LMFDB - Embedded newform 888.2.bu.a.547.1

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			547.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	888.547
Dual form			888.2.bu.a.763.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-0.866025 - 0.500000i) q^{3} -2.00000i q^{4} +(0.500000 - 0.133975i) q^{5} +(1.36603 - 0.366025i) q^{6} +(2.36603 + 1.36603i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-0.866025 - 0.500000i) q^{3} -2.00000i q^{4} +(0.500000 - 0.133975i) q^{5} +(1.36603 - 0.366025i) q^{6} +(2.36603 + 1.36603i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.366025 + 0.633975i) q^{10} -1.26795i q^{11} +(-1.00000 + 1.73205i) q^{12} +(-5.09808 + 1.36603i) q^{13} +(-3.73205 + 1.00000i) q^{14} +(-0.500000 - 0.133975i) q^{15} -4.00000 q^{16} +(5.96410 + 1.59808i) q^{17} +(-1.36603 - 0.366025i) q^{18} +(1.09808 + 4.09808i) q^{19} +(-0.267949 - 1.00000i) q^{20} +(-1.36603 - 2.36603i) q^{21} +(1.26795 + 1.26795i) q^{22} +(-0.732051 - 0.732051i) q^{23} +(-0.732051 - 2.73205i) q^{24} +(-4.09808 + 2.36603i) q^{25} +(3.73205 - 6.46410i) q^{26} -1.00000i q^{27} +(2.73205 - 4.73205i) q^{28} +(4.83013 - 4.83013i) q^{29} +(0.633975 - 0.366025i) q^{30} +(3.19615 - 3.19615i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-0.633975 + 1.09808i) q^{33} +(-7.56218 + 4.36603i) q^{34} +(1.36603 + 0.366025i) q^{35} +(1.73205 - 1.00000i) q^{36} +(-5.50000 + 2.59808i) q^{37} +(-5.19615 - 3.00000i) q^{38} +(5.09808 + 1.36603i) q^{39} +(1.26795 + 0.732051i) q^{40} +(9.86603 + 5.69615i) q^{41} +(3.73205 + 1.00000i) q^{42} +(1.00000 - 1.00000i) q^{43} -2.53590 q^{44} +(0.366025 + 0.366025i) q^{45} +1.46410 q^{46} +2.19615i q^{47} +(3.46410 + 2.00000i) q^{48} +(0.232051 + 0.401924i) q^{49} +(1.73205 - 6.46410i) q^{50} +(-4.36603 - 4.36603i) q^{51} +(2.73205 + 10.1962i) q^{52} +(-11.1962 + 6.46410i) q^{53} +(1.00000 + 1.00000i) q^{54} +(-0.169873 - 0.633975i) q^{55} +(2.00000 + 7.46410i) q^{56} +(1.09808 - 4.09808i) q^{57} +9.66025i q^{58} +(13.6603 + 3.66025i) q^{59} +(-0.267949 + 1.00000i) q^{60} +(2.13397 + 7.96410i) q^{61} +6.39230i q^{62} +2.73205i q^{63} +8.00000i q^{64} +(-2.36603 + 1.36603i) q^{65} +(-0.464102 - 1.73205i) q^{66} +(11.3660 + 6.56218i) q^{67} +(3.19615 - 11.9282i) q^{68} +(0.267949 + 1.00000i) q^{69} +(-1.73205 + 1.00000i) q^{70} +(10.0981 + 5.83013i) q^{71} +(-0.732051 + 2.73205i) q^{72} +(2.90192 - 8.09808i) q^{74} +4.73205 q^{75} +(8.19615 - 2.19615i) q^{76} +(1.73205 - 3.00000i) q^{77} +(-6.46410 + 3.73205i) q^{78} +(-3.36603 + 0.901924i) q^{79} +(-2.00000 + 0.535898i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-15.5622 + 4.16987i) q^{82} +(1.46410 + 2.53590i) q^{83} +(-4.73205 + 2.73205i) q^{84} +3.19615 q^{85} +2.00000i q^{86} +(-6.59808 + 1.76795i) q^{87} +(2.53590 - 2.53590i) q^{88} +(-0.696152 + 2.59808i) q^{89} -0.732051 q^{90} +(-13.9282 - 3.73205i) q^{91} +(-1.46410 + 1.46410i) q^{92} +(-4.36603 + 1.16987i) q^{93} +(-2.19615 - 2.19615i) q^{94} +(1.09808 + 1.90192i) q^{95} +(-5.46410 + 1.46410i) q^{96} +(-12.7583 + 12.7583i) q^{97} +(-0.633975 - 0.169873i) q^{98} +(1.09808 - 0.633975i) 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 $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

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	−	0.133975i	0.223607	−	0.0599153i	−0.145276	−	0.989391i	$-0.546407\pi$
$5$	0.500000	−	0.133975i	0.223607	−	0.0599153i	0.368883	+	0.929476i	$0.379740\pi$
$6$	1.36603	−	0.366025i	0.557678	−	0.149429i
$7$	2.36603	+	1.36603i	0.894274	+	0.516309i	0.875338	−	0.483512i	$-0.160639\pi$
$7$	2.36603	+	1.36603i	0.894274	+	0.516309i	0.0189356	+	0.999821i	$0.493972\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.366025	+	0.633975i	−0.115747	+	0.200480i
$11$		−	1.26795i		−	0.382301i	−0.981561	−	0.191151i	$-0.938778\pi$
$11$		−	1.26795i		−	0.382301i	0.981561	−	0.191151i	$-0.0612219\pi$
$12$	−1.00000	+	1.73205i	−0.288675	+	0.500000i
$13$	−5.09808	+	1.36603i	−1.41395	+	0.378867i	−0.883334	−	0.468744i	$-0.844707\pi$
$13$	−5.09808	+	1.36603i	−1.41395	+	0.378867i	−0.530618	+	0.847611i	$0.678040\pi$
$14$	−3.73205	+	1.00000i	−0.997433	+	0.267261i
$15$	−0.500000	−	0.133975i	−0.129099	−	0.0345921i
$16$	−4.00000			−1.00000
$17$	5.96410	+	1.59808i	1.44651	+	0.387590i	0.894807	−	0.446452i	$-0.147313\pi$
$17$	5.96410	+	1.59808i	1.44651	+	0.387590i	0.551700	+	0.834043i	$0.313979\pi$
$18$	−1.36603	−	0.366025i	−0.321975	−	0.0862730i
$19$	1.09808	+	4.09808i	0.251916	+	0.940163i	0.969780	+	0.243980i	$0.0784532\pi$
$19$	1.09808	+	4.09808i	0.251916	+	0.940163i	−0.717864	+	0.696183i	$0.754880\pi$
$20$	−0.267949	−	1.00000i	−0.0599153	−	0.223607i
$21$	−1.36603	−	2.36603i	−0.298091	−	0.516309i
$22$	1.26795	+	1.26795i	0.270328	+	0.270328i
$23$	−0.732051	−	0.732051i	−0.152643	−	0.152643i	0.626654	−	0.779297i	$-0.284424\pi$
$23$	−0.732051	−	0.732051i	−0.152643	−	0.152643i	−0.779297	+	0.626654i	$0.784424\pi$
$24$	−0.732051	−	2.73205i	−0.149429	−	0.557678i
$25$	−4.09808	+	2.36603i	−0.819615	+	0.473205i
$26$	3.73205	−	6.46410i	0.731915	−	1.26771i
$27$		−	1.00000i		−	0.192450i
$28$	2.73205	−	4.73205i	0.516309	−	0.894274i
$29$	4.83013	−	4.83013i	0.896932	−	0.896932i	−0.0982315	−	0.995164i	$-0.531319\pi$
$29$	4.83013	−	4.83013i	0.896932	−	0.896932i	0.995164	+	0.0982315i	$0.0313186\pi$
$30$	0.633975	−	0.366025i	0.115747	−	0.0668268i
$31$	3.19615	−	3.19615i	0.574046	−	0.574046i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	3.19615	−	3.19615i	0.574046	−	0.574046i	0.933257	+	0.359211i	$0.116954\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	−0.633975	+	1.09808i	−0.110361	+	0.191151i
$34$	−7.56218	+	4.36603i	−1.29690	+	0.748767i
$35$	1.36603	+	0.366025i	0.230900	+	0.0618696i
$36$	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
$39$	5.09808	+	1.36603i	0.816346	+	0.218739i
$40$	1.26795	+	0.732051i	0.200480	+	0.115747i
$41$	9.86603	+	5.69615i	1.54081	+	0.889590i	0.998788	+	0.0492283i	$0.0156762\pi$
$41$	9.86603	+	5.69615i	1.54081	+	0.889590i	0.542027	+	0.840361i	$0.317657\pi$
$42$	3.73205	+	1.00000i	0.575868	+	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	$0.215609\pi$
$44$	−2.53590			−0.382301
$45$	0.366025	+	0.366025i	0.0545638	+	0.0545638i
$46$	1.46410			0.215870
$47$			2.19615i			0.320342i	0.987089	+	0.160171i	$0.0512045\pi$
$47$			2.19615i			0.320342i	−0.987089	+	0.160171i	$0.948795\pi$
$48$	3.46410	+	2.00000i	0.500000	+	0.288675i
$49$	0.232051	+	0.401924i	0.0331501	+	0.0574177i
$50$	1.73205	−	6.46410i	0.244949	−	0.914162i
$51$	−4.36603	−	4.36603i	−0.611366	−	0.611366i
$52$	2.73205	+	10.1962i	0.378867	+	1.41395i
$53$	−11.1962	+	6.46410i	−1.53791	+	0.887913i	−0.538949	+	0.842338i	$0.681178\pi$
$53$	−11.1962	+	6.46410i	−1.53791	+	0.887913i	−0.998961	+	0.0455742i	$0.985488\pi$
$54$	1.00000	+	1.00000i	0.136083	+	0.136083i
$55$	−0.169873	−	0.633975i	−0.0229057	−	0.0854851i
$56$	2.00000	+	7.46410i	0.267261	+	0.997433i
$57$	1.09808	−	4.09808i	0.145444	−	0.542803i
$58$			9.66025i			1.26845i
$59$	13.6603	+	3.66025i	1.77841	+	0.476524i	0.990293	−	0.138996i	$-0.0443876\pi$
$59$	13.6603	+	3.66025i	1.77841	+	0.476524i	0.788121	+	0.615521i	$0.211054\pi$
$60$	−0.267949	+	1.00000i	−0.0345921	+	0.129099i
$61$	2.13397	+	7.96410i	0.273227	+	1.01970i	0.957020	+	0.290022i	$0.0936627\pi$
$61$	2.13397	+	7.96410i	0.273227	+	1.01970i	−0.683792	+	0.729677i	$0.739671\pi$
$62$			6.39230i			0.811824i
$63$			2.73205i			0.344206i
$64$			8.00000i			1.00000i
$65$	−2.36603	+	1.36603i	−0.293469	+	0.169435i
$66$	−0.464102	−	1.73205i	−0.0571270	−	0.213201i
$67$	11.3660	+	6.56218i	1.38858	+	0.801698i	0.993155	−	0.116800i	$-0.0372638\pi$
$67$	11.3660	+	6.56218i	1.38858	+	0.801698i	0.395426	+	0.918498i	$0.370597\pi$
$68$	3.19615	−	11.9282i	0.387590	−	1.44651i
$69$	0.267949	+	1.00000i	0.0322573	+	0.120386i
$70$	−1.73205	+	1.00000i	−0.207020	+	0.119523i
$71$	10.0981	+	5.83013i	1.19842	+	0.691909i	0.960203	−	0.279303i	$-0.0901034\pi$
$71$	10.0981	+	5.83013i	1.19842	+	0.691909i	0.238218	+	0.971212i	$0.423437\pi$
$72$	−0.732051	+	2.73205i	−0.0862730	+	0.321975i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	2.90192	−	8.09808i	0.337342	−	0.941382i
$75$	4.73205			0.546410
$76$	8.19615	−	2.19615i	0.940163	−	0.251916i
$77$	1.73205	−	3.00000i	0.197386	−	0.341882i
$78$	−6.46410	+	3.73205i	−0.731915	+	0.422572i
$79$	−3.36603	+	0.901924i	−0.378707	+	0.101474i	−0.443151	−	0.896447i	$-0.646139\pi$
$79$	−3.36603	+	0.901924i	−0.378707	+	0.101474i	0.0644435	+	0.997921i	$0.479473\pi$
$80$	−2.00000	+	0.535898i	−0.223607	+	0.0599153i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−15.5622	+	4.16987i	−1.71856	+	0.460485i
$83$	1.46410	+	2.53590i	0.160706	+	0.278351i	0.935122	−	0.354326i	$-0.115290\pi$
