LMFDB - Embedded newform 360.2.br.b.173.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(77,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 10, 3]))

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

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

chi := DirichletCharacter("360.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.br (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:	$2.87461447277$
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			173.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	360.173
Dual form			360.2.br.b.77.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(1.50000 - 0.866025i) q^{3} -2.00000i q^{4} +(-2.23205 + 0.133975i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(1.13397 + 4.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.50000 - 0.866025i) q^{3} -2.00000i q^{4} +(-2.23205 + 0.133975i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(1.13397 + 4.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +(2.09808 - 2.36603i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-1.73205 - 3.00000i) q^{12} +(1.73205 + 0.464102i) q^{13} +(-5.36603 - 3.09808i) q^{14} +(-3.23205 + 2.13397i) q^{15} -4.00000 q^{16} +(3.00000 + 3.00000i) q^{17} +(1.09808 + 4.09808i) q^{18} +4.73205 q^{19} +(0.267949 + 4.46410i) q^{20} +(5.36603 + 5.36603i) q^{21} +(-0.732051 - 2.73205i) q^{22} +(0.866025 + 0.232051i) q^{23} +(4.73205 + 1.26795i) q^{24} +(4.96410 - 0.598076i) q^{25} +(-2.19615 + 1.26795i) q^{26} -5.19615i q^{27} +(8.46410 - 2.26795i) q^{28} +(-2.76795 - 1.59808i) q^{29} +(1.09808 - 5.36603i) q^{30} +(4.09808 + 7.09808i) q^{31} +(4.00000 - 4.00000i) q^{32} +3.46410i q^{33} -6.00000 q^{34} +(-3.09808 - 9.29423i) q^{35} +(-5.19615 - 3.00000i) q^{36} +(0.464102 + 0.464102i) q^{37} +(-4.73205 + 4.73205i) q^{38} +(3.00000 - 0.803848i) q^{39} +(-4.73205 - 4.19615i) q^{40} +(-5.59808 + 3.23205i) q^{41} -10.7321 q^{42} +(-2.36603 - 8.83013i) q^{43} +(3.46410 + 2.00000i) q^{44} +(-3.00000 + 6.00000i) q^{45} +(-1.09808 + 0.633975i) q^{46} +(-1.50000 + 0.401924i) q^{47} +(-6.00000 + 3.46410i) q^{48} +(-10.5622 + 6.09808i) q^{49} +(-4.36603 + 5.56218i) q^{50} +(7.09808 + 1.90192i) q^{51} +(0.928203 - 3.46410i) q^{52} +(5.19615 + 5.19615i) q^{53} +(5.19615 + 5.19615i) q^{54} +(2.00000 - 4.00000i) q^{55} +(-6.19615 + 10.7321i) q^{56} +(7.09808 - 4.09808i) q^{57} +(4.36603 - 1.16987i) q^{58} +(-1.56218 + 0.901924i) q^{59} +(4.26795 + 6.46410i) q^{60} +(-12.6962 - 7.33013i) q^{61} +(-11.1962 - 3.00000i) q^{62} +(12.6962 + 3.40192i) q^{63} +8.00000i q^{64} +(-3.92820 - 0.803848i) q^{65} +(-3.46410 - 3.46410i) q^{66} +(-1.96410 + 7.33013i) q^{67} +(6.00000 - 6.00000i) q^{68} +(1.50000 - 0.401924i) q^{69} +(12.3923 + 6.19615i) q^{70} -12.0000i q^{71} +(8.19615 - 2.19615i) q^{72} +(-10.1962 - 10.1962i) q^{73} -0.928203 q^{74} +(6.92820 - 5.19615i) q^{75} -9.46410i q^{76} +(-8.46410 - 2.26795i) q^{77} +(-2.19615 + 3.80385i) q^{78} +(1.90192 + 1.09808i) q^{79} +(8.92820 - 0.535898i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.36603 - 8.83013i) q^{82} +(11.3301 - 3.03590i) q^{83} +(10.7321 - 10.7321i) q^{84} +(-7.09808 - 6.29423i) q^{85} +(11.1962 + 6.46410i) q^{86} -5.53590 q^{87} +(-5.46410 + 1.46410i) q^{88} +2.66025 q^{89} +(-3.00000 - 9.00000i) q^{90} +7.85641i q^{91} +(0.464102 - 1.73205i) q^{92} +(12.2942 + 7.09808i) q^{93} +(1.09808 - 1.90192i) q^{94} +(-10.5622 + 0.633975i) q^{95} +(2.53590 - 9.46410i) q^{96} +(1.83013 + 6.83013i) q^{97} +(4.46410 - 16.6603i) q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 8 q^{7} + 8 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 6 * q^3 - 2 * q^5 - 6 * q^6 + 8 * q^7 + 8 * q^8 + 6 * q^9	$ 4 q - 4 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 8 q^{7} + 8 q^{8} + 6 q^{9} - 2 q^{10} - 4 q^{11} - 18 q^{14} - 6 q^{15} - 16 q^{16} + 12 q^{17} - 6 q^{18} + 12 q^{19} + 8 q^{20} + 18 q^{21} + 4 q^{22} + 12 q^{24} + 6 q^{25} + 12 q^{26} + 20 q^{28} - 18 q^{29} - 6 q^{30} + 6 q^{31} + 16 q^{32} - 24 q^{34} - 2 q^{35} - 12 q^{37} - 12 q^{38} + 12 q^{39} - 12 q^{40} - 12 q^{41} - 36 q^{42} - 6 q^{43} - 12 q^{45} + 6 q^{46} - 6 q^{47} - 24 q^{48} - 18 q^{49} - 14 q^{50} + 18 q^{51} - 24 q^{52} + 8 q^{55} - 4 q^{56} + 18 q^{57} + 14 q^{58} + 18 q^{59} + 24 q^{60} - 30 q^{61} - 24 q^{62} + 30 q^{63} + 12 q^{65} + 6 q^{67} + 24 q^{68} + 6 q^{69} + 8 q^{70} + 12 q^{72} - 20 q^{73} + 24 q^{74} - 20 q^{77} + 12 q^{78} + 18 q^{79} + 8 q^{80} - 18 q^{81} + 6 q^{82} + 28 q^{83} + 36 q^{84} - 18 q^{85} + 24 q^{86} - 36 q^{87} - 8 q^{88} - 24 q^{89} - 12 q^{90} - 12 q^{92} + 18 q^{93} - 6 q^{94} - 18 q^{95} + 24 q^{96} - 10 q^{97} + 4 q^{98} + 12 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 6 * q^3 - 2 * q^5 - 6 * q^6 + 8 * q^7 + 8 * q^8 + 6 * q^9 - 2 * q^10 - 4 * q^11 - 18 * q^14 - 6 * q^15 - 16 * q^16 + 12 * q^17 - 6 * q^18 + 12 * q^19 + 8 * q^20 + 18 * q^21 + 4 * q^22 + 12 * q^24 + 6 * q^25 + 12 * q^26 + 20 * q^28 - 18 * q^29 - 6 * q^30 + 6 * q^31 + 16 * q^32 - 24 * q^34 - 2 * q^35 - 12 * q^37 - 12 * q^38 + 12 * q^39 - 12 * q^40 - 12 * q^41 - 36 * q^42 - 6 * q^43 - 12 * q^45 + 6 * q^46 - 6 * q^47 - 24 * q^48 - 18 * q^49 - 14 * q^50 + 18 * q^51 - 24 * q^52 + 8 * q^55 - 4 * q^56 + 18 * q^57 + 14 * q^58 + 18 * q^59 + 24 * q^60 - 30 * q^61 - 24 * q^62 + 30 * q^63 + 12 * q^65 + 6 * q^67 + 24 * q^68 + 6 * q^69 + 8 * q^70 + 12 * q^72 - 20 * q^73 + 24 * q^74 - 20 * q^77 + 12 * q^78 + 18 * q^79 + 8 * q^80 - 18 * q^81 + 6 * q^82 + 28 * q^83 + 36 * q^84 - 18 * q^85 + 24 * q^86 - 36 * q^87 - 8 * q^88 - 24 * q^89 - 12 * q^90 - 12 * q^92 + 18 * q^93 - 6 * q^94 - 18 * q^95 + 24 * q^96 - 10 * q^97 + 4 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$		−	2.00000i		−	1.00000i
