−	0.0366982i
$428$	−9.80385	+	5.66025i	−0.473887	+	0.273599i
$429$	−1.73205	+	0.464102i	−0.0836242	+	0.0224070i
$430$	3.73205	+	1.00000i	0.179975	+	0.0482243i
$431$	27.2224	+	7.29423i	1.31126	+	0.351351i	0.845696	−	0.533665i	$-0.179186\pi$
$431$	27.2224	+	7.29423i	1.31126	+	0.351351i	0.465562	+	0.885015i	$0.345852\pi$
$432$			4.00000i			0.192450i
$433$	−26.6603			−1.28121			−0.640605	−	0.767871i	$-0.721316\pi$
$433$	−26.6603			−1.28121			−0.640605	+	0.767871i	$0.721316\pi$
$434$	−5.26795	−	9.12436i	−0.252870	−	0.437983i
$435$	9.06218	+	5.23205i	0.434498	+	0.250858i
$436$	−10.2679	−	38.3205i	−0.491746	−	1.83522i
$437$	−8.19615	−	14.1962i	−0.392075	−	0.679094i
$438$		0			0
$439$	1.73205	+	0.464102i	0.0826663	+	0.0221504i	0.299915	−	0.953966i	$-0.403042\pi$
$439$	1.73205	+	0.464102i	0.0826663	+	0.0221504i	−0.217249	+	0.976116i	$0.569708\pi$
$440$	−12.9282	−	22.3923i	−0.616328	−	1.06751i
$441$	3.23205	+	5.59808i	0.153907	+	0.266575i
$442$	1.41154	−	1.41154i	0.0671402	−	0.0671402i
$443$		−	9.85641i		−	0.468292i	−0.972201	−	0.234146i	$-0.924771\pi$
$443$		−	9.85641i		−	0.468292i	0.972201	−	0.234146i	$-0.0752294\pi$
$444$	1.00000	+	12.1244i	0.0474579	+	0.575396i
$445$		−	19.3923i		−	0.919283i
$446$	2.39230	+	2.39230i	0.113279	+	0.113279i
$447$	6.23205	+	10.7942i	0.294766	+	0.510549i
$448$	2.92820	+	5.07180i	0.138345	+	0.239620i
$449$	7.63397	+	2.04552i	0.360270	+	0.0965339i	0.434413	−	0.900714i	$-0.356956\pi$
$449$	7.63397	+	2.04552i	0.360270	+	0.0965339i	−0.0741438	+	0.997248i	$0.523622\pi$
$450$	−0.464102	+	1.73205i	−0.0218780	+	0.0816497i
$451$	−22.2224	−	38.4904i	−1.04641	−	1.81244i
$452$	6.73205	+	25.1244i	0.316649	+	1.18175i
$453$	10.2679	+	5.92820i	0.482430	+	0.278531i
$454$	−31.7321	+	18.3205i	−1.48926	+	0.859824i
$455$	−0.535898			−0.0251233
$456$	−10.3923	−	6.00000i	−0.486664	−	0.280976i
$457$	34.8205	+	9.33013i	1.62883	+	0.436445i	0.953580	−	0.301140i	$-0.0973671\pi$
$457$	34.8205	+	9.33013i	1.62883	+	0.436445i	0.675255	+	0.737585i	$0.264034\pi$
$458$	−0.222432	+	0.830127i	−0.0103936	+	0.0387893i
$459$	−3.59808	+	0.964102i	−0.167944	+	0.0450004i
$460$	−7.46410	−	12.9282i	−0.348016	−	0.602781i
$461$	−7.29423	+	1.95448i	−0.339726	+	0.0910293i	−0.424649	−	0.905358i	$-0.639602\pi$
$461$	−7.29423	+	1.95448i	−0.339726	+	0.0910293i	0.0849226	+	0.996388i	$0.472936\pi$
$462$	4.73205	−	1.26795i	0.220155	−	0.0589903i
$463$	−2.36603	+	8.83013i	−0.109959	+	0.410371i	−0.998860	−	0.0477268i	$-0.984802\pi$
$463$	−2.36603	+	8.83013i	−0.109959	+	0.410371i	0.888902	+	0.458098i	$0.151469\pi$
$464$	15.3205	−	15.3205i	0.711237	−	0.711237i
$465$	17.0263	+	9.83013i	0.789575	+	0.455861i
$466$	−10.4641	−	10.4641i	−0.484740	−	0.484740i
$467$	−10.9282	+	10.9282i	−0.505697	+	0.505697i	−0.913203	−	0.407506i	$-0.866399\pi$
$467$	−10.9282	+	10.9282i	−0.505697	+	0.505697i	0.407506	+	0.913203i	$0.366399\pi$
$468$	−0.535898	+	0.535898i	−0.0247719	+	0.0247719i
$469$	4.07180	−	7.05256i	0.188018	−	0.325657i
$470$	19.3923	−	11.1962i	0.894500	−	0.516440i
$471$	5.39230			0.248464
$472$	20.0000	−	34.6410i	0.920575	−	1.59448i
$473$	−4.73205	−	4.73205i	−0.217580	−	0.217580i
$474$	−7.73205	−	4.46410i	−0.355145	−	0.205043i
$475$	−3.80385	−	3.80385i	−0.174532	−	0.174532i
$476$	−3.85641	+	3.85641i	−0.176758	+	0.176758i
$477$	−0.803848	+	0.464102i	−0.0368057	+	0.0212498i
$478$	−2.26795	+	3.92820i	−0.103734	+	0.179672i
$479$	36.0526	−	9.66025i	1.64728	−	0.441388i	0.688433	−	0.725300i	$-0.258299\pi$
$479$	36.0526	−	9.66025i	1.64728	−	0.441388i	0.958850	+	0.283912i	$0.0916322\pi$
$480$	−9.46410	−	5.46410i	−0.431975	−	0.249401i
$481$	−1.49038	+	1.75833i	−0.0679555	+	0.0801730i
$482$	4.60770	−	2.66025i	0.209875	−	0.121171i
$483$	2.73205	−	0.732051i	0.124313	−	0.0333095i
$484$			22.7846i			1.03566i
$485$	−13.3301	−	23.0885i	−0.605290	−	1.04839i
$486$	1.36603	−	0.366025i	0.0619642	−	0.0166032i
$487$	−23.4641	−	23.4641i	−1.06326	−	1.06326i	−0.997859	−	0.0654009i	$-0.979167\pi$
$487$	−23.4641	−	23.4641i	−1.06326	−	1.06326i	−0.0654009	−	0.997859i	$-0.520833\pi$
$488$	5.66025	+	9.80385i	0.256228	+	0.443799i
$489$	−8.66025	+	8.66025i	−0.391630	+	0.391630i
$490$	−17.6603			−0.797809
$491$	20.7321			0.935624			0.467812	−	0.883828i	$-0.345042\pi$
$491$	20.7321			0.935624			0.467812	+	0.883828i	$0.345042\pi$
$492$	−16.2679	−	9.39230i	−0.733416	−	0.423438i
$493$	17.4737	+	10.0885i	0.786977	+	0.454361i
$494$	−0.588457	−	2.19615i	−0.0264759	−	0.0988096i
$495$	−6.46410	+	6.46410i	−0.290540	+	0.290540i
$496$	28.7846	−	28.7846i	1.29247	−	1.29247i
$497$	2.07180	−	3.58846i	0.0929328	−	0.160964i
$498$	−10.9282	−	10.9282i	−0.489704	−	0.489704i
$499$	−3.90192	+	14.5622i	−0.174674	+	0.651893i	0.821933	+	0.569584i	$0.192896\pi$
$499$	−3.90192	+	14.5622i	−0.174674	+	0.651893i	−0.996607	+	0.0823082i	$0.973771\pi$
$500$	−17.1244	−	17.1244i	−0.765824	−	0.765824i
$501$	2.00000	+	7.46410i	0.0893534	+	0.333471i
$502$	−32.2487			−1.43933
$503$	37.4186	−	10.0263i	1.66841	−	0.447050i	0.703730	−	0.710467i	$-0.251516\pi$
$503$	37.4186	−	10.0263i	1.66841	−	0.447050i	0.964682	+	0.263418i	$0.0848497\pi$
$504$	1.46410	−	1.46410i	0.0652163	−	0.0652163i
$505$	6.42820	−	23.9904i	0.286051	−	1.06756i