$83$	1.46410	+	2.53590i	0.160706	+	0.278351i	−0.774416	+	0.632677i	$0.781956\pi$
$84$	−4.73205	+	2.73205i	−0.516309	+	0.298091i
$85$	3.19615			0.346671
$86$			2.00000i			0.215666i
$87$	−6.59808	+	1.76795i	−0.707388	+	0.189544i
$88$	2.53590	−	2.53590i	0.270328	−	0.270328i
$89$	−0.696152	+	2.59808i	−0.0737920	+	0.275396i	−0.992957	−	0.118478i	$-0.962199\pi$
$89$	−0.696152	+	2.59808i	−0.0737920	+	0.275396i	0.919165	+	0.393873i	$0.128865\pi$
$90$	−0.732051			−0.0771649
$91$	−13.9282	−	3.73205i	−1.46007	−	0.391225i
$92$	−1.46410	+	1.46410i	−0.152643	+	0.152643i
$93$	−4.36603	+	1.16987i	−0.452736	+	0.121310i
$94$	−2.19615	−	2.19615i	−0.226516	−	0.226516i
$95$	1.09808	+	1.90192i	0.112660	+	0.195133i
$96$	−5.46410	+	1.46410i	−0.557678	+	0.149429i
$97$	−12.7583	+	12.7583i	−1.29541	+	1.29541i	−0.364022	+	0.931390i	$0.618597\pi$
$97$	−12.7583	+	12.7583i	−1.29541	+	1.29541i	−0.931390	+	0.364022i	$0.881403\pi$
$98$	−0.633975	−	0.169873i	−0.0640411	−	0.0171598i
$99$	1.09808	−	0.633975i	0.110361	−	0.0637168i
$100$	4.73205	+	8.19615i	0.473205	+	0.819615i
$101$	−14.8564			−1.47827			−0.739134	−	0.673559i	$-0.764765\pi$
$101$	−14.8564			−1.47827			−0.739134	+	0.673559i	$0.764765\pi$
$102$	8.73205			0.864602
$103$	4.46410	−	4.46410i	0.439861	−	0.439861i	−0.452104	−	0.891965i	$-0.649326\pi$
$103$	4.46410	−	4.46410i	0.439861	−	0.439861i	0.891965	+	0.452104i	$0.149326\pi$
$104$	−12.9282	−	7.46410i	−1.26771	−	0.731915i
$105$	−1.00000	−	1.00000i	−0.0975900	−	0.0975900i
$106$	4.73205	−	17.6603i	0.459617	−	1.71532i
$107$	5.83013	−	10.0981i	0.563620	−	0.976218i	−0.433557	−	0.901126i	$-0.642742\pi$
$107$	5.83013	−	10.0981i	0.563620	−	0.976218i	0.997177	−	0.0750917i	$-0.0239250\pi$
$108$	−2.00000			−0.192450
$109$	1.83975	−	6.86603i	0.176216	−	0.657646i	−0.820126	−	0.572183i	$-0.806097\pi$
$109$	1.83975	−	6.86603i	0.176216	−	0.657646i	0.996341	−	0.0854625i	$-0.0272368\pi$
$110$	0.803848	+	0.464102i	0.0766439	+	0.0442504i
$111$	6.06218	+	0.500000i	0.575396	+	0.0474579i
$112$	−9.46410	−	5.46410i	−0.894274	−	0.516309i
$113$	−0.437822	+	1.63397i	−0.0411868	+	0.153711i	−0.983457	−	0.181143i	$-0.942020\pi$
$113$	−0.437822	+	1.63397i	−0.0411868	+	0.153711i	0.942270	+	0.334854i	$0.108687\pi$
$114$	3.00000	+	5.19615i	0.280976	+	0.486664i
$115$	−0.464102	−	0.267949i	−0.0432777	−	0.0249864i
$116$	−9.66025	−	9.66025i	−0.896932	−	0.896932i
$117$	−3.73205	−	3.73205i	−0.345028	−	0.345028i
$118$	−17.3205	+	10.0000i	−1.59448	+	0.920575i
$119$	11.9282	+	11.9282i	1.09346	+	1.09346i
$120$	−0.732051	−	1.26795i	−0.0668268	−	0.115747i
$121$	9.39230			0.853846
$122$	−10.0981	−	5.83013i	−0.914237	−	0.527835i
$123$	−5.69615	−	9.86603i	−0.513605	−	0.889590i
$124$	−6.39230	−	6.39230i	−0.574046	−	0.574046i
$125$	−3.56218	+	3.56218i	−0.318611	+	0.318611i
$126$	−2.73205	−	2.73205i	−0.243390	−	0.243390i
$127$	11.6603	−	6.73205i	1.03468	−	0.597373i	0.116358	−	0.993207i	$-0.462878\pi$
$127$	11.6603	−	6.73205i	1.03468	−	0.597373i	0.918322	+	0.395834i	$0.129545\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$	−1.36603	+	0.366025i	−0.120272	+	0.0322267i
$130$	1.00000	−	3.73205i	0.0877058	−	0.327323i
$131$	4.73205	−	17.6603i	0.413441	−	1.54298i	−0.374496	−	0.927228i	$-0.622184\pi$
$131$	4.73205	−	17.6603i	0.413441	−	1.54298i	0.787938	−	0.615755i	$-0.211149\pi$
$132$	2.19615	+	1.26795i	0.191151	+	0.110361i
$133$	−3.00000	+	11.1962i	−0.260133	+	0.970830i
$134$	−17.9282	+	4.80385i	−1.54876	+	0.414989i
$135$	−0.133975	−	0.500000i	−0.0115307	−	0.0430331i
$136$	8.73205	+	15.1244i	0.748767	+	1.29690i
$137$	13.7321			1.17321			0.586604	−	0.809874i	$-0.300464\pi$
$137$	13.7321			1.17321			0.586604	+	0.809874i	$0.300464\pi$
$138$	−1.26795	−	0.732051i	−0.107935	−	0.0623163i
$139$	8.19615	−	4.73205i	0.695189	−	0.401367i	−0.110364	−	0.993891i	$-0.535202\pi$
$139$	8.19615	−	4.73205i	0.695189	−	0.401367i	0.805553	+	0.592524i	$0.201868\pi$
$140$	0.732051	−	2.73205i	0.0618696	−	0.230900i
$141$	1.09808	−	1.90192i	0.0924747	−	0.160171i
$142$	−15.9282	+	4.26795i	−1.33667	+	0.358158i
$143$	1.73205	+	6.46410i	0.144841	+	0.540555i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	1.76795	−	3.06218i	0.146820	−	0.254300i
$146$		0			0
$147$		−	0.464102i		−	0.0382785i
$148$	5.19615	+	11.0000i	0.427121	+	0.904194i
$149$			5.53590i			0.453518i	0.973951	+	0.226759i	$0.0728131\pi$
$149$			5.53590i			0.453518i	−0.973951	+	0.226759i	$0.927187\pi$
$150$	−4.73205	+	4.73205i	−0.386370	+	0.386370i
$151$	−7.92820	+	13.7321i	−0.645188	+	1.11750i	0.339070	+	0.940761i	$0.389888\pi$
$151$	−7.92820	+	13.7321i	−0.645188	+	1.11750i	−0.984258	+	0.176737i	$0.943446\pi$
$152$	−6.00000	+	10.3923i	−0.486664	+	0.842927i
$153$	1.59808	+	5.96410i	0.129197	+	0.482169i
$154$	1.26795	+	4.73205i	0.102174	+	0.381320i
$155$	1.16987	−	2.02628i	0.0939665	−	0.162755i
$156$	2.73205	−	10.1962i	0.218739	−	0.816346i
$157$	13.3301	−	7.69615i	1.06386	−	0.614220i	0.137362	−	0.990521i	$-0.456137\pi$
$157$	13.3301	−	7.69615i	1.06386	−	0.614220i	0.926497	+	0.376301i	$0.122804\pi$
$158$	2.46410	−	4.26795i	0.196033	−	0.339540i
$159$	12.9282			1.02527
$160$	1.46410	−	2.53590i	0.115747	−	0.200480i
$161$	−0.732051	−	2.73205i	−0.0576937	−	0.215316i
$162$	−0.366025	−	1.36603i	−0.0287577	−	0.107325i
$163$	−3.16987	+	11.8301i	−0.248284	+	0.926607i	0.723421	+	0.690407i	$0.242569\pi$
$163$	−3.16987	+	11.8301i	−0.248284	+	0.926607i	−0.971705	+	0.236200i	$0.924098\pi$
$164$	11.3923	−	19.7321i	0.889590	−	1.54081i
$165$	−0.169873	+	0.633975i	−0.0132246	+	0.0493549i
$166$	−4.00000	−	1.07180i	−0.310460	−	0.0831876i
$167$	−2.00000	+	0.535898i	−0.154765	+	0.0414691i	−0.335369	−	0.942087i	$-0.608861\pi$
$167$	−2.00000	+	0.535898i	−0.154765	+	0.0414691i	0.180605	+	0.983556i	$0.442194\pi$
$168$	2.00000	−	7.46410i	0.154303	−	0.575868i
$169$	12.8660	−	7.42820i	0.989694	−	0.571400i
$170$	−3.19615	+	3.19615i	−0.245134	+	0.245134i
$171$	−3.00000	+	3.00000i	−0.229416	+	0.229416i
$172$	−2.00000	−	2.00000i	−0.152499	−	0.152499i
$173$	−2.33013	−	4.03590i	−0.177156	−	0.306844i	0.763749	−	0.645513i	$-0.223356\pi$
$173$	−2.33013	−	4.03590i	−0.177156	−	0.306844i	−0.940905	+	0.338670i	$0.890023\pi$
$174$	4.83013	−	8.36603i	0.366171	−	0.634227i
$175$	−12.9282			−0.977280
$176$			5.07180i			0.382301i
$177$	−10.0000	−	10.0000i	−0.751646	−	0.751646i
$178$	−1.90192	−	3.29423i	−0.142555	−	0.246913i
$179$	−14.7321	−	14.7321i	−1.10113	−	1.10113i	−0.994275	−	0.106850i	$-0.965924\pi$
$179$	−14.7321	−	14.7321i	−1.10113	−	1.10113i	−0.106850	−	0.994275i	$-0.534076\pi$
$180$	0.732051	−	0.732051i	0.0545638	−	0.0545638i
$181$	10.0359	+	5.79423i	0.745962	+	0.430682i	0.824233	−	0.566251i	$-0.191607\pi$
$181$	10.0359	+	5.79423i	0.745962	+	0.430682i	−0.0782707	+	0.996932i	$0.524940\pi$
$182$	17.6603	−	10.1962i	1.30907	−	0.755789i
$183$	2.13397	−	7.96410i	0.157748	−	0.588723i
$184$		−	2.92820i		−	0.215870i
$185$	−2.40192	+	2.03590i	−0.176593	+	0.149682i
$186$	3.19615	−	5.53590i	0.234353	−	0.405912i
$187$	2.02628	−	7.56218i	0.148176	−	0.553001i
$188$	4.39230			0.320342
$189$	1.36603	−	2.36603i	0.0993637	−	0.172103i
$190$	−3.00000	−	0.803848i	−0.217643	−	0.0583172i
$191$	−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
$193$	−12.0981	+	12.0981i	−0.870839	+	0.870839i	−0.992564	−	0.121725i	$-0.961157\pi$
$193$	−12.0981	+	12.0981i	−0.870839	+	0.870839i	0.121725	+	0.992564i	$0.461157\pi$
$194$		−	25.5167i		−	1.83199i
$195$	2.73205			0.195646
$196$	0.803848	−	0.464102i	0.0574177	−	0.0331501i
$197$	0.866025	−	0.500000i	0.0617018	−	0.0356235i	−0.468832	−	0.883287i	$-0.655325\pi$
$197$	0.866025	−	0.500000i	0.0617018	−	0.0356235i	0.530534	+	0.847664i	$0.321992\pi$
$198$	−0.464102	+	1.73205i	−0.0329823	+	0.123091i
$199$	19.0526	−	19.0526i	1.35060	−	1.35060i	0.465610	−	0.884990i	$-0.345835\pi$
$199$	19.0526	−	19.0526i	1.35060	−	1.35060i	0.884990	−	0.465610i	$-0.154165\pi$
$200$	−12.9282	−	3.46410i	−0.914162	−	0.244949i
$201$	−6.56218	−	11.3660i	−0.462860	−	0.801698i
$202$	14.8564	−	14.8564i	1.04529	−	1.04529i
$203$	18.0263	−	4.83013i	1.26520	−	0.339008i
$204$	−8.73205	+	8.73205i	−0.611366	+	0.611366i
$205$	5.69615	+	1.52628i	0.397837	+	0.106600i
$206$			8.92820i			0.622057i
$207$	0.267949	−	1.00000i	0.0186238	−	0.0695048i
$208$	20.3923	−	5.46410i	1.41395	−	0.378867i
$209$	5.19615	−	1.39230i	0.359425	−	0.0963077i
$210$	2.00000			0.138013
$211$	−19.1244			−1.31657			−0.658287	−	0.752767i	$-0.728719\pi$
$211$	−19.1244			−1.31657			−0.658287	+	0.752767i	$0.728719\pi$
$212$	12.9282	+	22.3923i	0.887913	+	1.53791i
$213$	−5.83013	−	10.0981i	−0.399474	−	0.691909i
$214$	4.26795	+	15.9282i	0.291751	+	1.08883i
$215$	0.366025	−	0.633975i	0.0249627	−	0.0432367i
$216$	2.00000	−	2.00000i	0.136083	−	0.136083i
$217$	11.9282	−	3.19615i	0.809739	−	0.216969i
$218$	5.02628	+	8.70577i	0.340423	+	0.589629i