$5$	−2.23205	+	0.133975i	−0.998203	+	0.0599153i
$5$	−2.23205	+	0.133975i	−0.998203	+	0.0599153i
$6$	−0.633975	+	2.36603i	−0.258819	+	0.965926i
$7$	1.13397	+	4.23205i	0.428602	+	1.59956i	0.755929	+	0.654654i	$0.227186\pi$
$7$	1.13397	+	4.23205i	0.428602	+	1.59956i	−0.327327	+	0.944911i	$0.606148\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	2.09808	−	2.36603i	0.663470	−	0.748203i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	−1.73205	−	3.00000i	−0.500000	−	0.866025i
$13$	1.73205	+	0.464102i	0.480384	+	0.128719i	0.490882	−	0.871226i	$-0.336675\pi$
$13$	1.73205	+	0.464102i	0.480384	+	0.128719i	−0.0104972	+	0.999945i	$0.503341\pi$
$14$	−5.36603	−	3.09808i	−1.43413	−	0.827996i
$15$	−3.23205	+	2.13397i	−0.834512	+	0.550990i
$16$	−4.00000			−1.00000
$17$	3.00000	+	3.00000i	0.727607	+	0.727607i	0.970143	−	0.242536i	$-0.0779791\pi$
$17$	3.00000	+	3.00000i	0.727607	+	0.727607i	−0.242536	+	0.970143i	$0.577979\pi$
$18$	1.09808	+	4.09808i	0.258819	+	0.965926i
$19$	4.73205			1.08561			0.542803	−	0.839860i	$-0.317363\pi$
$19$	4.73205			1.08561			0.542803	+	0.839860i	$0.317363\pi$
$20$	0.267949	+	4.46410i	0.0599153	+	0.998203i
$21$	5.36603	+	5.36603i	1.17096	+	1.17096i
$22$	−0.732051	−	2.73205i	−0.156074	−	0.582475i
$23$	0.866025	+	0.232051i	0.180579	+	0.0483859i	0.347975	−	0.937504i	$-0.386869\pi$
$23$	0.866025	+	0.232051i	0.180579	+	0.0483859i	−0.167396	+	0.985890i	$0.553536\pi$
$24$	4.73205	+	1.26795i	0.965926	+	0.258819i
$25$	4.96410	−	0.598076i	0.992820	−	0.119615i
$26$	−2.19615	+	1.26795i	−0.430701	+	0.248665i
$27$		−	5.19615i		−	1.00000i
$28$	8.46410	−	2.26795i	1.59956	−	0.428602i
$29$	−2.76795	−	1.59808i	−0.513995	−	0.296755i	0.220479	−	0.975392i	$-0.429238\pi$
$29$	−2.76795	−	1.59808i	−0.513995	−	0.296755i	−0.734474	+	0.678636i	$0.762571\pi$
$30$	1.09808	−	5.36603i	0.200480	−	0.979698i
$31$	4.09808	+	7.09808i	0.736036	+	1.27485i	0.954267	+	0.298955i	$0.0966380\pi$
$31$	4.09808	+	7.09808i	0.736036	+	1.27485i	−0.218231	+	0.975897i	$0.570029\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$			3.46410i			0.603023i
$34$	−6.00000			−1.02899
$35$	−3.09808	−	9.29423i	−0.523670	−	1.57101i
$36$	−5.19615	−	3.00000i	−0.866025	−	0.500000i
$37$	0.464102	+	0.464102i	0.0762978	+	0.0762978i	0.744226	−	0.667928i	$-0.232819\pi$
$37$	0.464102	+	0.464102i	0.0762978	+	0.0762978i	−0.667928	+	0.744226i	$0.732819\pi$
$38$	−4.73205	+	4.73205i	−0.767640	+	0.767640i
$39$	3.00000	−	0.803848i	0.480384	−	0.128719i
$40$	−4.73205	−	4.19615i	−0.748203	−	0.663470i
$41$	−5.59808	+	3.23205i	−0.874273	+	0.504762i	−0.868766	−	0.495223i	$-0.835086\pi$
$41$	−5.59808	+	3.23205i	−0.874273	+	0.504762i	−0.00550690	+	0.999985i	$0.501753\pi$
$42$	−10.7321			−1.65599
$43$	−2.36603	−	8.83013i	−0.360815	−	1.34658i	−0.873006	−	0.487710i	$-0.837832\pi$
$43$	−2.36603	−	8.83013i	−0.360815	−	1.34658i	0.512190	−	0.858872i	$-0.328834\pi$
$44$	3.46410	+	2.00000i	0.522233	+	0.301511i
$45$	−3.00000	+	6.00000i	−0.447214	+	0.894427i
$46$	−1.09808	+	0.633975i	−0.161903	+	0.0934745i
$47$	−1.50000	+	0.401924i	−0.218797	+	0.0586266i	−0.366552	−	0.930397i	$-0.619462\pi$
$47$	−1.50000	+	0.401924i	−0.218797	+	0.0586266i	0.147755	+	0.989024i	$0.452795\pi$
$48$	−6.00000	+	3.46410i	−0.866025	+	0.500000i
$49$	−10.5622	+	6.09808i	−1.50888	+	0.871154i
$50$	−4.36603	+	5.56218i	−0.617449	+	0.786611i
$51$	7.09808	+	1.90192i	0.993929	+	0.266323i
$52$	0.928203	−	3.46410i	0.128719	−	0.480384i
$53$	5.19615	+	5.19615i	0.713746	+	0.713746i	0.967317	−	0.253570i	$-0.0816050\pi$
$53$	5.19615	+	5.19615i	0.713746	+	0.713746i	−0.253570	+	0.967317i	$0.581605\pi$
$54$	5.19615	+	5.19615i	0.707107	+	0.707107i
$55$	2.00000	−	4.00000i	0.269680	−	0.539360i
$56$	−6.19615	+	10.7321i	−0.827996	+	1.43413i
$57$	7.09808	−	4.09808i	0.940163	−	0.542803i
$58$	4.36603	−	1.16987i	0.573287	−	0.153612i
$59$	−1.56218	+	0.901924i	−0.203378	+	0.117420i	−0.598230	−	0.801324i	$-0.704129\pi$
$59$	−1.56218	+	0.901924i	−0.203378	+	0.117420i	0.394852	+	0.918745i	$0.370796\pi$
$60$	4.26795	+	6.46410i	0.550990	+	0.834512i
$61$	−12.6962	−	7.33013i	−1.62558	−	0.938527i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−12.6962	−	7.33013i	−1.62558	−	0.938527i	−0.640184	−	0.768221i	$-0.721142\pi$
$62$	−11.1962	−	3.00000i	−1.42191	−	0.381000i
$63$	12.6962	+	3.40192i	1.59956	+	0.428602i
$64$			8.00000i			1.00000i
$65$	−3.92820	−	0.803848i	−0.487234	−	0.0997050i
$66$	−3.46410	−	3.46410i	−0.426401	−	0.426401i