$506$			25.8564i			1.14946i
$507$	12.8564			0.570973
$508$	−6.53590	+	11.3205i	−0.289984	+	0.502266i
$509$	9.33013	−	16.1603i	0.413551	−	0.716291i	−0.581724	−	0.813386i	$-0.697622\pi$
$509$	9.33013	−	16.1603i	0.413551	−	0.716291i	0.995275	+	0.0970952i	$0.0309551\pi$
$510$	2.63397	−	9.83013i	0.116634	−	0.435285i
$511$		0			0
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−1.09808	+	4.09808i	−0.0484812	+	0.180934i
$514$	−35.1506	−	20.2942i	−1.55043	−	0.895140i
$515$	3.36603	+	5.83013i	0.148325	+	0.256906i
$516$	−2.73205	−	0.732051i	−0.120272	−	0.0322267i
$517$	−38.7846			−1.70575
$518$	4.07180	−	4.80385i	0.178904	−	0.211069i
$519$		−	12.6603i		−	0.555723i
$520$	−0.535898	−	2.00000i	−0.0235007	−	0.0877058i
$521$	6.00000	−	3.46410i	0.262865	−	0.151765i	−0.362776	−	0.931876i	$-0.618171\pi$
$521$	6.00000	−	3.46410i	0.262865	−	0.151765i	0.625641	+	0.780111i	$0.284838\pi$
$522$	−6.63397	−	3.83013i	−0.290361	−	0.167640i
$523$	−29.5885	−	7.92820i	−1.29381	−	0.346676i	−0.454705	−	0.890642i	$-0.650255\pi$
$523$	−29.5885	−	7.92820i	−1.29381	−	0.346676i	−0.839107	+	0.543966i	$0.816922\pi$
$524$	−0.679492	−	2.53590i	−0.0296837	−	0.110781i
$525$	0.803848	−	0.464102i	0.0350828	−	0.0202551i
$526$	9.46410	+	2.53590i	0.412654	+	0.110570i
$527$	32.8301	+	18.9545i	1.43010	+	0.825670i
$528$	9.46410	+	16.3923i	0.411872	+	0.713384i
$529$		−	8.07180i		−	0.350948i
$530$		−	2.53590i		−	0.110152i
$531$	−13.6603	−	3.66025i	−0.592805	−	0.158841i
$532$	1.60770	+	6.00000i	0.0697024	+	0.260133i
$533$	−0.921162	−	3.43782i	−0.0398999	−	0.148909i
$534$			14.1962i			0.614328i
$535$	−10.5622	+	2.83013i	−0.456643	+	0.122357i
$536$	30.3923	+	8.14359i	1.31275	+	0.351750i
$537$	−15.3923	−	4.12436i	−0.664227	−	0.177979i
$538$	10.0000	+	10.0000i	0.431131	+	0.431131i
$539$	26.4904	+	15.2942i	1.14102	+	0.658769i
$540$	−1.00000	+	3.73205i	−0.0430331	+	0.160602i
$541$	8.63397	+	8.63397i	0.371204	+	0.371204i	0.867915	−	0.496712i	$-0.165459\pi$
$541$	8.63397	+	8.63397i	0.371204	+	0.371204i	−0.496712	+	0.867915i	$0.665459\pi$
$542$	22.6603	−	6.07180i	0.973341	−	0.260806i
$543$	9.79423	−	16.9641i	0.420311	−	0.727999i
$544$	−18.2487	−	10.5359i	−0.782407	−	0.451723i
$545$		−	38.3205i		−	1.64147i
$546$	0.392305			0.0167891
$547$	16.2679	+	16.2679i	0.695567	+	0.695567i	0.963451	−	0.267884i	$-0.0863244\pi$
$547$	16.2679	+	16.2679i	0.695567	+	0.695567i	−0.267884	+	0.963451i	$0.586324\pi$
$548$		−	20.5359i		−	0.877250i
$549$	2.83013	−	2.83013i	0.120787	−	0.120787i
$550$	2.19615	+	8.19615i	0.0936443	+	0.349485i
$551$	19.9019	−	11.4904i	0.847850	−	0.489507i
$552$	5.46410	+	9.46410i	0.232568	+	0.402819i
$553$	1.19615	+	4.46410i	0.0508656	+	0.189833i
$554$	−30.8827	+	17.8301i	−1.31208	+	0.757530i
$555$	−2.09808	+	11.5622i	−0.0890584	+	0.490787i
$556$	−2.53590	+	4.39230i	−0.107546	+	0.186275i
$557$	−5.79423	−	21.6244i	−0.245509	−	0.916253i	−0.973127	−	0.230270i	$-0.926039\pi$
$557$	−5.79423	−	21.6244i	−0.245509	−	0.916253i	0.727617	−	0.685983i	$-0.240628\pi$
$558$	−12.4641	−	7.19615i	−0.527647	−	0.304637i
$559$	−0.267949	−	0.464102i	−0.0113330	−	0.0196294i
$560$	1.46410	+	5.46410i	0.0618696	+	0.230900i
$561$	−12.4641	+	12.4641i	−0.526235	+	0.526235i
$562$	−15.4186	−	8.90192i	−0.650394	−	0.375505i
$563$	−20.9808	+	20.9808i	−0.884234	+	0.884234i	−0.993962	−	0.109728i	$-0.965002\pi$
$563$	−20.9808	+	20.9808i	−0.884234	+	0.884234i	0.109728	+	0.993962i	$0.465002\pi$
$564$	−14.1962	+	8.19615i	−0.597766	+	0.345120i
$565$			25.1244i			1.05699i
$566$	−5.92820	−	10.2679i	−0.249181	−	0.431594i
$567$	−0.633975	−	0.366025i	−0.0266244	−	0.0153716i
$568$	15.4641	+	4.14359i	0.648859	+	0.173861i
$569$	1.49038	+	1.49038i	0.0624800	+	0.0624800i	0.737656	−	0.675176i	$-0.235932\pi$
$569$	1.49038	+	1.49038i	0.0624800	+	0.0624800i	−0.675176	+	0.737656i	$0.735932\pi$
$570$	−8.19615	−	8.19615i	−0.343299	−	0.343299i
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	−0.252893	−	0.967494i	$-0.581382\pi$
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	0.964321	−	0.264735i	$-0.0852845\pi$
$572$	−0.928203	+	3.46410i	−0.0388101	+	0.144841i
$573$	−16.3923	−	4.39230i	−0.684798	−	0.183491i
$574$	2.51666	+	9.39230i	0.105043	+	0.392027i
$575$	1.26795	+	4.73205i	0.0528771	+	0.197340i
$576$	6.92820	+	4.00000i	0.288675	+	0.166667i
$577$	4.29423	+	16.0263i	0.178771	+	0.667183i	0.995879	+	0.0906973i	$0.0289096\pi$
$577$	4.29423	+	16.0263i	0.178771	+	0.667183i	−0.817107	+	0.576485i	$0.804424\pi$
$578$	−1.14359	+	4.26795i	−0.0475672	+	0.177523i
$579$	−2.52628	+	9.42820i	−0.104989	+	0.391823i
$580$	18.1244	−	10.4641i	0.752573	−	0.434498i
$581$			8.00000i			0.331896i
$582$	9.75833	+	16.9019i	0.404496	+	0.700607i
$583$	−2.19615	+	3.80385i	−0.0909553	+	0.157539i
$584$		0			0
$585$	−0.633975	+	0.366025i	−0.0262116	+	0.0151333i
$586$	7.56218	−	28.2224i	0.312391	−	1.16586i
$587$	1.92820	−	7.19615i	0.0795855	−	0.297017i	−0.914648	−	0.404250i	$-0.867532\pi$
$587$	1.92820	−	7.19615i	0.0795855	−	0.297017i	0.994234	+	0.107233i	$0.0341992\pi$
$588$	12.9282			0.533150
$589$	37.3923	−	21.5885i	1.54072	−	0.889537i
$590$	27.3205	−	27.3205i	1.12477	−	1.12477i
$591$	−1.00000			−0.0411345