$219$		0			0
$220$	−1.26795	+	0.339746i	−0.0854851	+	0.0229057i
$221$	−32.5885			−2.19214
$222$	−6.56218	+	5.56218i	−0.440425	+	0.373309i
$223$			18.3923i			1.23164i	0.787887	+	0.615820i	$0.211175\pi$
$223$			18.3923i			1.23164i	−0.787887	+	0.615820i	$0.788825\pi$
$224$	14.9282	−	4.00000i	0.997433	−	0.267261i
$225$	−4.09808	−	2.36603i	−0.273205	−	0.157735i
$226$	−1.19615	−	2.07180i	−0.0795669	−	0.137814i
$227$	5.97372	+	22.2942i	0.396490	+	1.47972i	0.819228	+	0.573468i	$0.194402\pi$
$227$	5.97372	+	22.2942i	0.396490	+	1.47972i	−0.422738	+	0.906252i	$0.638931\pi$
$228$	−8.19615	−	2.19615i	−0.542803	−	0.145444i
$229$	−18.5263	−	10.6962i	−1.22425	−	0.706822i	−0.258430	−	0.966030i	$-0.583205\pi$
$229$	−18.5263	−	10.6962i	−1.22425	−	0.706822i	−0.965821	+	0.259208i	$0.916538\pi$
$230$	0.732051	−	0.196152i	0.0482700	−	0.0129339i
$231$	−3.00000	+	1.73205i	−0.197386	+	0.113961i
$232$	19.3205			1.26845
$233$			3.53590i			0.231644i	0.993270	+	0.115822i	$0.0369503\pi$
$233$			3.53590i			0.231644i	−0.993270	+	0.115822i	$0.963050\pi$
$234$	7.46410			0.487944
$235$	0.294229	+	1.09808i	0.0191934	+	0.0716306i
$236$	7.32051	−	27.3205i	0.476524	−	1.77841i
$237$	3.36603	+	0.901924i	0.218647	+	0.0585862i
$238$	−23.8564			−1.54638
$239$	−2.09808	+	7.83013i	−0.135713	+	0.506489i	0.864281	+	0.503010i	$0.167774\pi$
$239$	−2.09808	+	7.83013i	−0.135713	+	0.506489i	−0.999994	+	0.00347897i	$0.998893\pi$
$240$	2.00000	+	0.535898i	0.129099	+	0.0345921i
$241$	−5.36603	−	20.0263i	−0.345656	−	1.29001i	−0.891844	−	0.452343i	$-0.850588\pi$
$241$	−5.36603	−	20.0263i	−0.345656	−	1.29001i	0.546188	−	0.837663i	$-0.316078\pi$
$242$	−9.39230	+	9.39230i	−0.603760	+	0.603760i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	15.9282	−	4.26795i	1.01970	−	0.273227i
$245$	0.169873	+	0.169873i	0.0108528	+	0.0108528i
$246$	15.5622	+	4.16987i	0.992208	+	0.265861i
$247$	−11.1962	−	19.3923i	−0.712394	−	1.23390i
$248$	12.7846			0.811824
$249$		−	2.92820i		−	0.185567i
$250$		−	7.12436i		−	0.450584i
$251$	−8.12436	−	8.12436i	−0.512805	−	0.512805i	0.402580	−	0.915385i	$-0.368114\pi$
$251$	−8.12436	−	8.12436i	−0.512805	−	0.512805i	−0.915385	+	0.402580i	$0.868114\pi$
$252$	5.46410			0.344206
$253$	−0.928203	+	0.928203i	−0.0583556	+	0.0583556i
$254$	−4.92820	+	18.3923i	−0.309223	+	1.15404i
$255$	−2.76795	−	1.59808i	−0.173336	−	0.100075i
$256$	16.0000			1.00000
$257$	−6.42820	−	1.72243i	−0.400980	−	0.107442i	0.0526923	−	0.998611i	$-0.483220\pi$
$257$	−6.42820	−	1.72243i	−0.400980	−	0.107442i	−0.453673	+	0.891168i	$0.649886\pi$
$258$	1.00000	−	1.73205i	0.0622573	−	0.107833i
$259$	−16.5622	−	1.36603i	−1.02912	−	0.0848807i
$260$	2.73205	+	4.73205i	0.169435	+	0.293469i
$261$	6.59808	+	1.76795i	0.408411	+	0.109433i
$262$	12.9282	+	22.3923i	0.798707	+	1.38340i
$263$	3.46410	−	6.00000i	0.213606	−	0.369976i	−0.739235	−	0.673448i	$-0.764813\pi$
$263$	3.46410	−	6.00000i	0.213606	−	0.369976i	0.952840	+	0.303472i	$0.0981459\pi$
$264$	−3.46410	+	0.928203i	−0.213201	+	0.0571270i
$265$	−4.73205	+	4.73205i	−0.290688	+	0.290688i
$266$	−8.19615	−	14.1962i	−0.502538	−	0.870422i
$267$	1.90192	−	1.90192i	0.116396	−	0.116396i
$268$	13.1244	−	22.7321i	0.801698	−	1.38858i
$269$		−	10.0000i		−	0.609711i	−0.952399	−	0.304855i	$-0.901392\pi$
$269$		−	10.0000i		−	0.609711i	0.952399	−	0.304855i	$-0.0986081\pi$
$270$	0.633975	+	0.366025i	0.0385825	+	0.0222756i
$271$	−12.6340	+	7.29423i	−0.767459	+	0.443093i	−0.831968	−	0.554824i	$-0.812785\pi$
$271$	−12.6340	+	7.29423i	−0.767459	+	0.443093i	0.0645082	+	0.997917i	$0.479452\pi$
$272$	−23.8564	−	6.39230i	−1.44651	−	0.387590i
$273$	10.1962	+	10.1962i	0.617099	+	0.617099i
$274$	−13.7321	+	13.7321i	−0.829584	+	0.829584i
$275$	3.00000	+	5.19615i	0.180907	+	0.313340i
$276$	2.00000	−	0.535898i	0.120386	−	0.0322573i
$277$	−3.35641	−	12.5263i	−0.201667	−	0.752631i	−0.990440	−	0.137946i	$-0.955950\pi$
$277$	−3.35641	−	12.5263i	−0.201667	−	0.752631i	0.788773	−	0.614685i	$-0.210717\pi$
$278$	−3.46410	+	12.9282i	−0.207763	+	0.775382i
$279$	4.36603	+	1.16987i	0.261387	+	0.0700385i
$280$	2.00000	+	3.46410i	0.119523	+	0.207020i
$281$	−19.2583	−	5.16025i	−1.14886	−	0.307835i	−0.366349	−	0.930477i	$-0.619392\pi$
$281$	−19.2583	−	5.16025i	−1.14886	−	0.307835i	−0.782506	+	0.622642i	$0.786059\pi$
$282$	0.803848	+	3.00000i	0.0478684	+	0.178647i
$283$	−10.8301	+	2.90192i	−0.643784	+	0.172501i	−0.565917	−	0.824462i	$-0.691478\pi$
$283$	−10.8301	+	2.90192i	−0.643784	+	0.172501i	−0.0778673	+	0.996964i	$0.524811\pi$
$284$	11.6603	−	20.1962i	0.691909	−	1.19842i
$285$		−	2.19615i		−	0.130089i
$286$	−8.19615	−	4.73205i	−0.484649	−	0.279812i
$287$	15.5622	+	26.9545i	0.918606	+	1.59107i
$288$	5.46410	+	1.46410i	0.321975	+	0.0862730i
$289$	18.2942	+	10.5622i	1.07613	+	0.621305i
$290$	1.29423	+	4.83013i	0.0759997	+	0.283635i
$291$	17.4282	−	4.66987i	1.02166	−	0.273753i
$292$		0			0
$293$	2.89230	+	1.66987i	0.168970	+	0.0975550i	0.582100	−	0.813117i	$-0.302231\pi$
$293$	2.89230	+	1.66987i	0.168970	+	0.0975550i	−0.413130	+	0.910672i	$0.635564\pi$
$294$	0.464102	+	0.464102i	0.0270670	+	0.0270670i
$295$	7.32051			0.426216
$296$	−16.1962	−	5.80385i	−0.941382	−	0.337342i
$297$	−1.26795			−0.0735739
$298$	−5.53590	−	5.53590i	−0.320686	−	0.320686i
$299$	4.73205	+	2.73205i	0.273662	+	0.157999i
$300$		−	9.46410i		−	0.546410i
$301$	3.73205	−	1.00000i	0.215112	−	0.0576390i
$302$	−5.80385	−	21.6603i	−0.333974	−	1.24641i
$303$	12.8660	+	7.42820i	0.739134	+	0.426739i
$304$	−4.39230	−	16.3923i	−0.251916	−	0.940163i
$305$	2.13397	+	3.69615i	0.122191	+	0.211641i
$306$	−7.56218	−	4.36603i	−0.432301	−	0.249589i
$307$		−	24.1962i		−	1.38095i	−0.723358	−	0.690474i	$-0.757402\pi$
$307$		−	24.1962i		−	1.38095i	0.723358	−	0.690474i	$-0.242598\pi$
$308$	−6.00000	−	3.46410i	−0.341882	−	0.197386i
$309$	−6.09808	+	1.63397i	−0.346907	+	0.0929536i
$310$	0.856406	+	3.19615i	0.0486406	+	0.181529i
$311$	1.09808	+	0.294229i	0.0622662	+	0.0166842i	0.289818	−	0.957082i	$-0.406405\pi$
$311$	1.09808	+	0.294229i	0.0622662	+	0.0166842i	−0.227551	+	0.973766i	$0.573072\pi$
$312$	7.46410	+	12.9282i	0.422572	+	0.731915i
$313$	−21.9904	−	5.89230i	−1.24297	−	0.333053i	−0.423353	−	0.905965i	$-0.639147\pi$
$313$	−21.9904	−	5.89230i	−1.24297	−	0.333053i	−0.819617	+	0.572912i	$0.805814\pi$
$314$	−5.63397	+	21.0263i	−0.317944	+	1.18658i
$315$	0.366025	+	1.36603i	0.0206232	+	0.0769668i
$316$	1.80385	+	6.73205i	0.101474	+	0.378707i
$317$	5.33013	+	9.23205i	0.299370	+	0.518524i	0.975992	−	0.217807i	$-0.0698903\pi$
$317$	5.33013	+	9.23205i	0.299370	+	0.518524i	−0.676622	+	0.736330i	$0.736557\pi$
$318$	−12.9282	+	12.9282i	−0.724978	+	0.724978i
$319$	−6.12436	−	6.12436i	−0.342898	−	0.342898i
$320$	1.07180	+	4.00000i	0.0599153	+	0.223607i
$321$	−10.0981	+	5.83013i	−0.563620	+	0.325406i
$322$	3.46410	+	2.00000i	0.193047	+	0.111456i
$323$			26.1962i			1.45759i
$324$	1.73205	+	1.00000i	0.0962250	+	0.0555556i
$325$	17.6603	−	17.6603i	0.979615	−	0.979615i
$326$	−8.66025	−	15.0000i	−0.479647	−	0.830773i
$327$	−5.02628	+	5.02628i	−0.277954	+	0.277954i
$328$	8.33975	+	31.1244i	0.460485	+	1.71856i
$329$	−3.00000	+	5.19615i	−0.165395	+	0.286473i
$330$	−0.464102	−	0.803848i	−0.0255480	−	0.0442504i
$331$	−15.9282	−	4.26795i	−0.875493	−	0.234588i	−0.207032	−	0.978334i	$-0.566380\pi$
$331$	−15.9282	−	4.26795i	−0.875493	−	0.234588i	−0.668462	+	0.743747i	$0.733047\pi$
$332$	5.07180	−	2.92820i	0.278351	−	0.160706i
$333$	−5.00000	−	3.46410i	−0.273998	−	0.189832i
$334$	1.46410	−	2.53590i	0.0801121	−	0.138758i
$335$	6.56218	+	1.75833i	0.358530	+	0.0960678i
$336$	5.46410	+	9.46410i	0.298091	+	0.516309i
$337$	−0.0621778	−	0.0358984i	−0.00338704	−	0.00195551i	0.498306	−	0.867002i	$-0.333956\pi$
$337$	−0.0621778	−	0.0358984i	−0.00338704	−	0.00195551i	−0.501693	+	0.865046i	$0.667289\pi$
$338$	−5.43782	+	20.2942i	−0.295779	+	1.10386i
$339$	1.19615	−	1.19615i	0.0649661	−	0.0649661i
$340$		−	6.39230i		−	0.346671i
$341$	−4.05256	−	4.05256i	−0.219458	−	0.219458i
$342$		−	6.00000i		−	0.324443i
$343$		−	17.8564i		−	0.964155i
$344$	4.00000			0.215666
$345$	0.267949	+	0.464102i	0.0144259	+	0.0249864i
$346$	6.36603	+	1.70577i	0.342240	+	0.0917028i
$347$	6.73205	+	6.73205i	0.361395	+	0.361395i	0.864327	−	0.502931i	$-0.167745\pi$
$347$	6.73205	+	6.73205i	0.361395	+	0.361395i	−0.502931	+	0.864327i	$0.667745\pi$
$348$	3.53590	+	13.1962i	0.189544	+	0.707388i
$349$	−5.76795	+	3.33013i	−0.308751	+	0.178258i	−0.646368	−	0.763026i	$-0.723713\pi$
$349$	−5.76795	+	3.33013i	−0.308751	+	0.178258i	0.337616	+	0.941284i	$0.390379\pi$
$350$	12.9282	−	12.9282i	0.691042	−	0.691042i
$351$	1.36603	+	5.09808i	0.0729130	+	0.272115i
$352$	−5.07180	−	5.07180i	−0.270328	−	0.270328i
$353$	5.96410	−	22.2583i	0.317437	−	1.18469i	−0.604262	−	0.796786i	$-0.706532\pi$