$67$	−1.96410	+	7.33013i	−0.239953	+	0.895518i	0.735900	+	0.677090i	$0.236759\pi$
$67$	−1.96410	+	7.33013i	−0.239953	+	0.895518i	−0.975853	+	0.218427i	$0.929907\pi$
$68$	6.00000	−	6.00000i	0.727607	−	0.727607i
$69$	1.50000	−	0.401924i	0.180579	−	0.0483859i
$70$	12.3923	+	6.19615i	1.48116	+	0.740582i
$71$		−	12.0000i		−	1.42414i	−0.702109	−	0.712069i	$-0.747758\pi$
$71$		−	12.0000i		−	1.42414i	0.702109	−	0.712069i	$-0.252242\pi$
$72$	8.19615	−	2.19615i	0.965926	−	0.258819i
$73$	−10.1962	−	10.1962i	−1.19337	−	1.19337i	−0.976115	−	0.217254i	$-0.930290\pi$
$73$	−10.1962	−	10.1962i	−1.19337	−	1.19337i	−0.217254	−	0.976115i	$-0.569710\pi$
$74$	−0.928203			−0.107901
$75$	6.92820	−	5.19615i	0.800000	−	0.600000i
$76$		−	9.46410i		−	1.08561i
$77$	−8.46410	−	2.26795i	−0.964574	−	0.258457i
$78$	−2.19615	+	3.80385i	−0.248665	+	0.430701i
$79$	1.90192	+	1.09808i	0.213983	+	0.123543i	0.603161	−	0.797619i	$-0.293908\pi$
$79$	1.90192	+	1.09808i	0.213983	+	0.123543i	−0.389178	+	0.921163i	$0.627241\pi$
$80$	8.92820	−	0.535898i	0.998203	−	0.0599153i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	2.36603	−	8.83013i	0.261284	−	0.975124i
$83$	11.3301	−	3.03590i	1.24364	−	0.333233i	0.423765	−	0.905772i	$-0.360708\pi$
$83$	11.3301	−	3.03590i	1.24364	−	0.333233i	0.819878	+	0.572539i	$0.194041\pi$
$84$	10.7321	−	10.7321i	1.17096	−	1.17096i
$85$	−7.09808	−	6.29423i	−0.769894	−	0.682705i
$86$	11.1962	+	6.46410i	1.20731	+	0.697042i
$87$	−5.53590			−0.593511
$88$	−5.46410	+	1.46410i	−0.582475	+	0.156074i
$89$	2.66025			0.281986			0.140993	−	0.990011i	$-0.454970\pi$
$89$	2.66025			0.281986			0.140993	+	0.990011i	$0.454970\pi$
$90$	−3.00000	−	9.00000i	−0.316228	−	0.948683i
$91$			7.85641i			0.823575i
$92$	0.464102	−	1.73205i	0.0483859	−	0.180579i
$93$	12.2942	+	7.09808i	1.27485	+	0.736036i
$94$	1.09808	−	1.90192i	0.113258	−	0.196168i
$95$	−10.5622	+	0.633975i	−1.08366	+	0.0650444i
$96$	2.53590	−	9.46410i	0.258819	−	0.965926i
$97$	1.83013	+	6.83013i	0.185821	+	0.693494i	0.994453	+	0.105180i	$0.0335417\pi$
$97$	1.83013	+	6.83013i	0.185821	+	0.693494i	−0.808632	+	0.588315i	$0.799792\pi$
$98$	4.46410	−	16.6603i	0.450942	−	1.68294i
$99$	3.00000	+	5.19615i	0.301511	+	0.522233i
$100$	−1.19615	−	9.92820i	−0.119615	−	0.992820i
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	−0.811976	−	0.583691i	$-0.801608\pi$
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	0.911479	+	0.411346i	$0.134941\pi$
$102$	−9.00000	+	5.19615i	−0.891133	+	0.514496i
$103$	4.16987	−	15.5622i	0.410870	−	1.53339i	−0.382097	−	0.924122i	$-0.624798\pi$
$103$	4.16987	−	15.5622i	0.410870	−	1.53339i	0.792967	−	0.609265i	$-0.208535\pi$
$104$	2.53590	+	4.39230i	0.248665	+	0.430701i
$105$	−12.6962	−	11.2583i	−1.23902	−	1.09870i
$106$	−10.3923			−1.00939
$107$	6.09808	−	6.09808i	0.589523	−	0.589523i	−0.347979	−	0.937502i	$-0.613132\pi$
$107$	6.09808	−	6.09808i	0.589523	−	0.589523i	0.937502	+	0.347979i	$0.113132\pi$
$108$	−10.3923			−1.00000
$109$	−8.66025			−0.829502			−0.414751	−	0.909935i	$-0.636131\pi$
$109$	−8.66025			−0.829502			−0.414751	+	0.909935i	$0.636131\pi$
$110$	2.00000	+	6.00000i	0.190693	+	0.572078i
$111$	1.09808	+	0.294229i	0.104225	+	0.0279269i
$112$	−4.53590	−	16.9282i	−0.428602	−	1.59956i
$113$	1.73205	+	0.464102i	0.162938	+	0.0436590i	0.339366	−	0.940655i	$-0.389788\pi$
$113$	1.73205	+	0.464102i	0.162938	+	0.0436590i	−0.176428	+	0.984314i	$0.556454\pi$
$114$	−3.00000	+	11.1962i	−0.280976	+	1.04862i
$115$	−1.96410	−	0.401924i	−0.183153	−	0.0374796i
$116$	−3.19615	+	5.53590i	−0.296755	+	0.513995i
$117$	3.80385	−	3.80385i	0.351666	−	0.351666i
$118$	0.660254	−	2.46410i	0.0607813	−	0.226839i
$119$	−9.29423	+	16.0981i	−0.852001	+	1.47571i
$120$	−10.7321	−	2.19615i	−0.979698	−	0.200480i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	20.0263	−	5.36603i	1.81309	−	0.485817i
$123$	−5.59808	+	9.69615i	−0.504762	+	0.874273i
$124$	14.1962	−	8.19615i	1.27485	−	0.736036i
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$	−16.0981	+	9.29423i	−1.43413	+	0.827996i
$127$	5.90192	−	5.90192i	0.523711	−	0.523711i	−0.394979	−	0.918690i	$-0.629248\pi$
$127$	5.90192	−	5.90192i	0.523711	−	0.523711i	0.918690	+	0.394979i	$0.129248\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$	−11.1962	−	11.1962i	−0.985766	−	0.985766i
$130$	4.73205	−	3.12436i	0.415028	−	0.274024i
$131$	−3.90192	−	6.75833i	−0.340913	−	0.590478i	0.643690	−	0.765287i	$-0.277403\pi$
$131$	−3.90192	−	6.75833i	−0.340913	−	0.590478i	−0.984602	+	0.174808i	$0.944069\pi$
$132$	6.92820			0.603023
$133$	5.36603	+	20.0263i	0.465293	+	1.73650i
$134$	−5.36603	−	9.29423i	−0.463554	−	0.802899i
$135$	0.696152	+	11.5981i	0.0599153	+	0.998203i
$136$			12.0000i			1.02899i
$137$	12.9282	−	3.46410i	1.10453	−	0.295958i	0.339923	−	0.940453i	$-0.389599\pi$
$137$	12.9282	−	3.46410i	1.10453	−	0.295958i	0.764608	+	0.644495i	$0.222932\pi$
$138$	−1.09808	+	1.90192i	−0.0934745	+	0.161903i
$139$	3.46410	+	6.00000i	0.293821	+	0.508913i	0.974710	−	0.223474i	$-0.0717396\pi$
$139$	3.46410	+	6.00000i	0.293821	+	0.508913i	−0.680889	+	0.732387i	$0.738406\pi$