$592$	22.0000	+	10.3923i	0.904194	+	0.427121i
$593$	−7.92820			−0.325572			−0.162786	−	0.986661i	$-0.552048\pi$
$593$	−7.92820			−0.325572			−0.162786	+	0.986661i	$0.552048\pi$
$594$	4.73205	−	4.73205i	0.194158	−	0.194158i
$595$	−4.56218	+	2.63397i	−0.187031	+	0.107982i
$596$	24.9282			1.02110
$597$	−6.97372	+	26.0263i	−0.285415	+	1.06518i
$598$	−0.535898	+	2.00000i	−0.0219145	+	0.0817861i
$599$	−18.6340	+	10.7583i	−0.761364	+	0.439573i	−0.829785	−	0.558083i	$-0.811537\pi$
$599$	−18.6340	+	10.7583i	−0.761364	+	0.439573i	0.0684215	+	0.997657i	$0.478204\pi$
$600$	2.53590	+	2.53590i	0.103528	+	0.103528i
$601$	16.1603	−	27.9904i	0.659191	−	1.14175i	−0.321635	−	0.946864i	$-0.604232\pi$
$601$	16.1603	−	27.9904i	0.659191	−	1.14175i	0.980826	−	0.194888i	$-0.0624343\pi$
$602$	0.732051	+	1.26795i	0.0298362	+	0.0516778i
$603$		−	11.1244i		−	0.453019i
$604$	20.5359	−	11.8564i	0.835594	−	0.482430i
$605$	−5.69615	+	21.2583i	−0.231582	+	0.864274i
$606$	−4.70577	+	17.5622i	−0.191159	+	0.713415i
$607$	−3.97372	−	14.8301i	−0.161288	−	0.601936i	−0.998485	−	0.0550336i	$-0.982473\pi$
$607$	−3.97372	−	14.8301i	−0.161288	−	0.601936i	0.837196	−	0.546903i	$-0.184193\pi$
$608$	−20.7846	+	12.0000i	−0.842927	+	0.486664i
$609$	1.02628	+	3.83013i	0.0415869	+	0.155205i
$610$	2.83013	+	10.5622i	0.114588	+	0.427650i
$611$	−3.00000	−	0.803848i	−0.121367	−	0.0325202i
$612$	−1.92820	+	7.19615i	−0.0779430	+	0.290887i
$613$	−14.8205	+	25.6699i	−0.598595	+	1.03680i	0.394434	+	0.918924i	$0.370941\pi$
$613$	−14.8205	+	25.6699i	−0.598595	+	1.03680i	−0.993029	+	0.117872i	$0.962393\pi$
$614$	13.8038	+	13.8038i	0.557078	+	0.557078i
$615$	−12.8301	−	12.8301i	−0.517361	−	0.517361i
$616$	2.53590	−	9.46410i	0.102174	−	0.381320i
$617$	−19.8564	−	11.4641i	−0.799389	−	0.461527i	0.0438686	−	0.999037i	$-0.486032\pi$
$617$	−19.8564	−	11.4641i	−0.799389	−	0.461527i	−0.843257	+	0.537510i	$0.819365\pi$
$618$	−2.46410	−	4.26795i	−0.0991207	−	0.171682i
$619$			49.3731i			1.98447i	0.124373	+	0.992236i	$0.460308\pi$
$619$			49.3731i			1.98447i	−0.124373	+	0.992236i	$0.539692\pi$
$620$	34.0526	−	19.6603i	1.36758	−	0.789575i
$621$	2.73205	−	2.73205i	0.109633	−	0.109633i
$622$	19.3923	+	11.1962i	0.777561	+	0.448925i
$623$	5.19615	−	5.19615i	0.208179	−	0.208179i
$624$	0.392305	+	1.46410i	0.0157048	+	0.0586110i
$625$	−8.52628	−	14.7679i	−0.341051	−	0.590718i
$626$	−18.8827	−	10.9019i	−0.754704	−	0.435729i
$627$	5.19615	+	19.3923i	0.207514	+	0.774454i
$628$	5.39230	−	9.33975i	0.215176	−	0.372696i
$629$	−4.04552	+	22.2942i	−0.161305	+	0.888929i
$630$	1.73205	−	1.00000i	0.0690066	−	0.0398410i
$631$	12.3397	+	46.0526i	0.491238	+	1.83332i	0.550158	+	0.835061i	$0.314568\pi$
$631$	12.3397	+	46.0526i	0.491238	+	1.83332i	−0.0589202	+	0.998263i	$0.518766\pi$
$632$	−15.4641	+	8.92820i	−0.615129	+	0.355145i
$633$	4.43782	−	2.56218i	0.176388	−	0.101837i
$634$	−2.43782	−	9.09808i	−0.0968183	−	0.361331i
$635$	−8.92820	+	8.92820i	−0.354305	+	0.354305i
$636$			1.85641i			0.0736113i
$637$	1.73205	+	1.73205i	0.0686264	+	0.0686264i
$638$	−36.2487			−1.43510
$639$		−	5.66025i		−	0.223916i
$640$	−18.9282	+	10.9282i	−0.748203	+	0.431975i
$641$	−8.96410	+	15.5263i	−0.354061	+	0.613251i	−0.986957	−	0.160986i	$-0.948533\pi$
$641$	−8.96410	+	15.5263i	−0.354061	+	0.613251i	0.632896	+	0.774237i	$0.281866\pi$
$642$	7.73205	−	2.07180i	0.305160	−	0.0817673i
$643$	−4.60770	−	4.60770i	−0.181710	−	0.181710i	0.610391	−	0.792100i	$-0.291012\pi$
$643$	−4.60770	−	4.60770i	−0.181710	−	0.181710i	−0.792100	+	0.610391i	$0.791012\pi$
$644$	1.46410	−	5.46410i	0.0576937	−	0.215316i
$645$	−2.36603	−	1.36603i	−0.0931622	−	0.0537872i
$646$	−15.8038	−	15.8038i	−0.621794	−	0.621794i
$647$	−8.63397	−	2.31347i	−0.339437	−	0.0909518i	0.0850743	−	0.996375i	$-0.472887\pi$
$647$	−8.63397	−	2.31347i	−0.339437	−	0.0909518i	−0.424511	+	0.905423i	$0.639554\pi$
$648$	0.732051	−	2.73205i	0.0287577	−	0.107325i
$649$	−64.6410	+	17.3205i	−2.53738	+	0.679889i
$650$			0.679492i			0.0266519i
$651$	1.92820	+	7.19615i	0.0755722	+	0.282039i
$652$	6.33975	+	23.6603i	0.248284	+	0.926607i
$653$	3.06218	+	0.820508i	0.119832	+	0.0321090i	0.318237	−	0.948011i	$-0.396909\pi$
$653$	3.06218	+	0.820508i	0.119832	+	0.0321090i	−0.198404	+	0.980120i	$0.563576\pi$
$654$			28.0526i			1.09694i
$655$		−	2.53590i		−	0.0990857i
$656$	−32.5359	+	18.7846i	−1.27031	+	0.733416i
$657$		0			0
$658$	8.19615	+	2.19615i	0.319519	+	0.0856149i
$659$	21.0000	−	12.1244i	0.818044	−	0.472298i	−0.0316976	−	0.999498i	$-0.510091\pi$
$659$	21.0000	−	12.1244i	0.818044	−	0.472298i	0.849741	+	0.527200i	$0.176758\pi$
$660$	4.73205	+	17.6603i	0.184195	+	0.687424i
$661$	1.03590	+	0.277568i	0.0402918	+	0.0107961i	0.278909	−	0.960318i	$-0.410027\pi$
$661$	1.03590	+	0.277568i	0.0402918	+	0.0107961i	−0.238617	+	0.971114i	$0.576694\pi$
$662$	9.80385	+	5.66025i	0.381037	+	0.219992i
$663$	−1.22243	+	0.705771i	−0.0474753	+	0.0274099i
$664$	−29.8564	+	8.00000i	−1.15865	+	0.310460i
$665$			6.00000i			0.232670i
$666$	1.53590	−	8.46410i	0.0595149	−	0.327977i
$667$	−20.9282			−0.810343
$668$	14.9282	+	4.00000i	0.577590	+	0.154765i
$669$	−1.19615	−	2.07180i	−0.0462459	−	0.0801003i