$353$	5.96410	−	22.2583i	0.317437	−	1.18469i	0.921699	−	0.387906i	$-0.126801\pi$
$354$	20.0000			1.06299
$355$	5.83013	+	1.56218i	0.309431	+	0.0829118i
$356$	5.19615	+	1.39230i	0.275396	+	0.0737920i
$357$	−4.36603	−	16.2942i	−0.231075	−	0.862382i
$358$	29.4641			1.55723
$359$		−	16.2487i		−	0.857574i	−0.903406	−	0.428787i	$-0.858941\pi$
$359$		−	16.2487i		−	0.857574i	0.903406	−	0.428787i	$-0.141059\pi$
$360$			1.46410i			0.0771649i
$361$	0.866025	−	0.500000i	0.0455803	−	0.0263158i
$362$	−15.8301	+	4.24167i	−0.832013	+	0.222937i
$363$	−8.13397	−	4.69615i	−0.426923	−	0.246484i
$364$	−7.46410	+	27.8564i	−0.391225	+	1.46007i
$365$		0			0
$366$	5.83013	+	10.0981i	0.304746	+	0.527835i
$367$	−19.8564	−	11.4641i	−1.03650	−	0.598421i	−0.117657	−	0.993054i	$-0.537538\pi$
$367$	−19.8564	−	11.4641i	−1.03650	−	0.598421i	−0.918839	+	0.394633i	$0.870872\pi$
$368$	2.92820	+	2.92820i	0.152643	+	0.152643i
$369$			11.3923i			0.593060i
$370$	0.366025	−	4.43782i	0.0190288	−	0.230711i
$371$	−35.3205			−1.83375
$372$	2.33975	+	8.73205i	0.121310	+	0.452736i
$373$	−7.13397	+	12.3564i	−0.369383	+	0.639790i	−0.989469	−	0.144743i	$-0.953764\pi$
$373$	−7.13397	+	12.3564i	−0.369383	+	0.639790i	0.620086	+	0.784534i	$0.287098\pi$
$374$	5.53590	+	9.58846i	0.286254	+	0.495807i
$375$	4.86603	−	1.30385i	0.251280	−	0.0673304i
$376$	−4.39230	+	4.39230i	−0.226516	+	0.226516i
$377$	−18.0263	+	31.2224i	−0.928401	+	1.60804i
$378$	1.00000	+	3.73205i	0.0514344	+	0.191956i
$379$	4.63397	+	8.02628i	0.238031	+	0.412282i	0.960149	−	0.279488i	$-0.0901646\pi$
$379$	4.63397	+	8.02628i	0.238031	+	0.412282i	−0.722118	+	0.691770i	$0.756831\pi$
$380$	3.80385	−	2.19615i	0.195133	−	0.112660i
$381$	−13.4641			−0.689787
$382$	24.0000			1.22795
$383$	−11.2942	+	3.02628i	−0.577108	+	0.154636i	−0.535555	−	0.844501i	$-0.679897\pi$
$383$	−11.2942	+	3.02628i	−0.577108	+	0.154636i	−0.0415536	+	0.999136i	$0.513231\pi$
$384$	2.92820	+	10.9282i	0.149429	+	0.557678i
$385$	0.464102	−	1.73205i	0.0236528	−	0.0882735i
$386$		−	24.1962i		−	1.23155i
$387$	1.36603	+	0.366025i	0.0694390	+	0.0186061i
$388$	25.5167	+	25.5167i	1.29541	+	1.29541i
$389$	21.5263	−	5.76795i	1.09143	−	0.292447i	0.332157	−	0.943224i	$-0.392224\pi$
$389$	21.5263	−	5.76795i	1.09143	−	0.292447i	0.759269	+	0.650777i	$0.225557\pi$
$390$	−2.73205	+	2.73205i	−0.138343	+	0.138343i
$391$	−3.19615	−	5.53590i	−0.161636	−	0.279962i
$392$	−0.339746	+	1.26795i	−0.0171598	+	0.0640411i
$393$	−12.9282	+	12.9282i	−0.652142	+	0.652142i
$394$	−0.366025	+	1.36603i	−0.0184401	+	0.0688194i
$395$	−1.56218	+	0.901924i	−0.0786017	+	0.0453807i
$396$	−1.26795	−	2.19615i	−0.0637168	−	0.110361i
$397$	0.607695			0.0304993			0.0152497	−	0.999884i	$-0.495146\pi$
$397$	0.607695			0.0304993			0.0152497	+	0.999884i	$0.495146\pi$
$398$			38.1051i			1.91004i
$399$	8.19615	−	8.19615i	0.410321	−	0.410321i
$400$	16.3923	−	9.46410i	0.819615	−	0.473205i
$401$	1.19615	+	1.19615i	0.0597330	+	0.0597330i	0.736342	−	0.676609i	$-0.236551\pi$
$401$	1.19615	+	1.19615i	0.0597330	+	0.0597330i	−0.676609	+	0.736342i	$0.736551\pi$
$402$	17.9282	+	4.80385i	0.894178	+	0.239594i
$403$	−11.9282	+	20.6603i	−0.594186	+	1.02916i
$404$			29.7128i			1.47827i
$405$	−0.133975	+	0.500000i	−0.00665725	+	0.0248452i
$406$	−13.1962	+	22.8564i	−0.654914	+	1.13434i
$407$	3.29423	+	6.97372i	0.163289	+	0.345674i
$408$		−	17.4641i		−	0.864602i
$409$	6.37564	−	23.7942i	0.315255	−	1.17655i	−0.608496	−	0.793557i	$-0.708227\pi$
$409$	6.37564	−	23.7942i	0.315255	−	1.17655i	0.923752	−	0.382992i	$-0.125106\pi$
$410$	−7.22243	+	4.16987i	−0.356690	+	0.205935i
$411$	−11.8923	−	6.86603i	−0.586604	−	0.338676i
$412$	−8.92820	−	8.92820i	−0.439861	−	0.439861i
$413$	27.3205	+	27.3205i	1.34435	+	1.34435i
$414$	0.732051	+	1.26795i	0.0359783	+	0.0623163i
$415$	1.07180	+	1.07180i	0.0526124	+	0.0526124i
$416$	−14.9282	+	25.8564i	−0.731915	+	1.26771i
$417$	−9.46410			−0.463459
$418$	−3.80385	+	6.58846i	−0.186052	+	0.322252i
$419$	4.56218	+	7.90192i	0.222877	+	0.386034i	0.955680	−	0.294406i	$-0.0951218\pi$
$419$	4.56218	+	7.90192i	0.222877	+	0.386034i	−0.732803	+	0.680440i	$0.761789\pi$
$420$	−2.00000	+	2.00000i	−0.0975900	+	0.0975900i
$421$	−16.1699	+	16.1699i	−0.788071	+	0.788071i	−0.981178	−	0.193106i	$-0.938144\pi$
$421$	−16.1699	+	16.1699i	−0.788071	+	0.788071i	0.193106	+	0.981178i	$0.438144\pi$
$422$	19.1244	−	19.1244i	0.930959	−	0.930959i
$423$	−1.90192	+	1.09808i	−0.0924747	+	0.0533903i
$424$	−35.3205	−	9.46410i	−1.71532	−	0.459617i
$425$	−28.2224	+	7.56218i	−1.36899	+	0.366820i
$426$	15.9282	+	4.26795i	0.771724	+	0.206783i
$427$	−5.83013	+	21.7583i	−0.282140	+	1.05296i
$428$	−20.1962	−	11.6603i	−0.976218	−	0.563620i
$429$	1.73205	−	6.46410i	0.0836242	−	0.312090i
$430$	0.267949	+	1.00000i	0.0129217	+	0.0482243i
$431$	−2.22243	−	8.29423i	−0.107051	−	0.399519i	0.891519	−	0.452983i	$-0.149640\pi$
$431$	−2.22243	−	8.29423i	−0.107051	−	0.399519i	−0.998570	+	0.0534644i	$0.982974\pi$
$432$			4.00000i			0.192450i
$433$	−9.33975			−0.448840			−0.224420	−	0.974493i	$-0.572049\pi$
$433$	−9.33975			−0.448840			−0.224420	+	0.974493i	$0.572049\pi$
$434$	−8.73205	+	15.1244i	−0.419152	+	0.725992i
$435$	−3.06218	+	1.76795i	−0.146820	+	0.0847667i
$436$	−13.7321	−	3.67949i	−0.657646	−	0.176216i
$437$	2.19615	−	3.80385i	0.105056	−	0.181963i
$438$		0			0
$439$	−1.73205	−	6.46410i	−0.0826663	−	0.308515i	0.912196	−	0.409755i	$-0.134386\pi$
$439$	−1.73205	−	6.46410i	−0.0826663	−	0.308515i	−0.994862	+	0.101240i	$0.967719\pi$
$440$	0.928203	−	1.60770i	0.0442504	−	0.0766439i
$441$	−0.232051	+	0.401924i	−0.0110500	+	0.0191392i
$442$	32.5885	−	32.5885i	1.55007	−	1.55007i
$443$			17.8564i			0.848383i	0.905572	+	0.424192i	$0.139442\pi$
$443$			17.8564i			0.848383i	−0.905572	+	0.424192i	$0.860558\pi$
$444$	1.00000	−	12.1244i	0.0474579	−	0.575396i
$445$			1.39230i			0.0660016i
$446$	−18.3923	−	18.3923i	−0.870901	−	0.870901i
$447$	2.76795	−	4.79423i	0.130920	−	0.226759i
$448$	−10.9282	+	18.9282i	−0.516309	+	0.894274i
$449$	9.36603	+	34.9545i	0.442010	+	1.64960i	0.723712	+	0.690102i	$0.242434\pi$
$449$	9.36603	+	34.9545i	0.442010	+	1.64960i	−0.281702	+	0.959502i	$0.590899\pi$
$450$	6.46410	−	1.73205i	0.304721	−	0.0816497i
$451$	7.22243	−	12.5096i	0.340091	−	0.589055i
$452$	3.26795	+	0.875644i	0.153711	+	0.0411868i
$453$	13.7321	−	7.92820i	0.645188	−	0.372499i
$454$	−28.2679	−	16.3205i	−1.32668	−	0.765959i
$455$	−7.46410			−0.349922
$456$	10.3923	−	6.00000i	0.486664	−	0.280976i
$457$	0.179492	+	0.669873i	0.00839628	+	0.0313353i	0.969997	−	0.243117i	$-0.0781700\pi$
$457$	0.179492	+	0.669873i	0.00839628	+	0.0313353i	−0.961601	+	0.274453i	$0.911503\pi$
$458$	29.2224	−	7.83013i	1.36547	−	0.365878i
$459$	1.59808	−	5.96410i	0.0745918	−	0.278380i
$460$	−0.535898	+	0.928203i	−0.0249864	+	0.0432777i
$461$	8.29423	−	30.9545i	0.386301	−	1.44169i	−0.449806	−	0.893127i	$-0.648507\pi$
$461$	8.29423	−	30.9545i	0.386301	−	1.44169i	0.836106	−	0.548567i	$-0.184827\pi$
$462$	1.26795	−	4.73205i	0.0589903	−	0.220155i
$463$	−0.633975	+	0.169873i	−0.0294633	+	0.00789467i	−0.273521	−	0.961866i	$-0.588188\pi$
$463$	−0.633975	+	0.169873i	−0.0294633	+	0.00789467i	0.244057	+	0.969761i	$0.421522\pi$
$464$	−19.3205	+	19.3205i	−0.896932	+	0.896932i
$465$	−2.02628	+	1.16987i	−0.0939665	+	0.0542516i
$466$	−3.53590	−	3.53590i	−0.163797	−	0.163797i
$467$	2.92820	−	2.92820i	0.135501	−	0.135501i	−0.636103	−	0.771604i	$-0.719455\pi$
$467$	2.92820	−	2.92820i	0.135501	−	0.135501i	0.771604	+	0.636103i	$0.219455\pi$
$468$	−7.46410	+	7.46410i	−0.345028	+	0.345028i
$469$	17.9282	+	31.0526i	0.827848	+	1.43387i
$470$	−1.39230	−	0.803848i	−0.0642222	−	0.0370787i
$471$	−15.3923			−0.709240
$472$	20.0000	+	34.6410i	0.920575	+	1.59448i
$473$	−1.26795	−	1.26795i	−0.0583004	−	0.0583004i
$474$	−4.26795	+	2.46410i	−0.196033	+	0.113180i
$475$	−14.1962	−	14.1962i	−0.651364	−	0.651364i
$476$	23.8564	−	23.8564i	1.09346	−	1.09346i
$477$	−11.1962	−	6.46410i	−0.512637	−	0.295971i
$478$	−5.73205	−	9.92820i	−0.262178	−	0.454105i
$479$	−2.05256	+	7.66025i	−0.0937838	+	0.350006i	−0.996832	−	0.0795328i	$-0.974657\pi$
$479$	−2.05256	+	7.66025i	−0.0937838	+	0.350006i	0.903048	+	0.429539i	$0.141324\pi$
$480$	−2.53590	+	1.46410i	−0.115747	+	0.0668268i
$481$	24.4904	−	20.7583i	1.11667	−	0.946498i
$482$	25.3923	+	14.6603i	1.15659	+	0.667756i
$483$	−0.732051	+	2.73205i	−0.0333095	+	0.124313i
$484$		−	18.7846i		−	0.853846i
$485$	−4.66987	+	8.08846i	−0.212048	+	0.367278i
$486$	−0.366025	+	1.36603i	−0.0166032	+	0.0619642i
$487$	−16.5359	−	16.5359i	−0.749313	−	0.749313i	0.225037	−	0.974350i	$-0.427750\pi$
$487$	−16.5359	−	16.5359i	−0.749313	−	0.749313i	−0.974350	+	0.225037i	$0.927750\pi$
$488$	−11.6603	+	20.1962i	−0.527835	+	0.914237i