$140$	−18.5885	+	6.19615i	−1.57101	+	0.523670i
$141$	−1.90192	+	1.90192i	−0.160171	+	0.160171i
$142$	12.0000	+	12.0000i	1.00702	+	1.00702i
$143$	−2.53590	+	2.53590i	−0.212062	+	0.212062i
$144$	−6.00000	+	10.3923i	−0.500000	+	0.866025i
$145$	6.39230	+	3.19615i	0.530852	+	0.265426i
$146$	20.3923			1.68768
$147$	−10.5622	+	18.2942i	−0.871154	+	1.50888i
$148$	0.928203	−	0.928203i	0.0762978	−	0.0762978i
$149$	6.06218	−	3.50000i	0.496633	−	0.286731i	−0.230689	−	0.973028i	$-0.574098\pi$
$149$	6.06218	−	3.50000i	0.496633	−	0.286731i	0.727322	+	0.686296i	$0.240765\pi$
$150$	−1.73205	+	12.1244i	−0.141421	+	0.989949i
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	9.46410	+	9.46410i	0.767640	+	0.767640i
$153$	12.2942	−	3.29423i	0.993929	−	0.266323i
$154$	10.7321	−	6.19615i	0.864813	−	0.499300i
$155$	−10.0981	−	15.2942i	−0.811097	−	1.22846i
$156$	−1.60770	−	6.00000i	−0.128719	−	0.480384i
$157$	−3.29423	+	12.2942i	−0.262908	+	0.981186i	0.700610	+	0.713544i	$0.252911\pi$
$157$	−3.29423	+	12.2942i	−0.262908	+	0.981186i	−0.963518	+	0.267642i	$0.913756\pi$
$158$	−3.00000	+	0.803848i	−0.238667	+	0.0639507i
$159$	12.2942	+	3.29423i	0.974996	+	0.261249i
$160$	−8.39230	+	9.46410i	−0.663470	+	0.748203i
$161$			3.92820i			0.309586i
$162$	12.2942	+	3.29423i	0.965926	+	0.258819i
$163$	−6.46410	+	6.46410i	−0.506308	+	0.506308i	−0.913391	−	0.407083i	$-0.866546\pi$
$163$	−6.46410	+	6.46410i	−0.506308	+	0.506308i	0.407083	+	0.913391i	$0.366546\pi$
$164$	6.46410	+	11.1962i	0.504762	+	0.874273i
$165$	−0.464102	−	7.73205i	−0.0361303	−	0.601939i
$166$	−8.29423	+	14.3660i	−0.643757	+	1.11502i
$167$	4.79423	−	17.8923i	0.370989	−	1.38455i	−0.488130	−	0.872771i	$-0.662321\pi$
$167$	4.79423	−	17.8923i	0.370989	−	1.38455i	0.859118	−	0.511777i	$-0.171013\pi$
$168$			21.4641i			1.65599i
$169$	−8.47372	−	4.89230i	−0.651825	−	0.376331i
$170$	13.3923	−	0.803848i	1.02714	−	0.0616523i
$171$	7.09808	−	12.2942i	0.542803	−	0.940163i
$172$	−17.6603	+	4.73205i	−1.34658	+	0.360815i
$173$	−2.73205	+	0.732051i	−0.207714	+	0.0556568i	−0.361176	−	0.932498i	$-0.617625\pi$
$173$	−2.73205	+	0.732051i	−0.207714	+	0.0556568i	0.153462	+	0.988155i	$0.450958\pi$
$174$	5.53590	−	5.53590i	0.419675	−	0.419675i
$175$	8.16025	+	20.3301i	0.616857	+	1.53681i
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$	−1.56218	+	2.70577i	−0.117420	+	0.203378i
$178$	−2.66025	+	2.66025i	−0.199394	+	0.199394i
$179$			6.39230i			0.477783i	0.971046	+	0.238892i	$0.0767841\pi$
$179$			6.39230i			0.477783i	−0.971046	+	0.238892i	$0.923216\pi$
$180$	12.0000	+	6.00000i	0.894427	+	0.447214i
$181$			3.00000i			0.222988i	0.993765	+	0.111494i	$0.0355636\pi$
$181$			3.00000i			0.222988i	−0.993765	+	0.111494i	$0.964436\pi$
$182$	−7.85641	−	7.85641i	−0.582356	−	0.582356i
$183$	−25.3923			−1.87705
$184$	1.26795	+	2.19615i	0.0934745	+	0.161903i
$185$	−1.09808	−	0.973721i	−0.0807322	−	0.0715894i
$186$	−19.3923	+	5.19615i	−1.42191	+	0.381000i
$187$	−8.19615	+	2.19615i	−0.599362	+	0.160599i
$188$	0.803848	+	3.00000i	0.0586266	+	0.218797i
$189$	21.9904	−	5.89230i	1.59956	−	0.428602i
$190$	9.92820	−	11.1962i	0.720268	−	0.812254i
$191$	−16.0981	−	9.29423i	−1.16482	−	0.672507i	−0.212362	−	0.977191i	$-0.568116\pi$
$191$	−16.0981	−	9.29423i	−1.16482	−	0.672507i	−0.952453	+	0.304684i	$0.901449\pi$
$192$	6.92820	+	12.0000i	0.500000	+	0.866025i
$193$	−3.66025	+	13.6603i	−0.263471	+	0.983287i	0.699709	+	0.714428i	$0.253313\pi$
$193$	−3.66025	+	13.6603i	−0.263471	+	0.983287i	−0.963180	+	0.268858i	$0.913354\pi$
$194$	−8.66025	−	5.00000i	−0.621770	−	0.358979i
$195$	−6.58846	+	2.19615i	−0.471809	+	0.157270i
$196$	12.1962	+	21.1244i	0.871154	+	1.50888i
$197$	−12.0000	+	12.0000i	−0.854965	+	0.854965i	−0.990740	−	0.135775i	$-0.956648\pi$
$197$	−12.0000	+	12.0000i	−0.854965	+	0.854965i	0.135775	+	0.990740i	$0.456648\pi$
$198$	−8.19615	−	2.19615i	−0.582475	−	0.156074i
$199$		−	4.19615i		−	0.297457i	−0.988878	−	0.148729i	$-0.952482\pi$
$199$		−	4.19615i		−	0.297457i	0.988878	−	0.148729i	$-0.0475181\pi$
$200$	11.1244	+	8.73205i	0.786611	+	0.617449i
$201$	3.40192	+	12.6962i	0.239953	+	0.895518i
$202$	0.732051	+	2.73205i	0.0515069	+	0.192226i
$203$	3.62436	−	13.5263i	0.254380	−	0.949359i
$204$	3.80385	−	14.1962i	0.266323	−	0.993929i
$205$	12.0622	−	7.96410i	0.842459	−	0.556237i
$206$	11.3923	+	19.7321i	0.793739	+	1.37480i
$207$	1.90192	−	1.90192i	0.132193	−	0.132193i
$208$	−6.92820	−	1.85641i	−0.480384	−	0.128719i
$209$	−4.73205	+	8.19615i	−0.327323	+	0.566940i
$210$	23.9545	−	1.43782i	1.65302	−	0.0992192i
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$	10.3923	−	10.3923i	0.713746	−	0.713746i
$213$	−10.3923	−	18.0000i	−0.712069	−	1.23334i
$214$			12.1962i			0.833712i
$215$	6.46410	+	19.3923i	0.440848	+	1.32254i
$216$	10.3923	−	10.3923i	0.707107	−	0.707107i
$217$	−25.3923	+	25.3923i	−1.72374	+	1.72374i
$218$	8.66025	−	8.66025i	0.586546	−	0.586546i
$219$	−24.1244	−	6.46410i	−1.63017	−	0.436804i
$220$	−8.00000	−	4.00000i	−0.539360	−	0.269680i
$221$	3.80385	+	6.58846i	0.255874	+	0.443188i
$222$	−1.39230	+	0.803848i	−0.0934454	+	0.0539507i