$670$	26.3205	+	15.1962i	1.01685	+	0.587079i
$671$	4.90192	−	18.2942i	0.189237	−	0.706241i
$672$	−1.07180	−	4.00000i	−0.0413455	−	0.154303i
$673$	−0.535898	−	0.928203i	−0.0206574	−	0.0357796i	0.855512	−	0.517783i	$-0.173243\pi$
$673$	−0.535898	−	0.928203i	−0.0206574	−	0.0357796i	−0.876169	+	0.482004i	$0.839909\pi$
$674$	−5.09808	+	19.0263i	−0.196371	+	0.732865i
$675$	0.633975	−	1.09808i	0.0244017	−	0.0422650i
$676$	12.8564	−	22.2679i	0.494477	−	0.856460i
$677$	−27.7321			−1.06583			−0.532915	−	0.846169i	$-0.678903\pi$
$677$	−27.7321			−1.06583			−0.532915	+	0.846169i	$0.678903\pi$
$678$		−	18.3923i		−	0.706352i
$679$	2.61474	−	9.75833i	0.100344	−	0.374490i
$680$	−14.3923	−	14.3923i	−0.551920	−	0.551920i
$681$	25.0263	−	6.70577i	0.959009	−	0.256966i
$682$	−68.1051			−2.60788
$683$	7.83013	+	29.2224i	0.299611	+	1.11817i	0.937485	+	0.348025i	$0.113147\pi$
$683$	7.83013	+	29.2224i	0.299611	+	1.11817i	−0.637874	+	0.770141i	$0.720186\pi$
$684$	6.00000	+	6.00000i	0.229416	+	0.229416i
$685$	5.13397	−	19.1603i	0.196159	−	0.732076i
$686$	−9.85641	−	9.85641i	−0.376319	−	0.376319i
$687$	0.303848	−	0.526279i	0.0115925	−	0.0200788i
$688$	−4.00000	+	4.00000i	−0.152499	+	0.152499i
$689$	−0.248711	+	0.248711i	−0.00947515	+	0.00947515i
$690$	2.73205	+	10.1962i	0.104007	+	0.388161i
$691$	20.8301	+	12.0263i	0.792415	+	0.457501i	0.840812	−	0.541327i	$-0.182078\pi$
$691$	20.8301	+	12.0263i	0.792415	+	0.457501i	−0.0483968	+	0.998828i	$0.515411\pi$
$692$	−21.9282	−	12.6603i	−0.833585	−	0.481271i
$693$	−3.46410			−0.131590
$694$	−6.53590			−0.248099
$695$	−3.46410	+	3.46410i	−0.131401	+	0.131401i
$696$	−13.2679	+	7.66025i	−0.502920	+	0.290361i
$697$	−24.7391	−	24.7391i	−0.937060	−	0.937060i
$698$	14.5622	−	3.90192i	0.551187	−	0.147690i
$699$	5.23205	+	9.06218i	0.197894	+	0.342763i
$700$		−	1.85641i		−	0.0701656i
$701$	−20.2224	+	5.41858i	−0.763791	+	0.204657i	−0.619627	−	0.784897i	$-0.712716\pi$
$701$	−20.2224	+	5.41858i	−0.763791	+	0.204657i	−0.144164	+	0.989554i	$0.546049\pi$
$702$	0.464102	−	0.267949i	0.0175164	−	0.0101131i
$703$	19.6865	+	16.6865i	0.742492	+	0.629345i
$704$	37.8564			1.42677
$705$	−15.2942	+	4.09808i	−0.576014	+	0.154342i
$706$	0.705771	−	1.22243i	0.0265621	−	0.0460068i
$707$	8.15064	−	4.70577i	0.306536	−	0.176979i
$708$	−20.0000	+	20.0000i	−0.751646	+	0.751646i
$709$	3.92820	+	3.92820i	0.147527	+	0.147527i	0.777012	−	0.629485i	$-0.216734\pi$
$709$	3.92820	+	3.92820i	0.147527	+	0.147527i	−0.629485	+	0.777012i	$0.716734\pi$
$710$	13.3923	+	7.73205i	0.502604	+	0.290179i
$711$	4.46410	+	4.46410i	0.167417	+	0.167417i
$712$	24.5885	+	14.1962i	0.921491	+	0.532023i
$713$	−39.3205			−1.47256
$714$	3.33975	−	1.92820i	0.124987	−	0.0721612i
$715$	−1.73205	+	3.00000i	−0.0647750	+	0.112194i
$716$	−22.5359	+	22.5359i	−0.842206	+	0.842206i
$717$	2.26795	−	2.26795i	0.0846981	−	0.0846981i
$718$	−32.2487	−	32.2487i	−1.20351	−	1.20351i
$719$	−39.0000	−	22.5167i	−1.45445	−	0.839730i	−0.455725	−	0.890121i	$-0.650620\pi$
$719$	−39.0000	−	22.5167i	−1.45445	−	0.839730i	−0.998730	+	0.0503909i	$0.983953\pi$
$720$	5.46410	+	5.46410i	0.203635	+	0.203635i
$721$	−0.660254	+	2.46410i	−0.0245891	+	0.0917679i
$722$	1.36603	−	0.366025i	0.0508382	−	0.0136221i
$723$	−3.63397	+	0.973721i	−0.135149	+	0.0362131i
$724$	−19.5885	−	33.9282i	−0.727999	−	1.26093i
$725$	−6.63397	+	1.77757i	−0.246380	+	0.0660172i
$726$	4.16987	−	15.5622i	0.154759	−	0.577567i
$727$	7.66025	+	2.05256i	0.284103	+	0.0761252i	0.398057	−	0.917361i	$-0.369685\pi$
$727$	7.66025	+	2.05256i	0.284103	+	0.0761252i	−0.113953	+	0.993486i	$0.536351\pi$
$728$	0.392305	−	0.679492i	0.0145398	−	0.0251836i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−4.56218	−	2.63397i	−0.168738	−	0.0974211i
$732$	−2.07180	−	7.73205i	−0.0765758	−	0.285785i
$733$	−6.39230	−	11.0718i	−0.236105	−	0.408946i	0.723488	−	0.690337i	$-0.242538\pi$
$733$	−6.39230	−	11.0718i	−0.236105	−	0.408946i	−0.959593	+	0.281391i	$0.909204\pi$
$734$	−3.32051	+	12.3923i	−0.122562	+	0.457408i
$735$	12.0622	+	3.23205i	0.444920	+	0.119216i
$736$	21.8564			0.805638
$737$	−26.3205	−	45.5885i	−0.969528	−	1.67927i
$738$	9.39230	+	9.39230i	0.345736	+	0.345736i
$739$			11.8564i			0.436145i	0.975933	+	0.218072i	$0.0699769\pi$
$739$			11.8564i			0.436145i	−0.975933	+	0.218072i	$0.930023\pi$
$740$	17.9282	+	15.1962i	0.659054	+	0.558622i
$741$			1.60770i			0.0590602i
$742$	0.679492	−	0.679492i	0.0249449	−	0.0249449i
$743$	−11.7583	−	20.3660i	−0.431371	−	0.747157i	0.565620	−	0.824666i	$-0.308637\pi$
$743$	−11.7583	−	20.3660i	−0.431371	−	0.747157i	−0.996992	+	0.0775087i	$0.975303\pi$
$744$	−24.9282	+	14.3923i	−0.913912	+	0.527647i
$745$	23.2583	+	6.23205i	0.852119	+	0.228325i
$746$	24.2224	+	6.49038i	0.886846	+	0.237630i
$747$	5.46410	+	9.46410i	0.199921	+	0.346273i
$748$	9.12436	+	34.0526i	0.333619	+	1.24508i
$749$	−3.58846	−	2.07180i	−0.131119	−	0.0757018i
$750$	8.56218	+	14.8301i	0.312647	+	0.541520i
$751$	47.6603			1.73915			0.869574	−	0.493803i	$-0.164394\pi$
$751$	47.6603			1.73915			0.869574	+	0.493803i	$0.164394\pi$
$752$			32.7846i			1.19553i
$753$	22.0263	+	5.90192i	0.802682	+	0.215078i