$489$	8.66025	−	8.66025i	0.391630	−	0.391630i
$490$	−0.339746			−0.0153482
$491$	17.2679			0.779292			0.389646	−	0.920965i	$-0.372597\pi$
$491$	17.2679			0.779292			0.389646	+	0.920965i	$0.372597\pi$
$492$	−19.7321	+	11.3923i	−0.889590	+	0.513605i
$493$	36.5263	−	21.0885i	1.64506	−	0.949776i
$494$	30.5885	+	8.19615i	1.37624	+	0.368762i
$495$	0.464102	−	0.464102i	0.0208598	−	0.0208598i
$496$	−12.7846	+	12.7846i	−0.574046	+	0.574046i
$497$	15.9282	+	27.5885i	0.714478	+	1.23751i
$498$	2.92820	+	2.92820i	0.131216	+	0.131216i
$499$	−9.09808	+	2.43782i	−0.407286	+	0.109132i	−0.456645	−	0.889649i	$-0.650949\pi$
$499$	−9.09808	+	2.43782i	−0.407286	+	0.109132i	0.0493588	+	0.998781i	$0.484282\pi$
$500$	7.12436	+	7.12436i	0.318611	+	0.318611i
$501$	2.00000	+	0.535898i	0.0893534	+	0.0239422i
$502$	16.2487			0.725215
$503$	−2.41858	+	9.02628i	−0.107839	+	0.402462i	−0.998652	−	0.0519093i	$-0.983469\pi$
$503$	−2.41858	+	9.02628i	−0.107839	+	0.402462i	0.890812	+	0.454371i	$0.150136\pi$
$504$	−5.46410	+	5.46410i	−0.243390	+	0.243390i
$505$	−7.42820	+	1.99038i	−0.330551	+	0.0885708i
$506$		−	1.85641i		−	0.0825273i
$507$	−14.8564			−0.659796
$508$	−13.4641	−	23.3205i	−0.597373	−	1.03468i
$509$	0.669873	+	1.16025i	0.0296916	+	0.0514274i	0.880489	−	0.474066i	$-0.157214\pi$
$509$	0.669873	+	1.16025i	0.0296916	+	0.0514274i	−0.850798	+	0.525493i	$0.823881\pi$
$510$	4.36603	−	1.16987i	0.193331	−	0.0518028i
$511$		0			0
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	4.09808	−	1.09808i	0.180934	−	0.0484812i
$514$	8.15064	−	4.70577i	0.359509	−	0.207563i
$515$	1.63397	−	2.83013i	0.0720015	−	0.124710i
$516$	0.732051	+	2.73205i	0.0322267	+	0.120272i
$517$	2.78461			0.122467
$518$	17.9282	−	15.1962i	0.787720	−	0.667681i
$519$			4.66025i			0.204562i
$520$	−7.46410	−	2.00000i	−0.327323	−	0.0877058i
$521$	6.00000	+	3.46410i	0.262865	+	0.151765i	0.625641	−	0.780111i	$-0.284838\pi$
$521$	6.00000	+	3.46410i	0.262865	+	0.151765i	−0.362776	+	0.931876i	$0.618171\pi$
$522$	−8.36603	+	4.83013i	−0.366171	+	0.211409i
$523$	1.58846	+	5.92820i	0.0694584	+	0.259222i	0.991920	−	0.126867i	$-0.0404922\pi$
$523$	1.58846	+	5.92820i	0.0694584	+	0.259222i	−0.922461	+	0.386090i	$0.873826\pi$
$524$	−35.3205	−	9.46410i	−1.54298	−	0.413441i
$525$	11.1962	+	6.46410i	0.488640	+	0.282117i
$526$	2.53590	+	9.46410i	0.110570	+	0.412654i
$527$	24.1699	−	13.9545i	1.05286	−	0.607867i
$528$	2.53590	−	4.39230i	0.110361	−	0.191151i
$529$		−	21.9282i		−	0.953400i
$530$		−	9.46410i		−	0.411094i
$531$	3.66025	+	13.6603i	0.158841	+	0.592805i
$532$	22.3923	+	6.00000i	0.970830	+	0.260133i
$533$	−58.0788	−	15.5622i	−2.51567	−	0.674073i
$534$			3.80385i			0.164609i
$535$	1.56218	−	5.83013i	0.0675388	−	0.252058i
$536$	9.60770	+	35.8564i	0.414989	+	1.54876i
$537$	5.39230	+	20.1244i	0.232695	+	0.868430i
$538$	10.0000	+	10.0000i	0.431131	+	0.431131i
$539$	0.509619	−	0.294229i	0.0219508	−	0.0126733i
$540$	−1.00000	+	0.267949i	−0.0430331	+	0.0115307i
$541$	10.3660	+	10.3660i	0.445670	+	0.445670i	0.893912	−	0.448242i	$-0.147950\pi$
$541$	10.3660	+	10.3660i	0.445670	+	0.445670i	−0.448242	+	0.893912i	$0.647950\pi$
$542$	5.33975	−	19.9282i	0.229362	−	0.855990i
$543$	−5.79423	−	10.0359i	−0.248654	−	0.430682i
$544$	30.2487	−	17.4641i	1.29690	−	0.748767i
$545$		−	3.67949i		−	0.157612i
$546$	−20.3923			−0.872710
$547$	19.7321	+	19.7321i	0.843682	+	0.843682i	0.989336	−	0.145654i	$-0.0465286\pi$
$547$	19.7321	+	19.7321i	0.843682	+	0.843682i	−0.145654	+	0.989336i	$0.546529\pi$
$548$		−	27.4641i		−	1.17321i
$549$	−5.83013	+	5.83013i	−0.248824	+	0.248824i
$550$	−8.19615	−	2.19615i	−0.349485	−	0.0936443i
$551$	25.0981	+	14.4904i	1.06921	+	0.617311i
$552$	−1.46410	+	2.53590i	−0.0623163	+	0.107935i
$553$	−9.19615	−	2.46410i	−0.391060	−	0.104784i
$554$	15.8827	+	9.16987i	0.674791	+	0.389591i
$555$	3.09808	−	0.562178i	0.131506	−	0.0238631i
$556$	−9.46410	−	16.3923i	−0.401367	−	0.695189i
$557$	9.79423	+	2.62436i	0.414995	+	0.111198i	0.460274	−	0.887777i	$-0.347751\pi$
$557$	9.79423	+	2.62436i	0.414995	+	0.111198i	−0.0452793	+	0.998974i	$0.514418\pi$
$558$	−5.53590	+	3.19615i	−0.234353	+	0.135304i
$559$	−3.73205	+	6.46410i	−0.157849	+	0.273402i
$560$	−5.46410	−	1.46410i	−0.230900	−	0.0618696i
$561$	−5.53590	+	5.53590i	−0.233726	+	0.233726i
$562$	24.4186	−	14.0981i	1.03004	−	0.594691i
$563$	30.9808	−	30.9808i	1.30568	−	1.30568i	0.381184	−	0.924499i	$-0.375516\pi$
$563$	30.9808	−	30.9808i	1.30568	−	1.30568i	0.924499	−	0.381184i	$-0.124484\pi$
$564$	−3.80385	−	2.19615i	−0.160171	−	0.0924747i
$565$			0.875644i			0.0368386i
$566$	7.92820	−	13.7321i	0.333247	−	0.577201i
$567$	−2.36603	+	1.36603i	−0.0993637	+	0.0573677i
$568$	8.53590	+	31.8564i	0.358158	+	1.33667i
$569$	−24.4904	−	24.4904i	−1.02669	−	1.02669i	−0.999634	−	0.0270563i	$-0.991387\pi$
$569$	−24.4904	−	24.4904i	−1.02669	−	1.02669i	−0.0270563	−	0.999634i	$-0.508613\pi$
$570$	2.19615	+	2.19615i	0.0919867	+	0.0919867i
$571$	17.0000	+	29.4449i	0.711428	+	1.23223i	0.964321	+	0.264735i	$0.0852845\pi$
$571$	17.0000	+	29.4449i	0.711428	+	1.23223i	−0.252893	+	0.967494i	$0.581382\pi$
$572$	12.9282	−	3.46410i	0.540555	−	0.144841i
$573$	4.39230	+	16.3923i	0.183491	+	0.684798i
$574$	−42.5167	−	11.3923i	−1.77461	−	0.475506i
$575$	4.73205	+	1.26795i	0.197340	+	0.0528771i
$576$	−6.92820	+	4.00000i	−0.288675	+	0.166667i
$577$	−11.2942	−	3.02628i	−0.470185	−	0.125986i	0.0159438	−	0.999873i	$-0.494925\pi$
$577$	−11.2942	−	3.02628i	−0.470185	−	0.125986i	−0.486129	+	0.873887i	$0.661591\pi$
$578$	−28.8564	+	7.73205i	−1.20027	+	0.321611i
$579$	16.5263	−	4.42820i	0.686809	−	0.184030i
$580$	−6.12436	−	3.53590i	−0.254300	−	0.146820i
$581$			8.00000i			0.331896i
$582$	−12.7583	+	22.0981i	−0.528850	+	0.915995i
$583$	8.19615	+	14.1962i	0.339450	+	0.587945i
$584$		0			0
$585$	−2.36603	−	1.36603i	−0.0978231	−	0.0564782i
$586$	−4.56218	+	1.22243i	−0.188462	+	0.0504982i
$587$	−11.9282	+	3.19615i	−0.492330	+	0.131919i	−0.496438	−	0.868072i	$-0.665359\pi$
$587$	−11.9282	+	3.19615i	−0.492330	+	0.131919i	0.00410827	+	0.999992i	$0.498692\pi$
$588$	−0.928203			−0.0382785
$589$	16.6077	+	9.58846i	0.684308	+	0.395085i
$590$	−7.32051	+	7.32051i	−0.301381	+	0.301381i
$591$	−1.00000			−0.0411345
$592$	22.0000	−	10.3923i	0.904194	−	0.427121i
$593$	5.92820			0.243442			0.121721	−	0.992564i	$-0.461159\pi$
$593$	5.92820			0.243442			0.121721	+	0.992564i	$0.461159\pi$
$594$	1.26795	−	1.26795i	0.0520246	−	0.0520246i
$595$	7.56218	+	4.36603i	0.310019	+	0.178990i
$596$	11.0718			0.453518
$597$	−26.0263	+	6.97372i	−1.06518	+	0.285415i
$598$	−7.46410	+	2.00000i	−0.305230	+	0.0817861i
$599$	−20.3660	−	11.7583i	−0.832133	−	0.480432i	0.0224493	−	0.999748i	$-0.492854\pi$
$599$	−20.3660	−	11.7583i	−0.832133	−	0.480432i	−0.854583	+	0.519316i	$0.826187\pi$
$600$	9.46410	+	9.46410i	0.386370	+	0.386370i
$601$	−1.16025	−	2.00962i	−0.0473277	−	0.0819741i	0.841391	−	0.540427i	$-0.181737\pi$
$601$	−1.16025	−	2.00962i	−0.0473277	−	0.0819741i	−0.888719	+	0.458453i	$0.848404\pi$
$602$	−2.73205	+	4.73205i	−0.111350	+	0.192864i
$603$			13.1244i			0.534465i
$604$	27.4641	+	15.8564i	1.11750	+	0.645188i
$605$	4.69615	−	1.25833i	0.190926	−	0.0511584i
$606$	−20.2942	+	5.43782i	−0.824397	+	0.220896i
$607$	−23.0263	−	6.16987i	−0.934608	−	0.250427i	−0.240789	−	0.970577i	$-0.577406\pi$
$607$	−23.0263	−	6.16987i	−0.934608	−	0.250427i	−0.693818	+	0.720150i	$0.744073\pi$
$608$	20.7846	+	12.0000i	0.842927	+	0.486664i
$609$	−18.0263	−	4.83013i	−0.730462	−	0.195727i
$610$	−5.83013	−	1.56218i	−0.236055	−	0.0632507i
$611$	−3.00000	−	11.1962i	−0.121367	−	0.452948i
$612$	11.9282	−	3.19615i	0.482169	−	0.129197i
$613$	19.8205	+	34.3301i	0.800543	+	1.38658i	0.919259	+	0.393653i	$0.128789\pi$
$613$	19.8205	+	34.3301i	0.800543	+	1.38658i	−0.118717	+	0.992928i	$0.537878\pi$
$614$	24.1962	+	24.1962i	0.976477	+	0.976477i
$615$	−4.16987	−	4.16987i	−0.168146	−	0.168146i
$616$	9.46410	−	2.53590i	0.381320	−	0.102174i
$617$	7.85641	−	4.53590i	0.316287	−	0.182608i	−0.333449	−	0.942768i	$-0.608213\pi$
$617$	7.85641	−	4.53590i	0.316287	−	0.182608i	0.649736	+	0.760160i	$0.274879\pi$
$618$	4.46410	−	7.73205i	0.179573	−	0.311029i
$619$		−	23.3731i		−	0.939443i	−0.882815	−	0.469721i	$-0.844354\pi$
$619$		−	23.3731i		−	0.939443i	0.882815	−	0.469721i	$-0.155646\pi$
$620$	−4.05256	−	2.33975i	−0.162755	−	0.0939665i
$621$	−0.732051	+	0.732051i	−0.0293762	+	0.0293762i
$622$	−1.39230	+	0.803848i	−0.0558263	+	0.0322314i
$623$	−5.19615	+	5.19615i	−0.208179	+	0.208179i
$624$	−20.3923	−	5.46410i	−0.816346	−	0.218739i
$625$	10.5263	−	18.2321i	0.421051	−	0.729282i
$626$	27.8827	−	16.0981i	1.11442	−	0.643409i
$627$	−5.19615	−	1.39230i	−0.207514	−	0.0556033i
$628$	−15.3923	−	26.6603i	−0.614220	−	1.06386i