$223$	−16.5263	+	4.42820i	−1.10668	+	0.296534i	−0.765483	−	0.643457i	$-0.777500\pi$
$223$	−16.5263	+	4.42820i	−1.10668	+	0.296534i	−0.341199	+	0.939991i	$0.610833\pi$
$224$	21.4641	+	12.3923i	1.43413	+	0.827996i
$225$	5.89230	−	13.7942i	0.392820	−	0.919615i
$226$	−2.19615	+	1.26795i	−0.146086	+	0.0843427i
$227$	2.70577	+	10.0981i	0.179588	+	0.670233i	0.995724	+	0.0923731i	$0.0294453\pi$
$227$	2.70577	+	10.0981i	0.179588	+	0.670233i	−0.816136	+	0.577860i	$0.803888\pi$
$228$	−8.19615	−	14.1962i	−0.542803	−	0.940163i
$229$	−5.76795	−	9.99038i	−0.381157	−	0.660183i	0.610071	−	0.792347i	$-0.291141\pi$
$229$	−5.76795	−	9.99038i	−0.381157	−	0.660183i	−0.991228	+	0.132164i	$0.957808\pi$
$230$	2.36603	−	1.56218i	0.156011	−	0.103007i
$231$	−14.6603	+	3.92820i	−0.964574	+	0.258457i
$232$	−2.33975	−	8.73205i	−0.153612	−	0.573287i
$233$	18.1244	−	18.1244i	1.18737	−	1.18737i	0.209573	−	0.977793i	$-0.432793\pi$
$233$	18.1244	−	18.1244i	1.18737	−	1.18737i	0.977793	−	0.209573i	$-0.0672074\pi$
$234$			7.60770i			0.497331i
$235$	3.29423	−	1.09808i	0.214892	−	0.0716306i
$236$	1.80385	+	3.12436i	0.117420	+	0.203378i
$237$	3.80385			0.247086
$238$	−6.80385	−	25.3923i	−0.441028	−	1.64594i
$239$	−9.46410	−	16.3923i	−0.612182	−	1.06033i	−0.990872	−	0.134807i	$-0.956959\pi$
$239$	−9.46410	−	16.3923i	−0.612182	−	1.06033i	0.378690	−	0.925524i	$-0.376375\pi$
$240$	12.9282	−	8.53590i	0.834512	−	0.550990i
$241$	9.40192	−	16.2846i	0.605631	−	1.04898i	−0.386320	−	0.922365i	$-0.626254\pi$
$241$	9.40192	−	16.2846i	0.605631	−	1.04898i	0.991951	−	0.126619i	$-0.0404126\pi$
$242$	−9.56218	−	2.56218i	−0.614680	−	0.164703i
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	−14.6603	+	25.3923i	−0.938527	+	1.62558i
$245$	22.7583	−	15.0263i	1.45398	−	0.959994i
$246$	−4.09808	−	15.2942i	−0.261284	−	0.975124i
$247$	8.19615	+	2.19615i	0.521509	+	0.139738i
$248$	−6.00000	+	22.3923i	−0.381000	+	1.42191i
$249$	14.3660	−	14.3660i	0.910410	−	0.910410i
$250$	9.00000	−	13.0000i	0.569210	−	0.822192i
$251$	26.5885			1.67825			0.839124	−	0.543940i	$-0.183068\pi$
$251$	26.5885			1.67825			0.839124	+	0.543940i	$0.183068\pi$
$252$	6.80385	−	25.3923i	0.428602	−	1.59956i
$253$	−1.26795	+	1.26795i	−0.0797153	+	0.0797153i
$254$			11.8038i			0.740639i
$255$	−16.0981	−	3.29423i	−1.00810	−	0.206293i
$256$	16.0000			1.00000
$257$	−4.22243	+	15.7583i	−0.263388	+	0.982978i	0.699842	+	0.714298i	$0.253254\pi$
$257$	−4.22243	+	15.7583i	−0.263388	+	0.982978i	−0.963230	+	0.268680i	$0.913413\pi$
$258$	22.3923			1.39408
$259$	−1.43782	+	2.49038i	−0.0893419	+	0.154745i
$260$	−1.60770	+	7.85641i	−0.0997050	+	0.487234i
$261$	−8.30385	+	4.79423i	−0.513995	+	0.296755i
$262$	10.6603	+	2.85641i	0.658593	+	0.176469i
$263$	3.63397	+	13.5622i	0.224080	+	0.836280i	0.982771	+	0.184828i	$0.0591729\pi$
$263$	3.63397	+	13.5622i	0.224080	+	0.836280i	−0.758690	+	0.651451i	$0.774160\pi$
$264$	−6.92820	+	6.92820i	−0.426401	+	0.426401i
$265$	−12.2942	−	10.9019i	−0.755228	−	0.669700i
$266$	−25.3923	−	14.6603i	−1.55690	−	0.898878i
$267$	3.99038	−	2.30385i	0.244207	−	0.140993i
$268$	14.6603	+	3.92820i	0.895518	+	0.239953i
$269$		−	1.00000i		−	0.0609711i	−0.999535	−	0.0304855i	$-0.990295\pi$
$269$		−	1.00000i		−	0.0609711i	0.999535	−	0.0304855i	$-0.00970535\pi$
$270$	−12.2942	−	10.9019i	−0.748203	−	0.663470i
$271$	4.58846			0.278729			0.139364	−	0.990241i	$-0.455494\pi$
$271$	4.58846			0.278729			0.139364	+	0.990241i	$0.455494\pi$
$272$	−12.0000	−	12.0000i	−0.727607	−	0.727607i
$273$	6.80385	+	11.7846i	0.411788	+	0.713237i
$274$	−9.46410	+	16.3923i	−0.571747	+	0.990295i
$275$	−3.92820	+	9.19615i	−0.236880	+	0.554549i
$276$	−0.803848	−	3.00000i	−0.0483859	−	0.180579i
$277$	−8.83013	+	2.36603i	−0.530551	+	0.142161i	−0.514143	−	0.857705i	$-0.671890\pi$
$277$	−8.83013	+	2.36603i	−0.530551	+	0.142161i	−0.0164083	+	0.999865i	$0.505223\pi$
$278$	−9.46410	−	2.53590i	−0.567619	−	0.152093i
$279$	24.5885			1.47207
$280$	12.3923	−	24.7846i	0.740582	−	1.48116i
$281$	−1.79423	−	1.03590i	−0.107035	−	0.0617965i	0.445527	−	0.895268i	$-0.353016\pi$
$281$	−1.79423	−	1.03590i	−0.107035	−	0.0617965i	−0.552562	+	0.833472i	$0.686350\pi$
$282$		−	3.80385i		−	0.226516i
$283$	4.50000	+	1.20577i	0.267497	+	0.0716757i	0.390074	−	0.920783i	$-0.372449\pi$
$283$	4.50000	+	1.20577i	0.267497	+	0.0716757i	−0.122577	+	0.992459i	$0.539116\pi$
$284$	−24.0000			−1.42414
$285$	−15.2942	+	10.0981i	−0.905952	+	0.598158i
$286$		−	5.07180i		−	0.299902i
$287$	−20.0263	−	20.0263i	−1.18211	−	1.18211i
$288$	−4.39230	−	16.3923i	−0.258819	−	0.965926i
$289$			1.00000i			0.0588235i
$290$	−9.58846	+	3.19615i	−0.563054	+	0.187685i
$291$	8.66025	+	8.66025i	0.507673	+	0.507673i
$292$	−20.3923	+	20.3923i	−1.19337	+	1.19337i
$293$	0.294229	−	1.09808i	0.0171890	−	0.0641503i	−0.956799	−	0.290751i	$-0.906095\pi$
$293$	0.294229	−	1.09808i	0.0171890	−	0.0641503i	0.973988	+	0.226601i	$0.0727614\pi$
$294$	−7.73205	−	28.8564i	−0.450942	−	1.68294i
$295$	3.36603	−	2.22243i	0.195978	−	0.129395i
$296$			1.85641i			0.107901i
$297$	9.00000	+	5.19615i	0.522233	+	0.301511i
$298$	−2.56218	+	9.56218i	−0.148423	+	0.553922i