$754$	−2.80385	−	0.751289i	−0.102110	−	0.0273603i
$755$	22.1244	−	5.92820i	0.805188	−	0.215749i
$756$	−1.26795	+	0.732051i	−0.0461149	+	0.0266244i
$757$	−41.0167	+	10.9904i	−1.49078	+	0.399452i	−0.909999	−	0.414611i	$-0.863918\pi$
$757$	−41.0167	+	10.9904i	−1.49078	+	0.399452i	−0.580777	+	0.814063i	$0.697251\pi$
$758$	4.66025	+	17.3923i	0.169268	+	0.631717i
$759$	4.73205	−	17.6603i	0.171763	−	0.641027i
$760$	−22.3923	+	6.00000i	−0.812254	+	0.217643i
$761$	7.50000	+	4.33013i	0.271875	+	0.156967i	0.629739	−	0.776807i	$-0.283162\pi$
$761$	7.50000	+	4.33013i	0.271875	+	0.156967i	−0.357865	+	0.933774i	$0.616495\pi$
$762$	6.53590	−	6.53590i	0.236771	−	0.236771i
$763$	10.2679	−	10.2679i	0.371725	−	0.371725i
$764$	−24.0000	+	24.0000i	−0.868290	+	0.868290i
$765$	−3.59808	+	6.23205i	−0.130089	+	0.225320i
$766$	11.7321	+	20.3205i	0.423896	+	0.734210i
$767$	−5.35898			−0.193502
$768$	13.8564	−	8.00000i	0.500000	−	0.288675i
$769$	16.1244	+	16.1244i	0.581459	+	0.581459i	0.935304	−	0.353845i	$-0.115126\pi$
$769$	16.1244	+	16.1244i	0.581459	+	0.581459i	−0.353845	+	0.935304i	$0.615126\pi$
$770$	4.73205	−	8.19615i	0.170531	−	0.295369i
$771$	20.2942	+	20.2942i	0.730879	+	0.730879i
$772$	13.8038	+	13.8038i	0.496811	+	0.496811i
$773$	−46.2391	+	26.6962i	−1.66310	+	0.960194i	−0.691885	+	0.722008i	$0.743220\pi$
$773$	−46.2391	+	26.6962i	−1.66310	+	0.960194i	−0.971220	+	0.238186i	$0.923447\pi$
$774$	1.73205	+	1.00000i	0.0622573	+	0.0359443i
$775$	−12.4641	+	3.33975i	−0.447724	+	0.119967i
$776$	39.0333			1.40121
$777$	−3.66025	+	2.53590i	−0.131311	+	0.0909748i
$778$	6.75833	+	11.7058i	0.242298	+	0.419672i
$779$	−38.4904	+	10.3135i	−1.37906	+	0.369518i
$780$			1.46410i			0.0524232i
$781$	−13.3923	−	23.1962i	−0.479214	−	0.830024i
$782$	5.26795	+	19.6603i	0.188381	+	0.703049i
$783$	3.83013	+	3.83013i	0.136878	+	0.136878i
$784$	12.9282	−	22.3923i	0.461722	−	0.799725i
$785$	7.36603	−	7.36603i	0.262905	−	0.262905i
$786$			1.85641i			0.0662158i
$787$	28.7846			1.02606			0.513030	−	0.858371i	$-0.328523\pi$
$787$	28.7846			1.02606			0.513030	+	0.858371i	$0.328523\pi$
$788$	−1.00000	+	1.73205i	−0.0356235	+	0.0617018i
$789$	−6.00000	−	3.46410i	−0.213606	−	0.123325i
$790$	−16.6603	+	4.46410i	−0.592745	+	0.158826i
$791$	−6.73205	+	6.73205i	−0.239364	+	0.239364i
$792$	−3.46410	−	12.9282i	−0.123091	−	0.459384i
$793$	0.758330	−	1.31347i	0.0269291	−	0.0466426i
$794$	−21.3923	+	21.3923i	−0.759184	+	0.759184i
$795$	−0.464102	+	1.73205i	−0.0164600	+	0.0614295i
$796$	38.1051	+	38.1051i	1.35060	+	1.35060i
$797$	3.84936	+	14.3660i	0.136352	+	0.508871i	0.999989	+	0.00475684i	$0.00151415\pi$
$797$	3.84936	+	14.3660i	0.136352	+	0.508871i	−0.863637	+	0.504114i	$0.831819\pi$
$798$		−	4.39230i		−	0.155486i
$799$	−29.4904	+	7.90192i	−1.04329	+	0.279550i
$800$	6.92820	−	1.85641i	0.244949	−	0.0656339i
$801$	2.59808	−	9.69615i	0.0917985	−	0.342597i
$802$	18.3923			0.649455
$803$		0			0
$804$	−19.2679	−	11.1244i	−0.679528	−	0.392326i
$805$	2.73205	−	4.73205i	0.0962921	−	0.166783i
$806$	−5.26795	−	1.41154i	−0.185556	−	0.0497195i
$807$	−5.00000	−	8.66025i	−0.176008	−	0.304855i
$808$	25.7128	+	25.7128i	0.904574	+	0.904574i
$809$	−3.95448	+	14.7583i	−0.139032	+	0.518875i	0.860916	+	0.508746i	$0.169891\pi$
$809$	−3.95448	+	14.7583i	−0.139032	+	0.518875i	−0.999949	+	0.0101290i	$0.996776\pi$
$810$	1.36603	−	2.36603i	0.0479972	−	0.0831337i
$811$	0.732051	+	1.26795i	0.0257058	+	0.0445237i	0.878592	−	0.477573i	$-0.158483\pi$
$811$	0.732051	+	1.26795i	0.0257058	+	0.0445237i	−0.852886	+	0.522097i	$0.825150\pi$
$812$	7.66025	+	2.05256i	0.268822	+	0.0720307i
$813$	−16.5885			−0.581783
$814$	−13.7321	−	38.3205i	−0.481308	−	1.34313i
$815$			23.6603i			0.828783i
$816$	10.5359	+	10.5359i	0.368830	+	0.368830i
$817$	−5.19615	+	3.00000i	−0.181790	+	0.104957i
$818$	−22.4186	+	38.8301i	−0.783847	+	1.35766i
$819$	−0.267949	−	0.0717968i	−0.00936290	−	0.00250878i
$820$	−35.0526	+	9.39230i	−1.22409	+	0.327994i
$821$	−25.8564	+	14.9282i	−0.902395	+	0.520998i	−0.877976	−	0.478704i	$-0.841107\pi$
$821$	−25.8564	+	14.9282i	−0.902395	+	0.520998i	−0.0244184	+	0.999702i	$0.507773\pi$
$822$	−3.75833	+	14.0263i	−0.131087	+	0.489223i
$823$	−7.39230	−	4.26795i	−0.257680	−	0.148771i	0.365596	−	0.930774i	$-0.380865\pi$
$823$	−7.39230	−	4.26795i	−0.257680	−	0.148771i	−0.623276	+	0.782002i	$0.714199\pi$
$824$	−9.85641			−0.343364
$825$		−	6.00000i		−	0.208893i
$826$	14.6410			0.509426
$827$	−49.7128	−	13.3205i	−1.72868	−	0.463199i	−0.748805	−	0.662791i	$-0.769372\pi$
$827$	−49.7128	−	13.3205i	−1.72868	−	0.463199i	−0.979879	+	0.199591i	$0.936039\pi$
$828$	−2.00000	−	7.46410i	−0.0695048	−	0.259395i
$829$	−6.29423	−	23.4904i	−0.218608	−	0.815855i	−0.984865	−	0.173321i	$-0.944550\pi$
$829$	−6.29423	−	23.4904i	−0.218608	−	0.815855i	0.766258	−	0.642533i	$-0.222117\pi$
$830$	−29.8564			−1.03633
$831$	24.3564	−	6.52628i	0.844914	−	0.226394i
$832$	2.92820	+	0.784610i	0.101517	+	0.0272014i
$833$	23.2583	+	6.23205i	0.805853	+	0.215928i
$834$	2.53590	−	2.53590i	0.0878110	−	0.0878110i
$835$	12.9282	+	7.46410i	0.447399	+	0.258306i
$836$	38.7846	+	10.3923i	1.34139	+	0.359425i
$837$	7.19615	+	7.19615i	0.248735	+	0.248735i