$629$	−36.9545	+	6.70577i	−1.47347	+	0.267377i
$630$	−1.73205	−	1.00000i	−0.0690066	−	0.0398410i
$631$	29.6603	+	7.94744i	1.18076	+	0.316383i	0.795226	−	0.606313i	$-0.207352\pi$
$631$	29.6603	+	7.94744i	1.18076	+	0.316383i	0.385530	+	0.922695i	$0.374019\pi$
$632$	−8.53590	−	4.92820i	−0.339540	−	0.196033i
$633$	16.5622	+	9.56218i	0.658287	+	0.380062i
$634$	−14.5622	−	3.90192i	−0.578338	−	0.154965i
$635$	4.92820	−	4.92820i	0.195570	−	0.195570i
$636$		−	25.8564i		−	1.02527i
$637$	−1.73205	−	1.73205i	−0.0686264	−	0.0686264i
$638$	12.2487			0.484931
$639$			11.6603i			0.461273i
$640$	−5.07180	−	2.92820i	−0.200480	−	0.115747i
$641$	−2.03590	−	3.52628i	−0.0804132	−	0.139280i	0.823014	−	0.568021i	$-0.192291\pi$
$641$	−2.03590	−	3.52628i	−0.0804132	−	0.139280i	−0.903427	+	0.428741i	$0.858957\pi$
$642$	4.26795	−	15.9282i	0.168443	−	0.628636i
$643$	−25.3923	−	25.3923i	−1.00137	−	1.00137i	−0.999999	−	0.00137570i	$-0.999562\pi$
$643$	−25.3923	−	25.3923i	−1.00137	−	1.00137i	−0.00137570	−	0.999999i	$-0.500438\pi$
$644$	−5.46410	+	1.46410i	−0.215316	+	0.0576937i
$645$	−0.633975	+	0.366025i	−0.0249627	+	0.0144122i
$646$	−26.1962	−	26.1962i	−1.03067	−	1.03067i
$647$	−10.3660	−	38.6865i	−0.407531	−	1.52092i	−0.799340	−	0.600878i	$-0.794818\pi$
$647$	−10.3660	−	38.6865i	−0.407531	−	1.52092i	0.391810	−	0.920046i	$-0.371849\pi$
$648$	−2.73205	+	0.732051i	−0.107325	+	0.0287577i
$649$	4.64102	−	17.3205i	0.182176	−	0.679889i
$650$			35.3205i			1.38538i
$651$	−11.9282	−	3.19615i	−0.467503	−	0.125267i
$652$	23.6603	+	6.33975i	0.926607	+	0.248284i
$653$	−9.06218	−	33.8205i	−0.354630	−	1.32350i	−0.880949	−	0.473211i	$-0.843095\pi$
$653$	−9.06218	−	33.8205i	−0.354630	−	1.32350i	0.526319	−	0.850287i	$-0.323572\pi$
$654$		−	10.0526i		−	0.393086i
$655$		−	9.46410i		−	0.369793i
$656$	−39.4641	−	22.7846i	−1.54081	−	0.889590i
$657$		0			0
$658$	−2.19615	−	8.19615i	−0.0856149	−	0.319519i
$659$	21.0000	+	12.1244i	0.818044	+	0.472298i	0.849741	−	0.527200i	$-0.176758\pi$
$659$	21.0000	+	12.1244i	0.818044	+	0.472298i	−0.0316976	+	0.999498i	$0.510091\pi$
$660$	1.26795	+	0.339746i	0.0493549	+	0.0132246i
$661$	7.96410	+	29.7224i	0.309768	+	1.15607i	0.928763	+	0.370674i	$0.120873\pi$
$661$	7.96410	+	29.7224i	0.309768	+	1.15607i	−0.618995	+	0.785395i	$0.712460\pi$
$662$	20.1962	−	11.6603i	0.784946	−	0.453189i
$663$	28.2224	+	16.2942i	1.09607	+	0.632815i
$664$	−2.14359	+	8.00000i	−0.0831876	+	0.310460i
$665$			6.00000i			0.232670i
$666$	8.46410	−	1.53590i	0.327977	−	0.0595149i
$667$	−7.07180			−0.273821
$668$	1.07180	+	4.00000i	0.0414691	+	0.154765i
$669$	9.19615	−	15.9282i	0.355544	−	0.615820i
$670$	−8.32051	+	4.80385i	−0.321449	+	0.185589i
$671$	10.0981	−	2.70577i	0.389832	−	0.104455i
$672$	−14.9282	−	4.00000i	−0.575868	−	0.154303i
$673$	−7.46410	+	12.9282i	−0.287720	+	0.498346i	−0.973265	−	0.229684i	$-0.926231\pi$
$673$	−7.46410	+	12.9282i	−0.287720	+	0.498346i	0.685545	+	0.728030i	$0.259564\pi$
$674$	0.0980762	−	0.0262794i	0.00377775	−	0.00101225i
$675$	2.36603	+	4.09808i	0.0910684	+	0.157735i
$676$	−14.8564	−	25.7321i	−0.571400	−	0.989694i
$677$	−24.2679			−0.932693			−0.466347	−	0.884602i	$-0.654430\pi$
$677$	−24.2679			−0.932693			−0.466347	+	0.884602i	$0.654430\pi$
$678$			2.39230i			0.0918759i
$679$	−47.6147	+	12.7583i	−1.82729	+	0.489620i
$680$	6.39230	+	6.39230i	0.245134	+	0.245134i
$681$	5.97372	−	22.2942i	0.228913	−	0.854317i
$682$	8.10512			0.310361
$683$	−0.830127	−	0.222432i	−0.0317639	−	0.00851112i	0.242902	−	0.970051i	$-0.421901\pi$
$683$	−0.830127	−	0.222432i	−0.0317639	−	0.00851112i	−0.274666	+	0.961540i	$0.588567\pi$
$684$	6.00000	+	6.00000i	0.229416	+	0.229416i
$685$	6.86603	−	1.83975i	0.262337	−	0.0702931i
$686$	17.8564	+	17.8564i	0.681761	+	0.681761i
$687$	10.6962	+	18.5263i	0.408084	+	0.706822i
$688$	−4.00000	+	4.00000i	−0.152499	+	0.152499i
$689$	48.2487	−	48.2487i	1.83813	−	1.83813i
$690$	−0.732051	−	0.196152i	−0.0278687	−	0.00746740i
$691$	12.1699	−	7.02628i	0.462964	−	0.267292i	−0.250326	−	0.968162i	$-0.580538\pi$
$691$	12.1699	−	7.02628i	0.462964	−	0.267292i	0.713290	+	0.700869i	$0.247204\pi$
$692$	−8.07180	+	4.66025i	−0.306844	+	0.177156i
$693$	3.46410			0.131590
$694$	−13.4641			−0.511090
$695$	3.46410	−	3.46410i	0.131401	−	0.131401i
$696$	−16.7321	−	9.66025i	−0.634227	−	0.366171i
$697$	49.7391	+	49.7391i	1.88400	+	1.88400i
$698$	2.43782	−	9.09808i	0.0922729	−	0.344367i
$699$	1.76795	−	3.06218i	0.0668700	−	0.115822i
$700$			25.8564i			0.977280i
$701$	9.22243	−	34.4186i	0.348326	−	1.29997i	−0.540351	−	0.841440i	$-0.681709\pi$
$701$	9.22243	−	34.4186i	0.348326	−	1.29997i	0.888678	−	0.458532i	$-0.151625\pi$
$702$	−6.46410	−	3.73205i	−0.243972	−	0.140857i
$703$	−16.6865	−	19.6865i	−0.629345	−	0.742492i
$704$	10.1436			0.382301
$705$	0.294229	−	1.09808i	0.0110813	−	0.0413559i
$706$	16.2942	+	28.2224i	0.613241	+	1.06217i
$707$	−35.1506	−	20.2942i	−1.32198	−	0.763243i
$708$	−20.0000	+	20.0000i	−0.751646	+	0.751646i
$709$	−9.92820	−	9.92820i	−0.372861	−	0.372861i	0.495657	−	0.868518i	$-0.334927\pi$
$709$	−9.92820	−	9.92820i	−0.372861	−	0.372861i	−0.868518	+	0.495657i	$0.834927\pi$
$710$	−7.39230	+	4.26795i	−0.277428	+	0.160173i
$711$	−2.46410	−	2.46410i	−0.0924110	−	0.0924110i
$712$	−6.58846	+	3.80385i	−0.246913	+	0.142555i
$713$	−4.67949			−0.175248
$714$	20.6603	+	11.9282i	0.773191	+	0.446402i
$715$	1.73205	+	3.00000i	0.0647750	+	0.112194i
$716$	−29.4641	+	29.4641i	−1.10113	+	1.10113i
$717$	5.73205	−	5.73205i	0.214067	−	0.214067i
$718$	16.2487	+	16.2487i	0.606397	+	0.606397i
$719$	−39.0000	+	22.5167i	−1.45445	+	0.839730i	−0.998730	−	0.0503909i	$-0.983953\pi$
$719$	−39.0000	+	22.5167i	−1.45445	+	0.839730i	−0.455725	+	0.890121i	$0.650620\pi$
$720$	−1.46410	−	1.46410i	−0.0545638	−	0.0545638i
$721$	16.6603	−	4.46410i	0.620460	−	0.166252i
$722$	−0.366025	+	1.36603i	−0.0136221	+	0.0508382i
$723$	−5.36603	+	20.0263i	−0.199565	+	0.744785i
$724$	11.5885	−	20.0718i	0.430682	−	0.745962i
$725$	−8.36603	+	31.2224i	−0.310706	+	1.15957i
$726$	12.8301	−	3.43782i	0.476171	−	0.127590i
$727$	−9.66025	−	36.0526i	−0.358279	−	1.33712i	−0.876308	−	0.481752i	$-0.840001\pi$
$727$	−9.66025	−	36.0526i	−0.358279	−	1.33712i	0.518029	−	0.855363i	$-0.326666\pi$
$728$	−20.3923	−	35.3205i	−0.755789	−	1.30907i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	7.56218	−	4.36603i	0.279697	−	0.161483i
$732$	−15.9282	−	4.26795i	−0.588723	−	0.157748i
$733$	14.3923	−	24.9282i	0.531592	−	0.920744i	−0.467728	−	0.883872i	$-0.654927\pi$
$733$	14.3923	−	24.9282i	0.531592	−	0.920744i	0.999320	−	0.0368718i	$-0.0117393\pi$
$734$	31.3205	−	8.39230i	1.15606	−	0.309766i
$735$	−0.0621778	−	0.232051i	−0.00229346	−	0.00855932i
$736$	−5.85641			−0.215870
$737$	8.32051	−	14.4115i	0.306490	−	0.530856i
$738$	−11.3923	−	11.3923i	−0.419357	−	0.419357i
$739$		−	15.8564i		−	0.583287i	−0.956527	−	0.291644i	$-0.905798\pi$
$739$		−	15.8564i		−	0.583287i	0.956527	−	0.291644i	$-0.0942021\pi$
$740$	4.07180	+	4.80385i	0.149682	+	0.176593i
$741$			22.3923i			0.822602i
$742$	35.3205	−	35.3205i	1.29666	−	1.29666i
$743$	10.7583	−	18.6340i	0.394685	−	0.683614i	−0.598376	−	0.801215i	$-0.704187\pi$
$743$	10.7583	−	18.6340i	0.394685	−	0.683614i	0.993061	+	0.117601i	$0.0375204\pi$
$744$	−11.0718	−	6.39230i	−0.405912	−	0.234353i
$745$	0.741670	+	2.76795i	0.0271727	+	0.101410i
$746$	−5.22243	−	19.4904i	−0.191207	−	0.713594i
$747$	−1.46410	+	2.53590i	−0.0535687	+	0.0927837i
$748$	−15.1244	−	4.05256i	−0.553001	−	0.148176i
$749$	27.5885	−	15.9282i	1.00806	−	0.582004i
$750$	−3.56218	+	6.16987i	−0.130072	+	0.225292i
$751$	30.3397			1.10711			0.553557	−	0.832812i	$-0.313270\pi$
$751$	30.3397			1.10711			0.553557	+	0.832812i	$0.313270\pi$
$752$		−	8.78461i		−	0.320342i
$753$	2.97372	+	11.0981i	0.108368	+	0.404436i
$754$	−13.1962	−	49.2487i	−0.480576	−	1.79353i
$755$	−2.12436	+	7.92820i	−0.0773132	+	0.288537i
$756$	−4.73205	−	2.73205i	−0.172103	−	0.0993637i
$757$	4.01666	−	14.9904i	0.145988	−	0.544835i	−0.853721	−	0.520730i	$-0.825660\pi$
$757$	4.01666	−	14.9904i	0.145988	−	0.544835i	0.999709	−	0.0241047i	$-0.00767350\pi$
$758$	−12.6603	−	3.39230i	−0.459841	−	0.123214i
$759$	1.26795	−	0.339746i	0.0460236	−	0.0123320i
$760$	−1.60770	+	6.00000i	−0.0583172	+	0.217643i
$761$	7.50000	−	4.33013i	0.271875	−	0.156967i	−0.357865	−	0.933774i	$-0.616495\pi$
$761$	7.50000	−	4.33013i	0.271875	−	0.156967i	0.629739	+	0.776807i	$0.283162\pi$
$762$	13.4641	−	13.4641i	0.487753	−	0.487753i
$763$	13.7321	−	13.7321i	0.497134	−	0.497134i
$764$	−24.0000	+	24.0000i	−0.868290	+	0.868290i
$765$	1.59808	+	2.76795i	0.0577786	+	0.100075i
$766$	8.26795	−	14.3205i	0.298733	−	0.517421i
$767$	−74.6410			−2.69513
$768$	−13.8564	−	8.00000i	−0.500000	−	0.288675i