$299$	1.39230	+	0.803848i	0.0805191	+	0.0464877i
$300$	−10.3923	−	13.8564i	−0.600000	−	0.800000i
$301$	34.6865	−	20.0263i	1.99930	−	1.15430i
$302$	5.85641	+	21.8564i	0.336998	+	1.25769i
$303$		−	3.46410i		−	0.199007i
$304$	−18.9282			−1.08561
$305$	29.3205	+	14.6603i	1.67889	+	0.839444i
$306$	−9.00000	+	15.5885i	−0.514496	+	0.891133i
$307$	14.3660	+	14.3660i	0.819912	+	0.819912i	0.986095	−	0.166183i	$-0.0531441\pi$
$307$	14.3660	+	14.3660i	0.819912	+	0.819912i	−0.166183	+	0.986095i	$0.553144\pi$
$308$	−4.53590	+	16.9282i	−0.258457	+	0.964574i
$309$	−7.22243	−	26.9545i	−0.410870	−	1.53339i
$310$	25.3923	+	5.19615i	1.44219	+	0.295122i
$311$	12.2942	−	7.09808i	0.697142	−	0.402495i	−0.109140	−	0.994026i	$-0.534810\pi$
$311$	12.2942	−	7.09808i	0.697142	−	0.402495i	0.806282	+	0.591531i	$0.201476\pi$
$312$	7.60770	+	4.39230i	0.430701	+	0.248665i
$313$	14.4641	−	3.87564i	0.817559	−	0.219064i	0.174280	−	0.984696i	$-0.444240\pi$
$313$	14.4641	−	3.87564i	0.817559	−	0.219064i	0.643279	+	0.765632i	$0.277573\pi$
$314$	−9.00000	−	15.5885i	−0.507899	−	0.879708i
$315$	−28.7942	−	5.89230i	−1.62237	−	0.331994i
$316$	2.19615	−	3.80385i	0.123543	−	0.213983i
$317$	−3.66025	−	13.6603i	−0.205580	−	0.767236i	−0.989272	−	0.146086i	$-0.953332\pi$
$317$	−3.66025	−	13.6603i	−0.205580	−	0.767236i	0.783692	−	0.621150i	$-0.213334\pi$
$318$	−15.5885	+	9.00000i	−0.874157	+	0.504695i
$319$	5.53590	−	3.19615i	0.309951	−	0.178950i
$320$	−1.07180	−	17.8564i	−0.0599153	−	0.998203i
$321$	3.86603	−	14.4282i	0.215780	−	0.805304i
$322$	−3.92820	−	3.92820i	−0.218910	−	0.218910i
$323$	14.1962	+	14.1962i	0.789895	+	0.789895i
$324$	−15.5885	+	9.00000i	−0.866025	+	0.500000i
$325$	8.87564	+	1.26795i	0.492332	+	0.0703332i
$326$		−	12.9282i		−	0.716027i
$327$	−12.9904	+	7.50000i	−0.718370	+	0.414751i
$328$	−17.6603	−	4.73205i	−0.975124	−	0.261284i
$329$	−3.40192	−	5.89230i	−0.187554	−	0.324853i
$330$	8.19615	+	7.26795i	0.451183	+	0.400087i
$331$	−0.509619	−	0.294229i	−0.0280112	−	0.0161723i	0.485929	−	0.873998i	$-0.338481\pi$
$331$	−0.509619	−	0.294229i	−0.0280112	−	0.0161723i	−0.513940	+	0.857826i	$0.671815\pi$
$332$	−6.07180	−	22.6603i	−0.333233	−	1.24364i
$333$	1.90192	−	0.509619i	0.104225	−	0.0279269i
$334$	13.0981	+	22.6865i	0.716695	+	1.24135i
$335$	3.40192	−	16.6244i	0.185867	−	0.908286i
$336$	−21.4641	−	21.4641i	−1.17096	−	1.17096i
$337$	−0.267949	−	0.0717968i	−0.0145961	−	0.00391102i	0.251514	−	0.967854i	$-0.419072\pi$
$337$	−0.267949	−	0.0717968i	−0.0145961	−	0.00391102i	−0.266110	+	0.963943i	$0.585738\pi$
$338$	13.3660	−	3.58142i	0.727016	−	0.194803i
$339$	3.00000	−	0.803848i	0.162938	−	0.0436590i
$340$	−12.5885	+	14.1962i	−0.682705	+	0.769894i
$341$	−16.3923			−0.887693
$342$	5.19615	+	19.3923i	0.280976	+	1.04862i
$343$	−16.0981	−	16.0981i	−0.869214	−	0.869214i
$344$	12.9282	−	22.3923i	0.697042	−	1.20731i
$345$	−3.29423	+	1.09808i	−0.177355	+	0.0591184i
$346$	2.00000	−	3.46410i	0.107521	−	0.186231i
$347$	7.09808	+	1.90192i	0.381045	+	0.102101i	0.444257	−	0.895899i	$-0.353468\pi$
$347$	7.09808	+	1.90192i	0.381045	+	0.102101i	−0.0632121	+	0.998000i	$0.520134\pi$
$348$			11.0718i			0.593511i
$349$	18.2321	−	31.5788i	0.975939	−	1.69038i	0.299139	−	0.954209i	$-0.403300\pi$
$349$	18.2321	−	31.5788i	0.975939	−	1.69038i	0.676800	−	0.736167i	$-0.263366\pi$
$350$	−28.4904	−	12.1699i	−1.52287	−	0.650507i
$351$	2.41154	−	9.00000i	0.128719	−	0.480384i
$352$	2.92820	+	10.9282i	0.156074	+	0.582475i
$353$	3.46410	+	12.9282i	0.184376	+	0.688099i	0.994763	+	0.102205i	$0.0325898\pi$
$353$	3.46410	+	12.9282i	0.184376	+	0.688099i	−0.810388	+	0.585894i	$0.800744\pi$
$354$	−1.14359	−	4.26795i	−0.0607813	−	0.226839i
$355$	1.60770	+	26.7846i	0.0853276	+	1.42158i
$356$		−	5.32051i		−	0.281986i
$357$			32.1962i			1.70400i
$358$	−6.39230	−	6.39230i	−0.337844	−	0.337844i
$359$	−2.19615			−0.115908			−0.0579542	−	0.998319i	$-0.518458\pi$
$359$	−2.19615			−0.115908			−0.0579542	+	0.998319i	$0.518458\pi$
$360$	−18.0000	+	6.00000i	−0.948683	+	0.316228i
$361$	3.39230			0.178542
$362$	−3.00000	−	3.00000i	−0.157676	−	0.157676i
$363$	10.5000	+	6.06218i	0.551107	+	0.318182i
$364$	15.7128			0.823575
$365$	24.1244	+	21.3923i	1.26273	+	1.11972i
$366$	25.3923	−	25.3923i	1.32728	−	1.32728i
$367$	2.56218	+	9.56218i	0.133745	+	0.499142i	1.00000		0.000459976i	$-0.000146415\pi$
$367$	2.56218	+	9.56218i	0.133745	+	0.499142i	−0.866255	+	0.499602i	$0.833480\pi$
$368$	−3.46410	−	0.928203i	−0.180579	−	0.0483859i
$369$			19.3923i			1.00952i
$370$	2.07180	−	0.124356i	0.107708	−	0.00646494i
$371$	−16.0981	+	27.8827i	−0.835770	+	1.44760i
$372$	14.1962	−	24.5885i	0.736036	−	1.27485i
$373$	3.63397	+	0.973721i	0.188160	+	0.0504173i	0.351669	−	0.936125i	$-0.385614\pi$
$373$	3.63397	+	0.973721i	0.188160	+	0.0504173i	−0.163508	+	0.986542i	$0.552281\pi$
$374$	6.00000	−	10.3923i	0.310253	−	0.537373i
$375$	−14.7679	+	12.5263i	−0.762614	+	0.646854i
$376$	−3.80385	−	2.19615i	−0.196168	−	0.113258i
$377$	−4.05256	−	4.05256i	−0.208717	−	0.208717i
$378$	−16.0981	+	27.8827i	−0.827996	+	1.43413i
$379$	−33.1244			−1.70148			−0.850742	−	0.525584i	$-0.823847\pi$