$838$	−5.53590	−	20.6603i	−0.191234	−	0.713697i
$839$	24.2679	−	42.0333i	0.837823	−	1.45115i	−0.0538887	−	0.998547i	$-0.517162\pi$
$839$	24.2679	−	42.0333i	0.837823	−	1.45115i	0.891711	−	0.452604i	$-0.149505\pi$
$840$		−	4.00000i		−	0.138013i
$841$		−	0.339746i		−	0.0117154i
$842$		−	49.6603i		−	1.71141i
$843$	8.90192	+	8.90192i	0.306599	+	0.306599i
$844$		−	10.2487i		−	0.352775i
$845$	17.5622	−	17.5622i	0.604157	−	0.604157i
$846$	11.1962	−	3.00000i	0.384932	−	0.103142i
$847$	−7.22243	+	4.16987i	−0.248166	+	0.143279i
$848$	3.21539	+	1.85641i	0.110417	+	0.0637493i
$849$	2.16987	+	8.09808i	0.0744698	+	0.277925i
$850$	3.33975	+	5.78461i	0.114552	+	0.198410i
$851$	−7.92820	−	22.1244i	−0.271775	−	0.758413i
$852$	−9.80385	−	5.66025i	−0.335874	−	0.193917i
$853$	−6.74871	−	25.1865i	−0.231071	−	0.862370i	−0.979881	−	0.199585i	$-0.936041\pi$
$853$	−6.74871	−	25.1865i	−0.231071	−	0.862370i	0.748809	−	0.662786i	$-0.230626\pi$
$854$	−2.07180	+	3.58846i	−0.0708954	+	0.122794i
$855$	4.09808	+	7.09808i	0.140151	+	0.242749i
$856$	4.14359	−	15.4641i	0.141625	−	0.528552i
$857$	30.6147	−	30.6147i	1.04578	−	1.04578i	0.0468789	−	0.998901i	$-0.485073\pi$
$857$	30.6147	−	30.6147i	1.04578	−	1.04578i	0.998901	−	0.0468789i	$-0.0149275\pi$
$858$	1.26795	−	2.19615i	0.0432871	−	0.0749754i
$859$	20.5167	−	20.5167i	0.700019	−	0.700019i	−0.264395	−	0.964414i	$-0.585172\pi$
$859$	20.5167	−	20.5167i	0.700019	−	0.700019i	0.964414	+	0.264395i	$0.0851723\pi$
$860$	−4.73205	+	2.73205i	−0.161362	+	0.0931622i
$861$		−	6.87564i		−	0.234321i
$862$	−34.5167	+	19.9282i	−1.17564	+	0.678757i
$863$	4.73205	+	2.73205i	0.161081	+	0.0930001i	0.578373	−	0.815772i	$-0.303688\pi$
$863$	4.73205	+	2.73205i	0.161081	+	0.0930001i	−0.417293	+	0.908772i	$0.637021\pi$
$864$	−4.00000	−	4.00000i	−0.136083	−	0.136083i
$865$	−17.2942	−	17.2942i	−0.588021	−	0.588021i
$866$	26.6603	−	26.6603i	0.905952	−	0.905952i
$867$	1.56218	−	2.70577i	0.0530543	−	0.0918928i
$868$	14.3923	+	3.85641i	0.488507	+	0.130895i
$869$	28.8564	+	7.73205i	0.978887	+	0.262292i
$870$	−14.2942	+	3.83013i	−0.484620	+	0.129853i
$871$	−1.09103	−	4.07180i	−0.0369683	−	0.137968i
$872$	48.5885	+	28.0526i	1.64541	+	0.949980i
$873$	−3.57180	−	13.3301i	−0.120887	−	0.451156i
$874$	22.3923	+	6.00000i	0.757431	+	0.202953i
$875$	2.29423	−	8.56218i	0.0775591	−	0.289454i
$876$		0			0
$877$		−	13.6410i		−	0.460624i	−0.973117	−	0.230312i	$-0.926025\pi$
$877$		−	13.6410i		−	0.460624i	0.973117	−	0.230312i	$-0.0739747\pi$
$878$	−2.19615	+	1.26795i	−0.0741166	+	0.0427912i
$879$	−10.3301	+	17.8923i	−0.348427	+	0.603492i
$880$	35.3205	+	9.46410i	1.19065	+	0.319035i
$881$	29.6769	−	17.1340i	0.999841	−	0.577258i	0.0916395	−	0.995792i	$-0.470789\pi$
$881$	29.6769	−	17.1340i	0.999841	−	0.577258i	0.908201	+	0.418534i	$0.137456\pi$
$882$	−8.83013	−	2.36603i	−0.297326	−	0.0796682i
$883$	−8.39230	+	31.3205i	−0.282424	+	1.05402i	0.668278	+	0.743912i	$0.267032\pi$
$883$	−8.39230	+	31.3205i	−0.282424	+	1.05402i	−0.950702	+	0.310107i	$0.899635\pi$
$884$			2.82309i			0.0949506i
$885$	−23.6603	+	13.6603i	−0.795331	+	0.459184i
$886$	9.85641	+	9.85641i	0.331132	+	0.331132i
$887$	10.6795			0.358582			0.179291	−	0.983796i	$-0.442620\pi$
$887$	10.6795			0.358582			0.179291	+	0.983796i	$0.442620\pi$
$888$	−13.1244	−	11.1244i	−0.440425	−	0.373309i
$889$	−4.78461			−0.160471
$890$	19.3923	+	19.3923i	0.650032	+	0.650032i
$891$	−4.09808	+	2.36603i	−0.137291	+	0.0792648i
$892$	−4.78461			−0.160201
$893$	−9.00000	+	33.5885i	−0.301174	+	1.12399i
$894$	−17.0263	−	4.56218i	−0.569444	−	0.152582i
$895$	−26.6603	+	15.3923i	−0.891154	+	0.514508i
$896$	−8.00000	−	2.14359i	−0.267261	−	0.0716124i
$897$	0.732051	−	1.26795i	0.0244425	−	0.0423356i
$898$	−9.67949	+	5.58846i	−0.323009	+	0.186489i
$899$		−	55.1244i		−	1.83850i
$900$	−1.26795	−	2.19615i	−0.0422650	−	0.0732051i
$901$	−0.894882	+	3.33975i	−0.0298128	+	0.111263i
$902$	60.7128	+	16.2679i	2.02152	+	0.541663i
$903$	−0.267949	−	1.00000i	−0.00891679	−	0.0332779i
$904$	−31.8564	−	18.3923i	−1.05953	−	0.611719i
$905$	−9.79423	−	36.5526i	−0.325571	−	1.21505i
$906$	−16.1962	+	4.33975i	−0.538081	+	0.144178i
$907$	−40.1506	−	10.7583i	−1.33318	−	0.357224i	−0.479280	−	0.877662i	$-0.659102\pi$
$907$	−40.1506	−	10.7583i	−1.33318	−	0.357224i	−0.853900	+	0.520437i	$0.825769\pi$
$908$	13.4115	−	50.0526i	0.445078	−	1.66105i
$909$	6.42820	−	11.1340i	0.213210	−	0.369291i
$910$	0.535898	−	0.535898i	0.0177649	−	0.0177649i
$911$	−25.6603	−	25.6603i	−0.850162	−	0.850162i	0.139991	−	0.990153i	$-0.455293\pi$
$911$	−25.6603	−	25.6603i	−0.850162	−	0.850162i	−0.990153	+	0.139991i	$0.955293\pi$
$912$	16.3923	−	4.39230i	0.542803	−	0.145444i
$913$	44.7846	+	25.8564i	1.48215	+	0.855722i
$914$	−44.1506	+	25.4904i	−1.46037	+	0.843147i
$915$		−	7.73205i		−	0.255614i
$916$	−0.607695	−	1.05256i	−0.0200788	−	0.0347775i
$917$	0.679492	−	0.679492i	0.0224388	−	0.0224388i
$918$	2.63397	−	4.56218i	0.0869341	−	0.150574i
$919$	31.1769	−	31.1769i	1.02843	−	1.02843i	0.0288477	−	0.999584i	$-0.490816\pi$
$919$	31.1769	−	31.1769i	1.02843	−	1.02843i	0.999584	−	0.0288477i	$-0.00918378\pi$
$920$	20.3923	+	5.46410i	0.672314	+	0.180146i