$769$	−8.12436	−	8.12436i	−0.292972	−	0.292972i	0.545281	−	0.838253i	$-0.316423\pi$
$769$	−8.12436	−	8.12436i	−0.292972	−	0.292972i	−0.838253	+	0.545281i	$0.816423\pi$
$770$	1.26795	+	2.19615i	0.0456937	+	0.0791438i
$771$	4.70577	+	4.70577i	0.169474	+	0.169474i
$772$	24.1962	+	24.1962i	0.870839	+	0.870839i
$773$	28.2391	+	16.3038i	1.01569	+	0.586409i	0.912852	−	0.408290i	$-0.133875\pi$
$773$	28.2391	+	16.3038i	1.01569	+	0.586409i	0.102837	+	0.994698i	$0.467208\pi$
$774$	−1.73205	+	1.00000i	−0.0622573	+	0.0359443i
$775$	−5.53590	+	20.6603i	−0.198855	+	0.742138i
$776$	−51.0333			−1.83199
$777$	13.6603	+	9.46410i	0.490059	+	0.339523i
$778$	−15.7583	+	27.2942i	−0.564964	+	0.978546i
$779$	−12.5096	+	46.6865i	−0.448204	+	1.67272i
$780$		−	5.46410i		−	0.195646i
$781$	7.39230	−	12.8038i	0.264517	−	0.458158i
$782$	8.73205	+	2.33975i	0.312257	+	0.0836691i
$783$	−4.83013	−	4.83013i	−0.172615	−	0.172615i
$784$	−0.928203	−	1.60770i	−0.0331501	−	0.0574177i
$785$	5.63397	−	5.63397i	0.201085	−	0.201085i
$786$		−	25.8564i		−	0.922267i
$787$	−12.7846			−0.455722			−0.227861	−	0.973694i	$-0.573173\pi$
$787$	−12.7846			−0.455722			−0.227861	+	0.973694i	$0.573173\pi$
$788$	−1.00000	−	1.73205i	−0.0356235	−	0.0617018i
$789$	−6.00000	+	3.46410i	−0.213606	+	0.123325i
$790$	0.660254	−	2.46410i	0.0234908	−	0.0876688i
$791$	−3.26795	+	3.26795i	−0.116195	+	0.116195i
$792$	3.46410	+	0.928203i	0.123091	+	0.0329823i
$793$	−21.7583	−	37.6865i	−0.772661	−	1.33829i
$794$	−0.607695	+	0.607695i	−0.0215663	+	0.0215663i
$795$	6.46410	−	1.73205i	0.229258	−	0.0614295i
$796$	−38.1051	−	38.1051i	−1.35060	−	1.35060i
$797$	47.1506	+	12.6340i	1.67016	+	0.447518i	0.965154	−	0.261682i	$-0.0842772\pi$
$797$	47.1506	+	12.6340i	1.67016	+	0.447518i	0.705007	+	0.709200i	$0.250944\pi$
$798$			16.3923i			0.580281i
$799$	−3.50962	+	13.0981i	−0.124161	+	0.463377i
$800$	−6.92820	+	25.8564i	−0.244949	+	0.914162i
$801$	−2.59808	+	0.696152i	−0.0917985	+	0.0245973i
$802$	−2.39230			−0.0844752
$803$		0			0
$804$	−22.7321	+	13.1244i	−0.801698	+	0.462860i
$805$	−0.732051	−	1.26795i	−0.0258014	−	0.0446893i
$806$	−8.73205	−	32.5885i	−0.307573	−	1.14788i
$807$	−5.00000	+	8.66025i	−0.176008	+	0.304855i
$808$	−29.7128	−	29.7128i	−1.04529	−	1.04529i
$809$	28.9545	−	7.75833i	1.01799	−	0.272768i	0.289023	−	0.957322i	$-0.406670\pi$
$809$	28.9545	−	7.75833i	1.01799	−	0.272768i	0.728962	+	0.684554i	$0.240003\pi$
$810$	−0.366025	−	0.633975i	−0.0128608	−	0.0222756i
$811$	−2.73205	+	4.73205i	−0.0959353	+	0.166165i	−0.909999	−	0.414611i	$-0.863918\pi$
$811$	−2.73205	+	4.73205i	−0.0959353	+	0.166165i	0.814063	+	0.580776i	$0.197251\pi$
$812$	−9.66025	−	36.0526i	−0.339008	−	1.26520i
$813$	14.5885			0.511640
$814$	−10.2679	−	3.67949i	−0.359891	−	0.128966i
$815$			6.33975i			0.222072i
$816$	17.4641	+	17.4641i	0.611366	+	0.611366i
$817$	5.19615	+	3.00000i	0.181790	+	0.104957i
$818$	17.4186	+	30.1699i	0.609027	+	1.05486i
$819$	−3.73205	−	13.9282i	−0.130408	−	0.486691i
$820$	3.05256	−	11.3923i	0.106600	−	0.397837i
$821$	1.85641	+	1.07180i	0.0647890	+	0.0374060i	0.532045	−	0.846716i	$-0.321424\pi$
$821$	1.85641	+	1.07180i	0.0647890	+	0.0374060i	−0.467256	+	0.884122i	$0.654757\pi$
$822$	18.7583	−	5.02628i	0.654272	−	0.175312i
$823$	13.3923	−	7.73205i	0.466826	−	0.269522i	−0.248084	−	0.968739i	$-0.579801\pi$
$823$	13.3923	−	7.73205i	0.466826	−	0.269522i	0.714910	+	0.699216i	$0.246468\pi$
$824$	17.8564			0.622057
$825$		−	6.00000i		−	0.208893i
$826$	−54.6410			−1.90120
$827$	5.71281	+	21.3205i	0.198654	+	0.741387i	0.991291	+	0.131692i	$0.0420411\pi$
$827$	5.71281	+	21.3205i	0.198654	+	0.741387i	−0.792637	+	0.609694i	$0.791292\pi$
$828$	−2.00000	−	0.535898i	−0.0695048	−	0.0186238i
$829$	9.29423	+	2.49038i	0.322802	+	0.0864945i	0.416581	−	0.909098i	$-0.363228\pi$
$829$	9.29423	+	2.49038i	0.322802	+	0.0864945i	−0.0937793	+	0.995593i	$0.529895\pi$
$830$	−2.14359			−0.0744052
$831$	−3.35641	+	12.5263i	−0.116432	+	0.434532i
$832$	−10.9282	−	40.7846i	−0.378867	−	1.41395i
$833$	0.741670	+	2.76795i	0.0256973	+	0.0959038i
$834$	9.46410	−	9.46410i	0.327715	−	0.327715i
$835$	−0.928203	+	0.535898i	−0.0321218	+	0.0185455i
$836$	−2.78461	−	10.3923i	−0.0963077	−	0.359425i
$837$	−3.19615	−	3.19615i	−0.110475	−	0.110475i
$838$	−12.4641	−	3.33975i	−0.430565	−	0.115370i
$839$	27.7321	+	48.0333i	0.957417	+	1.65829i	0.728738	+	0.684792i	$0.240107\pi$
$839$	27.7321	+	48.0333i	0.957417	+	1.65829i	0.228679	+	0.973502i	$0.426560\pi$
$840$		−	4.00000i		−	0.138013i
$841$		−	17.6603i		−	0.608974i
$842$		−	32.3397i		−	1.11450i
$843$	14.0981	+	14.0981i	0.485564	+	0.485564i
$844$			38.2487i			1.31657i
$845$	5.43782	−	5.43782i	0.187067	−	0.187067i
$846$	0.803848	−	3.00000i	0.0276368	−	0.103142i
$847$	22.2224	+	12.8301i	0.763572	+	0.440848i
$848$	44.7846	−	25.8564i	1.53791	−	0.887913i
$849$	10.8301	+	2.90192i	0.371689	+	0.0995938i
$850$	20.6603	−	35.7846i	0.708641	−	1.22740i
$851$	5.92820	+	2.12436i	0.203216	+	0.0728220i
$852$	−20.1962	+	11.6603i	−0.691909	+	0.399474i
$853$	41.7487	+	11.1865i	1.42945	+	0.383020i	0.888826	−	0.458245i	$-0.151522\pi$
$853$	41.7487	+	11.1865i	1.42945	+	0.383020i	0.540623	+	0.841265i	$0.318189\pi$
$854$	−15.9282	−	27.5885i	−0.545052	−	0.944058i
$855$	−1.09808	+	1.90192i	−0.0375534	+	0.0650444i
$856$	31.8564	−	8.53590i	1.08883	−	0.291751i
$857$	−19.6147	+	19.6147i	−0.670027	+	0.670027i	−0.957722	−	0.287695i	$-0.907111\pi$
$857$	−19.6147	+	19.6147i	−0.670027	+	0.670027i	0.287695	+	0.957722i	$0.407111\pi$
$858$	4.73205	+	8.19615i	0.161550	+	0.279812i
$859$	−24.5167	+	24.5167i	−0.836498	+	0.836498i	−0.988396	−	0.151898i	$-0.951461\pi$
$859$	−24.5167	+	24.5167i	−0.836498	+	0.836498i	0.151898	+	0.988396i	$0.451461\pi$
$860$	−1.26795	−	0.732051i	−0.0432367	−	0.0249627i
$861$		−	31.1244i		−	1.06072i
$862$	10.5167	+	6.07180i	0.358199	+	0.206806i
$863$	1.26795	−	0.732051i	0.0431615	−	0.0249193i	−0.478264	−	0.878216i	$-0.658734\pi$
$863$	1.26795	−	0.732051i	0.0431615	−	0.0249193i	0.521425	+	0.853297i	$0.325400\pi$
$864$	−4.00000	−	4.00000i	−0.136083	−	0.136083i
$865$	−1.70577	−	1.70577i	−0.0579980	−	0.0579980i
$866$	9.33975	−	9.33975i	0.317377	−	0.317377i
$867$	−10.5622	−	18.2942i	−0.358710	−	0.621305i
$868$	−6.39230	−	23.8564i	−0.216969	−	0.809739i
$869$	1.14359	+	4.26795i	0.0387938	+	0.144780i
$870$	1.29423	−	4.83013i	0.0438785	−	0.163757i
$871$	−66.9090	−	17.9282i	−2.26712	−	0.607474i
$872$	17.4115	−	10.0526i	0.589629	−	0.340423i
$873$	−17.4282	−	4.66987i	−0.589855	−	0.158051i
$874$	1.60770	+	6.00000i	0.0543811	+	0.202953i
$875$	−13.2942	+	3.56218i	−0.449427	+	0.120424i
$876$		0			0
$877$			55.6410i			1.87886i	0.342736	+	0.939432i	$0.388646\pi$
$877$			55.6410i			1.87886i	−0.342736	+	0.939432i	$0.611354\pi$
$878$	8.19615	+	4.73205i	0.276607	+	0.159699i
$879$	−1.66987	−	2.89230i	−0.0563234	−	0.0975550i
$880$	0.679492	+	2.53590i	0.0229057	+	0.0854851i
$881$	−32.6769	−	18.8660i	−1.10091	−	0.635613i	−0.164453	−	0.986385i	$-0.552586\pi$
$881$	−32.6769	−	18.8660i	−1.10091	−	0.635613i	−0.936461	+	0.350772i	$0.885919\pi$
$882$	−0.169873	−	0.633975i	−0.00571992	−	0.0213470i
$883$	12.3923	−	3.32051i	0.417034	−	0.111744i	−0.0441993	−	0.999023i	$-0.514074\pi$
$883$	12.3923	−	3.32051i	0.417034	−	0.111744i	0.461234	+	0.887279i	$0.347407\pi$
$884$			65.1769i			2.19214i
$885$	−6.33975	−	3.66025i	−0.213108	−	0.123038i
$886$	−17.8564	−	17.8564i	−0.599898	−	0.599898i
$887$	45.3205			1.52171			0.760857	−	0.648920i	$-0.224779\pi$
$887$	45.3205			1.52171			0.760857	+	0.648920i	$0.224779\pi$
$888$	11.1244	+	13.1244i	0.373309	+	0.440425i
$889$	36.7846			1.23372
$890$	−1.39230	−	1.39230i	−0.0466702	−	0.0466702i
$891$	1.09808	+	0.633975i	0.0367869	+	0.0212389i
$892$	36.7846			1.23164
$893$	−9.00000	+	2.41154i	−0.301174	+	0.0806992i
$894$	2.02628	+	7.56218i	0.0677689	+	0.252917i
$895$	−9.33975	−	5.39230i	−0.312193	−	0.180245i
$896$	−8.00000	−	29.8564i	−0.267261	−	0.997433i
$897$	−2.73205	−	4.73205i	−0.0912205	−	0.157999i
$898$	−44.3205	−	25.5885i	−1.47899	−	0.853898i
$899$		−	30.8756i		−	1.02976i
$900$	−4.73205	+	8.19615i	−0.157735	+	0.273205i
$901$	−77.1051	+	20.6603i	−2.56874	+	0.688293i
$902$	5.28719	+	19.7321i	0.176044	+	0.657005i
$903$	−3.73205	−	1.00000i	−0.124195	−	0.0332779i
$904$	−4.14359	+	2.39230i	−0.137814	+	0.0795669i
$905$	5.79423	+	1.55256i	0.192607	+	0.0516088i
$906$	−5.80385	+	21.6603i	−0.192820	+	0.719614i
$907$	3.15064	+	11.7583i	0.104615	+	0.390429i	0.998301	−	0.0582638i	$-0.0185564\pi$
$907$	3.15064	+	11.7583i	0.104615	+	0.390429i	−0.893686	+	0.448693i	$0.851890\pi$
$908$	44.5885	−	11.9474i	1.47972	−	0.396490i
$909$	−7.42820	−	12.8660i	−0.246378	−	0.426739i
$910$	7.46410	−	7.46410i	0.247433	−	0.247433i
$911$	−8.33975	−	8.33975i	−0.276308	−	0.276308i	0.555325	−	0.831633i	$-0.312594\pi$