$379$	−33.1244			−1.70148			−0.850742	+	0.525584i	$0.823847\pi$
$380$	1.26795	+	21.1244i	0.0650444	+	1.08366i
$381$	3.74167	−	13.9641i	0.191692	−	0.715403i
$382$	25.3923	−	6.80385i	1.29918	−	0.348115i
$383$	27.7583	+	7.43782i	1.41838	+	0.380055i	0.884910	−	0.465761i	$-0.154220\pi$
$383$	27.7583	+	7.43782i	1.41838	+	0.380055i	0.533474	+	0.845816i	$0.320886\pi$
$384$	−18.9282	−	5.07180i	−0.965926	−	0.258819i
$385$	19.1962	+	3.92820i	0.978327	+	0.200200i
$386$	−10.0000	−	17.3205i	−0.508987	−	0.881591i
$387$	−26.4904	−	7.09808i	−1.34658	−	0.360815i
$388$	13.6603	−	3.66025i	0.693494	−	0.185821i
$389$	15.0622	+	8.69615i	0.763683	+	0.440912i	0.830616	−	0.556845i	$-0.187988\pi$
$389$	15.0622	+	8.69615i	0.763683	+	0.440912i	−0.0669337	+	0.997757i	$0.521322\pi$
$390$	4.39230	−	8.78461i	0.222413	−	0.444826i
$391$	1.90192	+	3.29423i	0.0961844	+	0.166596i
$392$	−33.3205	−	8.92820i	−1.68294	−	0.450942i
$393$	−11.7058	−	6.75833i	−0.590478	−	0.340913i
$394$		−	24.0000i		−	1.20910i
$395$	−4.39230	−	2.19615i	−0.221001	−	0.110500i
$396$	10.3923	−	6.00000i	0.522233	−	0.301511i
$397$	−0.803848	−	0.803848i	−0.0403440	−	0.0403440i	0.686647	−	0.726991i	$-0.259082\pi$
$397$	−0.803848	−	0.803848i	−0.0403440	−	0.0403440i	−0.726991	+	0.686647i	$0.759082\pi$
$398$	4.19615	+	4.19615i	0.210334	+	0.210334i
$399$	25.3923	+	25.3923i	1.27121	+	1.27121i
$400$	−19.8564	+	2.39230i	−0.992820	+	0.119615i
$401$	−31.3923	+	18.1244i	−1.56766	+	0.905087i	−0.571215	+	0.820800i	$0.693528\pi$
$401$	−31.3923	+	18.1244i	−1.56766	+	0.905087i	−0.996442	+	0.0842869i	$0.973139\pi$
$402$	−16.0981	−	9.29423i	−0.802899	−	0.463554i
$403$	3.80385	+	14.1962i	0.189483	+	0.707161i
$404$	−3.46410	−	2.00000i	−0.172345	−	0.0995037i
$405$	11.0885	+	16.7942i	0.550990	+	0.834512i
$406$	9.90192	+	17.1506i	0.491424	+	0.851172i
$407$	−1.26795	+	0.339746i	−0.0628499	+	0.0168406i
$408$	10.3923	+	18.0000i	0.514496	+	0.891133i
$409$	5.19615	−	3.00000i	0.256933	−	0.148340i	−0.366002	−	0.930614i	$-0.619274\pi$
$409$	5.19615	−	3.00000i	0.256933	−	0.148340i	0.622935	+	0.782274i	$0.285940\pi$
$410$	−4.09808	+	20.0263i	−0.202390	+	0.989027i
$411$	16.3923	−	16.3923i	0.808573	−	0.808573i
$412$	−31.1244	−	8.33975i	−1.53339	−	0.410870i
$413$	−5.58846	−	5.58846i	−0.274990	−	0.274990i
$414$			3.80385i			0.186949i
$415$	−24.8827	+	8.29423i	−1.22144	+	0.407148i
$416$	8.78461	−	5.07180i	0.430701	−	0.248665i
$417$	10.3923	+	6.00000i	0.508913	+	0.293821i
$418$	−3.46410	−	12.9282i	−0.169435	−	0.632339i
$419$	−10.7321	+	6.19615i	−0.524295	+	0.302702i	−0.738690	−	0.674045i	$-0.764555\pi$
$419$	−10.7321	+	6.19615i	−0.524295	+	0.302702i	0.214395	+	0.976747i	$0.431222\pi$
$420$	−22.5167	+	25.3923i	−1.09870	+	1.23902i
$421$	−4.60770	−	2.66025i	−0.224565	−	0.129653i	0.383497	−	0.923542i	$-0.374720\pi$
$421$	−4.60770	−	2.66025i	−0.224565	−	0.129653i	−0.608062	+	0.793889i	$0.708053\pi$
$422$		0			0
$423$	−1.20577	+	4.50000i	−0.0586266	+	0.218797i
$424$			20.7846i			1.00939i
$425$	16.6865	+	13.0981i	0.809416	+	0.635350i
$426$	28.3923	+	7.60770i	1.37561	+	0.368594i
$427$	16.6244	−	62.0429i	0.804509	−	3.00247i
$428$	−12.1962	−	12.1962i	−0.589523	−	0.589523i
$429$	−1.60770	+	6.00000i	−0.0776203	+	0.289683i
$430$	−25.8564	−	12.9282i	−1.24691	−	0.623453i
$431$			22.0526i			1.06223i	0.847298	+	0.531117i	$0.178228\pi$
$431$			22.0526i			1.06223i	−0.847298	+	0.531117i	$0.821772\pi$
$432$			20.7846i			1.00000i
$433$	−15.3923	−	15.3923i	−0.739707	−	0.739707i	0.232814	−	0.972521i	$-0.425207\pi$
$433$	−15.3923	−	15.3923i	−0.739707	−	0.739707i	−0.972521	+	0.232814i	$0.925207\pi$
$434$		−	50.7846i		−	2.43774i
$435$	12.3564	−	0.741670i	0.592444	−	0.0355603i
$436$			17.3205i			0.829502i
$437$	4.09808	+	1.09808i	0.196038	+	0.0525281i
$438$	30.5885	−	17.6603i	1.46157	−	0.843840i
$439$	16.2679	+	9.39230i	0.776427	+	0.448270i	0.835162	−	0.550003i	$-0.185374\pi$
$439$	16.2679	+	9.39230i	0.776427	+	0.448270i	−0.0587356	+	0.998274i	$0.518707\pi$
$440$	12.0000	−	4.00000i	0.572078	−	0.190693i
$441$			36.5885i			1.74231i
$442$	−10.3923	−	2.78461i	−0.494312	−	0.132450i
$443$	−37.2846	+	9.99038i	−1.77145	+	0.474657i	−0.988982	−	0.148039i	$-0.952704\pi$
$443$	−37.2846	+	9.99038i	−1.77145	+	0.474657i	−0.782464	+	0.622696i	$0.786037\pi$
$444$	0.588457	−	2.19615i	0.0279269	−	0.104225i
$445$	−5.93782	+	0.356406i	−0.281480	+	0.0168953i
$446$	12.0981	−	20.9545i	0.572861	−	0.992224i
$447$	6.06218	−	10.5000i	0.286731	−	0.496633i
$448$	−33.8564	+	9.07180i	−1.59956	+	0.428602i
$449$	−32.7846			−1.54720			−0.773601	−	0.633673i	$-0.781546\pi$
$449$	−32.7846			−1.54720			−0.773601	+	0.633673i	$0.781546\pi$
$450$	7.90192	+	19.6865i	0.372500	+	0.928032i
$451$		−	12.9282i		−	0.608765i
$452$	0.928203	−	3.46410i	0.0436590	−	0.162938i
$453$		−	27.7128i		−	1.30206i
$454$	−12.8038	−	7.39230i	−0.600914	−	0.346938i
$455$	−1.05256	−	17.5359i	−0.0493447	−	0.822096i
$456$	22.3923	+	6.00000i	1.04862	+	0.280976i
$457$	−2.63397	−	9.83013i	−0.123212	−	0.459834i	0.876558	−	0.481297i	$-0.159834\pi$
$457$	−2.63397	−	9.83013i	−0.123212	−	0.459834i	−0.999770	+	0.0214632i	$0.993168\pi$