$921$	−6.90192	−	11.9545i	−0.227426	−	0.393914i
$922$	5.33975	−	9.24871i	0.175855	−	0.304590i
$923$	−0.555136	−	2.07180i	−0.0182725	−	0.0681940i
$924$	−3.46410	+	6.00000i	−0.113961	+	0.197386i
$925$	−4.39230	−	6.33975i	−0.144418	−	0.208450i
$926$	−6.46410	−	11.1962i	−0.212424	−	0.367928i
$927$	0.901924	+	3.36603i	0.0296231	+	0.110555i
$928$			30.6410i			1.00584i
$929$	−13.2058	+	7.62436i	−0.433267	+	0.250147i	−0.700738	−	0.713419i	$-0.747146\pi$
$929$	−13.2058	+	7.62436i	−0.433267	+	0.250147i	0.267470	+	0.963566i	$0.413812\pi$
$930$	−26.8564	+	7.19615i	−0.880656	+	0.235971i
$931$	19.3923	−	19.3923i	0.635557	−	0.635557i
$932$	20.9282			0.685526
$933$	−11.1962	−	11.1962i	−0.366546	−	0.366546i
$934$		−	21.8564i		−	0.715163i
$935$			34.0526i			1.11364i
$936$		−	1.07180i		−	0.0350328i
$937$	−17.3301	+	30.0167i	−0.566151	+	0.980602i	0.430791	+	0.902452i	$0.358235\pi$
$937$	−17.3301	+	30.0167i	−0.566151	+	0.980602i	−0.996942	+	0.0781499i	$0.975099\pi$
$938$	2.98076	+	11.1244i	0.0973253	+	0.363223i
$939$	10.9019	+	10.9019i	0.355771	+	0.355771i
$940$	−8.19615	+	30.5885i	−0.267329	+	0.997685i
$941$	−6.69615	−	3.86603i	−0.218288	−	0.126029i	0.386869	−	0.922135i	$-0.373557\pi$
$941$	−6.69615	−	3.86603i	−0.218288	−	0.126029i	−0.605157	+	0.796106i	$0.706890\pi$
$942$	−5.39230	+	5.39230i	−0.175691	+	0.175691i
$943$	35.0526	+	9.39230i	1.14147	+	0.305856i
$944$	14.6410	+	54.6410i	0.476524	+	1.77841i
$945$	−1.36603	+	0.366025i	−0.0444368	+	0.0119068i
$946$	9.46410			0.307704
$947$	−5.85641	−	21.8564i	−0.190308	−	0.710238i	−0.993432	−	0.114426i	$-0.963497\pi$
$947$	−5.85641	−	21.8564i	−0.190308	−	0.710238i	0.803124	−	0.595812i	$-0.203170\pi$
$948$	12.1962	−	3.26795i	0.396113	−	0.106138i
$949$		0			0
$950$	7.60770			0.246826
$951$			6.66025i			0.215974i
$952$		−	7.71281i		−	0.249974i
$953$	−7.39230	−	4.26795i	−0.239460	−	0.138252i	0.375468	−	0.926835i	$-0.377482\pi$
$953$	−7.39230	−	4.26795i	−0.239460	−	0.138252i	−0.614929	+	0.788583i	$0.710815\pi$
$954$	0.339746	−	1.26795i	0.0109997	−	0.0410514i
$955$	−28.3923	+	16.3923i	−0.918753	+	0.530443i
$956$	−1.66025	−	6.19615i	−0.0536965	−	0.200398i
$957$	24.7583	+	6.63397i	0.800323	+	0.214446i
$958$	−26.3923	+	45.7128i	−0.852697	+	1.47691i
$959$	6.50962	−	3.75833i	0.210207	−	0.121363i
$960$	14.9282	−	4.00000i	0.481806	−	0.129099i
$961$		−	72.5692i		−	2.34094i
$962$	−0.267949	−	3.24871i	−0.00863903	−	0.104743i
$963$	−5.66025			−0.182399
$964$	−1.94744	+	7.26795i	−0.0627229	+	0.234085i
$965$	9.42820	+	16.3301i	0.303505	+	0.525685i
$966$	−2.00000	+	3.46410i	−0.0643489	+	0.111456i
$967$	2.39230	−	8.92820i	0.0769313	−	0.287112i	−0.916733	−	0.399501i	$-0.869184\pi$
$967$	2.39230	−	8.92820i	0.0769313	−	0.287112i	0.993664	+	0.112389i	$0.0358502\pi$
$968$	−22.7846	−	22.7846i	−0.732325	−	0.732325i
$969$	7.90192	+	13.6865i	0.253846	+	0.439675i
$970$	36.4186	+	9.75833i	1.16933	+	0.313321i
$971$	14.3205	−	24.8038i	0.459567	−	0.795993i	−0.539371	−	0.842068i	$-0.681338\pi$
$971$	14.3205	−	24.8038i	0.459567	−	0.795993i	0.998938	+	0.0460749i	$0.0146713\pi$
$972$	−1.00000	+	1.73205i	−0.0320750	+	0.0555556i
$973$	−1.85641			−0.0595137
$974$	46.9282			1.50368
$975$	0.124356	−	0.464102i	0.00398257	−	0.0148631i
$976$	−15.4641	−	4.14359i	−0.494994	−	0.132633i
$977$	−24.9545	+	6.68653i	−0.798365	+	0.213921i	−0.634866	−	0.772622i	$-0.718945\pi$
$977$	−24.9545	+	6.68653i	−0.798365	+	0.213921i	−0.163499	+	0.986544i	$0.552278\pi$
$978$		−	17.3205i		−	0.553849i
$979$	−12.2942	−	45.8827i	−0.392925	−	1.46642i
$980$	17.6603	−	17.6603i	0.564136	−	0.564136i
$981$	5.13397	−	19.1603i	0.163915	−	0.611740i
$982$	−20.7321	+	20.7321i	−0.661586	+	0.661586i
$983$	−13.2224	+	22.9019i	−0.421730	+	0.730458i	−0.996109	−	0.0881317i	$-0.971910\pi$
$983$	−13.2224	+	22.9019i	−0.421730	+	0.730458i	0.574379	+	0.818590i	$0.305244\pi$
$984$	25.6603	−	6.87564i	0.818019	−	0.219188i
$985$	−1.36603	+	1.36603i	−0.0435252	+	0.0435252i
$986$	−27.5622	+	7.38526i	−0.877759	+	0.235195i
$987$	−5.19615	−	3.00000i	−0.165395	−	0.0954911i
$988$	2.78461	+	1.60770i	0.0885902	+	0.0511476i
$989$	5.46410			0.173748
$990$		−	12.9282i		−	0.410885i
$991$	−27.4449	+	27.4449i	−0.871815	+	0.871815i	−0.992670	−	0.120855i	$-0.961436\pi$
$991$	−27.4449	+	27.4449i	−0.871815	+	0.871815i	0.120855	+	0.992670i	$0.461436\pi$
$992$			57.5692i			1.82782i
$993$	−5.66025	−	5.66025i	−0.179623	−	0.179623i
$994$	1.51666	+	5.66025i	0.0481055	+	0.179532i
$995$	26.0263	+	45.0788i	0.825089	+	1.42910i
$996$	21.8564			0.692547
$997$	14.2224	−	3.81089i	0.450429	−	0.120692i	−0.0264712	−	0.999650i	$-0.508427\pi$
$997$	14.2224	−	3.81089i	0.450429	−	0.120692i	0.476900	+	0.878958i	$0.341760\pi$
$998$	−10.6603	−	18.4641i	−0.337444	−	0.584471i
$999$	−2.59808	+	5.50000i	−0.0821995	+	0.174012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.bu.a.643.1	✓	4
8.3	odd	2		888.2.bu.b.643.1	yes	4
37.8	odd	12		888.2.bu.b.859.1	yes	4
296.267	even	12	inner	888.2.bu.a.859.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.bu.a.643.1	✓	4	1.1	even	1	trivial
888.2.bu.a.859.1	yes	4	296.267	even	12	inner
888.2.bu.b.643.1	yes	4	8.3	odd	2