$911$	−8.33975	−	8.33975i	−0.276308	−	0.276308i	−0.831633	+	0.555325i	$0.812594\pi$
$912$	−4.39230	+	16.3923i	−0.145444	+	0.542803i
$913$	3.21539	−	1.85641i	0.106414	−	0.0614381i
$914$	−0.849365	−	0.490381i	−0.0280945	−	0.0162204i
$915$		−	4.26795i		−	0.141094i
$916$	−21.3923	+	37.0526i	−0.706822	+	1.22425i
$917$	35.3205	−	35.3205i	1.16639	−	1.16639i
$918$	4.36603	+	7.56218i	0.144100	+	0.249589i
$919$	−31.1769	+	31.1769i	−1.02843	+	1.02843i	−0.0288477	+	0.999584i	$0.509184\pi$
$919$	−31.1769	+	31.1769i	−1.02843	+	1.02843i	−0.999584	+	0.0288477i	$0.990816\pi$
$920$	−0.392305	−	1.46410i	−0.0129339	−	0.0482700i
$921$	−12.0981	+	20.9545i	−0.398645	+	0.690474i
$922$	22.6603	+	39.2487i	0.746276	+	1.29259i
$923$	−59.4449	−	15.9282i	−1.95665	−	0.524283i
$924$	3.46410	+	6.00000i	0.113961	+	0.197386i
$925$	16.3923	−	23.6603i	0.538976	−	0.777944i
$926$	0.464102	−	0.803848i	0.0152513	−	0.0264161i
$927$	6.09808	+	1.63397i	0.200287	+	0.0536668i
$928$		−	38.6410i		−	1.26845i
$929$	−28.7942	−	16.6244i	−0.944708	−	0.545427i	−0.0532750	−	0.998580i	$-0.516966\pi$
$929$	−28.7942	−	16.6244i	−0.944708	−	0.545427i	−0.891433	+	0.453152i	$0.850299\pi$
$930$	0.856406	−	3.19615i	0.0280827	−	0.104806i
$931$	−1.39230	+	1.39230i	−0.0456309	+	0.0456309i
$932$	7.07180			0.231644
$933$	−0.803848	−	0.803848i	−0.0263168	−	0.0263168i
$934$			5.85641i			0.191627i
$935$		−	4.05256i		−	0.132533i
$936$		−	14.9282i		−	0.487944i
$937$	−8.66987	−	15.0167i	−0.283232	−	0.490573i	0.688947	−	0.724812i	$-0.258073\pi$
$937$	−8.66987	−	15.0167i	−0.283232	−	0.490573i	−0.972179	+	0.234239i	$0.924740\pi$
$938$	−48.9808	−	13.1244i	−1.59928	−	0.428525i
$939$	16.0981	+	16.0981i	0.525341	+	0.525341i
$940$	2.19615	−	0.588457i	0.0716306	−	0.0191934i
$941$	3.69615	−	2.13397i	0.120491	−	0.0695656i	−0.438543	−	0.898710i	$-0.644505\pi$
$941$	3.69615	−	2.13397i	0.120491	−	0.0695656i	0.559034	+	0.829145i	$0.311172\pi$
$942$	15.3923	−	15.3923i	0.501508	−	0.501508i
$943$	−3.05256	−	11.3923i	−0.0994050	−	0.370984i
$944$	−54.6410	−	14.6410i	−1.77841	−	0.476524i
$945$	0.366025	−	1.36603i	0.0119068	−	0.0444368i
$946$	2.53590			0.0824492
$947$	21.8564	+	5.85641i	0.710238	+	0.190308i	0.595812	−	0.803124i	$-0.296830\pi$
$947$	21.8564	+	5.85641i	0.710238	+	0.190308i	0.114426	+	0.993432i	$0.463497\pi$
$948$	1.80385	−	6.73205i	0.0585862	−	0.218647i
$949$		0			0
$950$	28.3923			0.921168
$951$		−	10.6603i		−	0.345682i
$952$			47.7128i			1.54638i
$953$	13.3923	−	7.73205i	0.433819	−	0.250466i	−0.267153	−	0.963654i	$-0.586083\pi$
$953$	13.3923	−	7.73205i	0.433819	−	0.250466i	0.700972	+	0.713188i	$0.252750\pi$
$954$	17.6603	−	4.73205i	0.571772	−	0.153206i
$955$	−7.60770	−	4.39230i	−0.246179	−	0.142132i
$956$	15.6603	+	4.19615i	0.506489	+	0.135713i
$957$	2.24167	+	8.36603i	0.0724629	+	0.270435i
$958$	−5.60770	−	9.71281i	−0.181176	−	0.313807i
$959$	32.4904	+	18.7583i	1.04917	+	0.605738i
$960$	1.07180	−	4.00000i	0.0345921	−	0.129099i
$961$			10.5692i			0.340943i
$962$	−3.73205	+	45.2487i	−0.120326	+	1.45888i
$963$	11.6603			0.375746
$964$	−40.0526	+	10.7321i	−1.29001	+	0.345656i
$965$	−4.42820	+	7.66987i	−0.142549	+	0.246902i
$966$	−2.00000	−	3.46410i	−0.0643489	−	0.111456i
$967$	−18.3923	+	4.92820i	−0.591457	+	0.158480i	−0.542119	−	0.840302i	$-0.682378\pi$
$967$	−18.3923	+	4.92820i	−0.591457	+	0.158480i	−0.0493378	+	0.998782i	$0.515711\pi$
$968$	18.7846	+	18.7846i	0.603760	+	0.603760i
$969$	13.0981	−	22.6865i	0.420771	−	0.728796i
$970$	−3.41858	−	12.7583i	−0.109764	−	0.409645i
$971$	−20.3205	−	35.1962i	−0.652116	−	1.12950i	−0.982608	−	0.185690i	$-0.940548\pi$
$971$	−20.3205	−	35.1962i	−0.652116	−	1.12950i	0.330492	−	0.943809i	$-0.392785\pi$
$972$	−1.00000	−	1.73205i	−0.0320750	−	0.0555556i
$973$	25.8564			0.828918
$974$	33.0718			1.05969
$975$	−24.1244	+	6.46410i	−0.772598	+	0.207017i
$976$	−8.53590	−	31.8564i	−0.273227	−	1.01970i
$977$	7.95448	−	29.6865i	0.254486	−	0.949756i	−0.713889	−	0.700259i	$-0.753068\pi$
$977$	7.95448	−	29.6865i	0.254486	−	0.949756i	0.968375	−	0.249497i	$-0.0802654\pi$
$978$			17.3205i			0.553849i
$979$	3.29423	+	0.882686i	0.105284	+	0.0282108i
$980$	0.339746	−	0.339746i	0.0108528	−	0.0108528i
$981$	6.86603	−	1.83975i	0.219215	−	0.0587386i
$982$	−17.2679	+	17.2679i	−0.551042	+	0.551042i
$983$	16.2224	+	28.0981i	0.517415	+	0.896189i	0.999795	+	0.0202275i	$0.00643905\pi$
$983$	16.2224	+	28.0981i	0.517415	+	0.896189i	−0.482380	+	0.875962i	$0.660228\pi$
$984$	8.33975	−	31.1244i	0.265861	−	0.992208i
$985$	0.366025	−	0.366025i	0.0116625	−	0.0116625i
$986$	−15.4378	+	57.6147i	−0.491640	+	1.83483i
$987$	5.19615	−	3.00000i	0.165395	−	0.0954911i
$988$	−38.7846	+	22.3923i	−1.23390	+	0.712394i
$989$	−1.46410			−0.0465557
$990$			0.928203i			0.0295002i
$991$	31.4449	−	31.4449i	0.998879	−	0.998879i	−0.00112036	−	0.999999i	$-0.500357\pi$
$991$	31.4449	−	31.4449i	0.998879	−	0.998879i	0.999999	+	0.00112036i	$0.000356621\pi$
$992$		−	25.5692i		−	0.811824i
$993$	11.6603	+	11.6603i	0.370027	+	0.370027i
$994$	−43.5167	−	11.6603i	−1.38026	−	0.369841i
$995$	6.97372	−	12.0788i	0.221082	−	0.382925i
$996$	−5.85641			−0.185567
$997$	−15.2224	+	56.8109i	−0.482099	+	1.79922i	0.110683	+	0.993856i	$0.464696\pi$
$997$	−15.2224	+	56.8109i	−0.482099	+	1.79922i	−0.592782	+	0.805363i	$0.701970\pi$
$998$	6.66025	−	11.5359i	0.210827	−	0.365162i
$999$	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.547.1	✓	4
8.3	odd	2		888.2.bu.b.547.1	yes	4
37.23	odd	12		888.2.bu.b.763.1	yes	4
296.171	even	12	inner	888.2.bu.a.763.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.bu.a.547.1	✓	4	1.1	even	1	trivial
888.2.bu.a.763.1	yes	4	296.171	even	12	inner
888.2.bu.b.547.1	yes	4	8.3	odd	2
888.2.bu.b.763.1	yes	4	37.23	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-0.866025 - 0.500000i) q^{3} -2.00000i q^{4} +(0.500000 - 0.133975i) q^{5} +(1.36603 - 0.366025i) q^{6} +(2.36603 + 1.36603i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-0.866025 - 0.500000i) q^{3} -2.00000i q^{4} +(0.500000 - 0.133975i) q^{5} +(1.36603 - 0.366025i) q^{6} +(2.36603 + 1.36603i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.366025 + 0.633975i) q^{10} -1.26795i q^{11} +(-1.00000 + 1.73205i) q^{12} +(-5.09808 + 1.36603i) q^{13} +(-3.73205 + 1.00000i) q^{14} +(-0.500000 - 0.133975i) q^{15} -4.00000 q^{16} +(5.96410 + 1.59808i) q^{17} +(-1.36603 - 0.366025i) q^{18} +(1.09808 + 4.09808i) q^{19} +(-0.267949 - 1.00000i) q^{20} +(-1.36603 - 2.36603i) q^{21} +(1.26795 + 1.26795i) q^{22} +(-0.732051 - 0.732051i) q^{23} +(-0.732051 - 2.73205i) q^{24} +(-4.09808 + 2.36603i) q^{25} +(3.73205 - 6.46410i) q^{26} -1.00000i q^{27} +(2.73205 - 4.73205i) q^{28} +(4.83013 - 4.83013i) q^{29} +(0.633975 - 0.366025i) q^{30} +(3.19615 - 3.19615i) q^{31} +(4.00000 - 4.00000i) q^{32} +(-0.633975 + 1.09808i) q^{33} +(-7.56218 + 4.36603i) q^{34} +(1.36603 + 0.366025i) q^{35} +(1.73205 - 1.00000i) q^{36} +(-5.50000 + 2.59808i) q^{37} +(-5.19615 - 3.00000i) q^{38} +(5.09808 + 1.36603i) q^{39} +(1.26795 + 0.732051i) q^{40} +(9.86603 + 5.69615i) q^{41} +(3.73205 + 1.00000i) q^{42} +(1.00000 - 1.00000i) q^{43} -2.53590 q^{44} +(0.366025 + 0.366025i) q^{45} +1.46410 q^{46} +2.19615i q^{47} +(3.46410 + 2.00000i) q^{48} +(0.232051 + 0.401924i) q^{49} +(1.73205 - 6.46410i) q^{50} +(-4.36603 - 4.36603i) q^{51} +(2.73205 + 10.1962i) q^{52} +(-11.1962 + 6.46410i) q^{53} +(1.00000 + 1.00000i) q^{54} +(-0.169873 - 0.633975i) q^{55} +(2.00000 + 7.46410i) q^{56} +(1.09808 - 4.09808i) q^{57} +9.66025i q^{58} +(13.6603 + 3.66025i) q^{59} +(-0.267949 + 1.00000i) q^{60} +(2.13397 + 7.96410i) q^{61} +6.39230i q^{62} +2.73205i q^{63} +8.00000i q^{64} +(-2.36603 + 1.36603i) q^{65} +(-0.464102 - 1.73205i) q^{66} +(11.3660 + 6.56218i) q^{67} +(3.19615 - 11.9282i) q^{68} +(0.267949 + 1.00000i) q^{69} +(-1.73205 + 1.00000i) q^{70} +(10.0981 + 5.83013i) q^{71} +(-0.732051 + 2.73205i) q^{72} +(2.90192 - 8.09808i) q^{74} +4.73205 q^{75} +(8.19615 - 2.19615i) q^{76} +(1.73205 - 3.00000i) q^{77} +(-6.46410 + 3.73205i) q^{78} +(-3.36603 + 0.901924i) q^{79} +(-2.00000 + 0.535898i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-15.5622 + 4.16987i) q^{82} +(1.46410 + 2.53590i) q^{83} +(-4.73205 + 2.73205i) q^{84} +3.19615 q^{85} +2.00000i q^{86} +(-6.59808 + 1.76795i) q^{87} +(2.53590 - 2.53590i) q^{88} +(-0.696152 + 2.59808i) q^{89} -0.732051 q^{90} +(-13.9282 - 3.73205i) q^{91} +(-1.46410 + 1.46410i) q^{92} +(-4.36603 + 1.16987i) q^{93} +(-2.19615 - 2.19615i) q^{94} +(1.09808 + 1.90192i) q^{95} +(-5.46410 + 1.46410i) q^{96} +(-12.7583 + 12.7583i) q^{97} +(-0.633975 - 0.169873i) q^{98} +(1.09808 - 0.633975i) 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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