888.2.bu.b.859.1	yes	4	37.8	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(0.866025 - 0.500000i) q^{3} -2.00000i q^{4} +(0.500000 - 1.86603i) q^{5} +(-0.366025 + 1.36603i) q^{6} +(0.633975 - 0.366025i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(0.866025 - 0.500000i) q^{3} -2.00000i q^{4} +(0.500000 - 1.86603i) q^{5} +(-0.366025 + 1.36603i) q^{6} +(0.633975 - 0.366025i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.500000 - 0.866025i) q^{9} +(1.36603 + 2.36603i) q^{10} -4.73205i q^{11} +(-1.00000 - 1.73205i) q^{12} +(0.0980762 - 0.366025i) q^{13} +(-0.267949 + 1.00000i) q^{14} +(-0.500000 - 1.86603i) q^{15} -4.00000 q^{16} +(-0.964102 - 3.59808i) q^{17} +(0.366025 + 1.36603i) q^{18} +(-4.09808 - 1.09808i) q^{19} +(-3.73205 - 1.00000i) q^{20} +(0.366025 - 0.633975i) q^{21} +(4.73205 + 4.73205i) q^{22} +(2.73205 + 2.73205i) q^{23} +(2.73205 + 0.732051i) q^{24} +(1.09808 + 0.633975i) q^{25} +(0.267949 + 0.464102i) q^{26} -1.00000i q^{27} +(-0.732051 - 1.26795i) q^{28} +(-3.83013 + 3.83013i) q^{29} +(2.36603 + 1.36603i) q^{30} +(-7.19615 + 7.19615i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-2.36603 - 4.09808i) q^{33} +(4.56218 + 2.63397i) q^{34} +(-0.366025 - 1.36603i) q^{35} +(-1.73205 - 1.00000i) q^{36} +(-5.50000 - 2.59808i) q^{37} +(5.19615 - 3.00000i) q^{38} +(-0.0980762 - 0.366025i) q^{39} +(4.73205 - 2.73205i) q^{40} +(8.13397 - 4.69615i) q^{41} +(0.267949 + 1.00000i) q^{42} +(1.00000 - 1.00000i) q^{43} -9.46410 q^{44} +(-1.36603 - 1.36603i) q^{45} -5.46410 q^{46} -8.19615i q^{47} +(-3.46410 + 2.00000i) q^{48} +(-3.23205 + 5.59808i) q^{49} +(-1.73205 + 0.464102i) q^{50} +(-2.63397 - 2.63397i) q^{51} +(-0.732051 - 0.196152i) q^{52} +(-0.803848 - 0.464102i) q^{53} +(1.00000 + 1.00000i) q^{54} +(-8.83013 - 2.36603i) q^{55} +(2.00000 + 0.535898i) q^{56} +(-4.09808 + 1.09808i) q^{57} -7.66025i q^{58} +(-3.66025 - 13.6603i) q^{59} +(-3.73205 + 1.00000i) q^{60} +(3.86603 + 1.03590i) q^{61} -14.3923i q^{62} -0.732051i q^{63} +8.00000i q^{64} +(-0.633975 - 0.366025i) q^{65} +(6.46410 + 1.73205i) q^{66} +(9.63397 - 5.56218i) q^{67} +(-7.19615 + 1.92820i) q^{68} +(3.73205 + 1.00000i) q^{69} +(1.73205 + 1.00000i) q^{70} +(4.90192 - 2.83013i) q^{71} +(2.73205 - 0.732051i) q^{72} +(8.09808 - 2.90192i) q^{74} +1.26795 q^{75} +(-2.19615 + 8.19615i) q^{76} +(-1.73205 - 3.00000i) q^{77} +(0.464102 + 0.267949i) q^{78} +(-1.63397 + 6.09808i) q^{79} +(-2.00000 + 7.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.43782 + 12.8301i) q^{82} +(-5.46410 + 9.46410i) q^{83} +(-1.26795 - 0.732051i) q^{84} -7.19615 q^{85} +2.00000i q^{86} +(-1.40192 + 5.23205i) q^{87} +(9.46410 - 9.46410i) q^{88} +(9.69615 - 2.59808i) q^{89} +2.73205 q^{90} +(-0.0717968 - 0.267949i) q^{91} +(5.46410 - 5.46410i) q^{92} +(-2.63397 + 9.83013i) q^{93} +(8.19615 + 8.19615i) q^{94} +(-4.09808 + 7.09808i) q^{95} +(1.46410 - 5.46410i) q^{96} +(9.75833 - 9.75833i) q^{97} +(-2.36603 - 8.83013i) q^{98} +(-4.09808 - 2.36603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 2 q^{5} + 2 q^{6} + 6 q^{7} + 8 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 2 * q^5 + 2 * q^6 + 6 * q^7 + 8 * q^8 + 2 * q^9	\( 4 q - 4 q^{2} + 2 q^{5} + 2 q^{6} + 6 q^{7} + 8 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{12} - 10 q^{13} - 8 q^{14} - 2 q^{15} - 16 q^{16} + 10 q^{17} - 2 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} + 12 q^{22} + 4 q^{23} + 4 q^{24} - 6 q^{25} + 8 q^{26} + 4 q^{28} + 2 q^{29} + 6 q^{30} - 8 q^{31} + 16 q^{32} - 6 q^{33} - 6 q^{34} + 2 q^{35} - 22 q^{37} + 10 q^{39} + 12 q^{40} + 36 q^{41} + 8 q^{42} + 4 q^{43} - 24 q^{44} - 2 q^{45} - 8 q^{46} - 6 q^{49} - 14 q^{51} + 4 q^{52} - 24 q^{53} + 4 q^{54} - 18 q^{55} + 8 q^{56} - 6 q^{57} + 20 q^{59} - 8 q^{60} + 12 q^{61} - 6 q^{65} + 12 q^{66} + 42 q^{67} - 8 q^{68} + 8 q^{69} + 30 q^{71} + 4 q^{72} + 22 q^{74} + 12 q^{75} + 12 q^{76} - 12 q^{78} - 10 q^{79} - 8 q^{80} - 2 q^{81} - 38 q^{82} - 8 q^{83} - 12 q^{84} - 8 q^{85} - 16 q^{87} + 24 q^{88} + 18 q^{89} + 4 q^{90} - 28 q^{91} + 8 q^{92} - 14 q^{93} + 12 q^{94} - 6 q^{95} - 8 q^{96} - 6 q^{97} - 6 q^{98} - 6 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 2 * q^5 + 2 * q^6 + 6 * q^7 + 8 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^12 - 10 * q^13 - 8 * q^14 - 2 * q^15 - 16 * q^16 + 10 * q^17 - 2 * q^18 - 6 * q^19 - 8 * q^20 - 2 * q^21 + 12 * q^22 + 4 * q^23 + 4 * q^24 - 6 * q^25 + 8 * q^26 + 4 * q^28 + 2 * q^29 + 6 * q^30 - 8 * q^31 + 16 * q^32 - 6 * q^33 - 6 * q^34 + 2 * q^35 - 22 * q^37 + 10 * q^39 + 12 * q^40 + 36 * q^41 + 8 * q^42 + 4 * q^43 - 24 * q^44 - 2 * q^45 - 8 * q^46 - 6 * q^49 - 14 * q^51 + 4 * q^52 - 24 * q^53 + 4 * q^54 - 18 * q^55 + 8 * q^56 - 6 * q^57 + 20 * q^59 - 8 * q^60 + 12 * q^61 - 6 * q^65 + 12 * q^66 + 42 * q^67 - 8 * q^68 + 8 * q^69 + 30 * q^71 + 4 * q^72 + 22 * q^74 + 12 * q^75 + 12 * q^76 - 12 * q^78 - 10 * q^79 - 8 * q^80 - 2 * q^81 - 38 * q^82 - 8 * q^83 - 12 * q^84 - 8 * q^85 - 16 * q^87 + 24 * q^88 + 18 * q^89 + 4 * q^90 - 28 * q^91 + 8 * q^92 - 14 * q^93 + 12 * q^94 - 6 * q^95 - 8 * q^96 - 6 * q^97 - 6 * q^98 - 6 * q^99

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