$458$	15.7583	+	4.22243i	0.736338	+	0.197301i
$459$	15.5885	−	15.5885i	0.727607	−	0.727607i
$460$	−0.803848	+	3.92820i	−0.0374796	+	0.183153i
$461$	−6.79423	+	11.7679i	−0.316439	+	0.548088i	−0.979742	−	0.200262i	$-0.935821\pi$
$461$	−6.79423	+	11.7679i	−0.316439	+	0.548088i	0.663304	+	0.748350i	$0.269154\pi$
$462$	10.7321	−	18.5885i	0.499300	−	0.864813i
$463$	−1.75833	+	6.56218i	−0.0817165	+	0.304970i	−0.994672	−	0.103089i	$-0.967127\pi$
$463$	−1.75833	+	6.56218i	−0.0817165	+	0.304970i	0.912956	+	0.408059i	$0.133794\pi$
$464$	11.0718	+	6.39230i	0.513995	+	0.296755i
$465$	−28.3923	−	14.1962i	−1.31666	−	0.658331i
$466$			36.2487i			1.67919i
$467$	8.60770	−	8.60770i	0.398317	−	0.398317i	−0.479322	−	0.877639i	$-0.659118\pi$
$467$	8.60770	−	8.60770i	0.398317	−	0.398317i	0.877639	+	0.479322i	$0.159118\pi$
$468$	−7.60770	−	7.60770i	−0.351666	−	0.351666i
$469$	−33.2487			−1.53528
$470$	−2.19615	+	4.39230i	−0.101301	+	0.202602i
$471$	5.70577	+	21.2942i	0.262908	+	0.981186i
$472$	−4.92820	−	1.32051i	−0.226839	−	0.0607813i
$473$	17.6603	+	4.73205i	0.812019	+	0.217580i
$474$	−3.80385	+	3.80385i	−0.174717	+	0.174717i
$475$	23.4904	−	2.83013i	1.07781	−	0.129855i
$476$	32.1962	+	18.5885i	1.47571	+	0.852001i
$477$	21.2942	−	5.70577i	0.974996	−	0.261249i
$478$	25.8564	+	6.92820i	1.18264	+	0.316889i
$479$	10.5622	−	18.2942i	0.482598	−	0.835885i	−0.517202	−	0.855863i	$-0.673026\pi$
$479$	10.5622	−	18.2942i	0.482598	−	0.835885i	0.999800	+	0.0199786i	$0.00635981\pi$
$480$	−4.39230	+	21.4641i	−0.200480	+	0.979698i
$481$	0.588457	+	1.01924i	0.0268313	+	0.0464732i
$482$	6.88269	+	25.6865i	0.313498	+	1.16999i
$483$	3.40192	+	5.89230i	0.154793	+	0.268109i
$484$	12.1244	−	7.00000i	0.551107	−	0.318182i
$485$	−5.00000	−	15.0000i	−0.227038	−	0.681115i
$486$	21.2942	−	5.70577i	0.965926	−	0.258819i
$487$	3.39230	−	3.39230i	0.153720	−	0.153720i	−0.626057	−	0.779777i	$-0.715332\pi$
$487$	3.39230	−	3.39230i	0.153720	−	0.153720i	0.779777	+	0.626057i	$0.215332\pi$
$488$	−10.7321	−	40.0526i	−0.485817	−	1.81309i
$489$	−4.09808	+	15.2942i	−0.185321	+	0.691629i
$490$	−7.73205	+	37.7846i	−0.349298	+	1.70693i
$491$	−12.3923	−	21.4641i	−0.559257	−	0.968661i	−0.997559	−	0.0698335i	$-0.977753\pi$
$491$	−12.3923	−	21.4641i	−0.559257	−	0.968661i	0.438302	−	0.898828i	$-0.355580\pi$
$492$	19.3923	+	11.1962i	0.874273	+	0.504762i
$493$	−3.50962	−	13.0981i	−0.158065	−	0.589908i
$494$	−10.3923	+	6.00000i	−0.467572	+	0.269953i
$495$	−7.39230	−	11.1962i	−0.332259	−	0.503230i
$496$	−16.3923	−	28.3923i	−0.736036	−	1.27485i
$497$	50.7846	−	13.6077i	2.27800	−	0.610389i
$498$			28.7321i			1.28751i
$499$	13.3923	+	23.1962i	0.599522	+	1.03840i	0.992892	+	0.119022i	$0.0379759\pi$
$499$	13.3923	+	23.1962i	0.599522	+	1.03840i	−0.393370	+	0.919380i	$0.628691\pi$
$500$	4.00000	+	22.0000i	0.178885	+	0.983870i
$501$	−8.30385	−	30.9904i	−0.370989	−	1.38455i
$502$	−26.5885	+	26.5885i	−1.18670	+	1.18670i
$503$	−3.97372	+	3.97372i	−0.177179	+	0.177179i	−0.790125	−	0.612946i	$-0.789984\pi$
$503$	−3.97372	+	3.97372i	−0.177179	+	0.177179i	0.612946	+	0.790125i	$0.289984\pi$
$504$	18.5885	+	32.1962i	0.827996	+	1.43413i
$505$	−2.00000	+	4.00000i	−0.0889988	+	0.177998i
$506$		−	2.53590i		−	0.112734i
$507$	−16.9474			−0.752662
$508$	−11.8038	−	11.8038i	−0.523711	−	0.523711i
$509$	6.57180	−	3.79423i	0.291290	−	0.168176i	−0.347234	−	0.937779i	$-0.612879\pi$
$509$	6.57180	−	3.79423i	0.291290	−	0.168176i	0.638523	+	0.769602i	$0.279546\pi$
$510$	19.3923	−	12.8038i	0.858706	−	0.566964i
$511$	31.5885	−	54.7128i	1.39739	−	2.42035i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$		−	24.5885i		−	1.08561i
$514$	−11.5359	−	19.9808i	−0.508827	−	0.881314i
$515$	−7.22243	+	35.2942i	−0.318258	+	1.55525i
$516$	−22.3923	+	22.3923i	−0.985766	+	0.985766i
$517$	0.803848	−	3.00000i	0.0353532	−	0.131940i
$518$	−1.05256	−	3.92820i	−0.0462468	−	0.172595i
$519$	−3.46410	+	3.46410i	−0.152057	+	0.152057i
$520$	−6.24871	−	9.46410i	−0.274024	−	0.415028i
$521$		−	14.6603i		−	0.642277i	−0.947032	−	0.321139i	$-0.895934\pi$
$521$		−	14.6603i		−	0.642277i	0.947032	−	0.321139i	$-0.104066\pi$
$522$	3.50962	−	13.0981i	0.153612	−	0.573287i
$523$	−1.56218	+	1.56218i	−0.0683093	+	0.0683093i	−0.740436	−	0.672127i	$-0.765381\pi$
$523$	−1.56218	+	1.56218i	−0.0683093	+	0.0683093i	0.672127	+	0.740436i	$0.265381\pi$
$524$	−13.5167	+	7.80385i	−0.590478	+	0.340913i
$525$	29.8468	+	23.4282i	1.30262	+	1.02249i
$526$	−17.1962	−	9.92820i	−0.749788	−	0.432890i
$527$	−9.00000	+	33.5885i	−0.392046	+	1.46314i
$528$		−	13.8564i		−	0.603023i
$529$	−19.2224	−	11.0981i	−0.835758	−	0.482525i
$530$	23.1962	−	1.39230i	1.00758	−	0.0604779i
$531$			5.41154i			0.234841i
$532$	40.0526	−	10.7321i	1.73650	−	0.465293i
$533$	−11.1962	+	3.00000i	−0.484959	+	0.129944i
$534$	−1.68653	+	6.29423i	−0.0729834	+	0.272378i
$535$	−12.7942	+	14.4282i	−0.553143	+	0.623786i
$536$	−18.5885	+	10.7321i	−0.802899	+	0.463554i
$537$	5.53590	+	9.58846i	0.238892	+	0.413772i
$538$	1.00000	+	1.00000i	0.0431131	+	0.0431131i
$539$		−	24.3923i		−	1.05065i
$540$	23.1962	−	1.39230i	0.998203	−	0.0599153i
$541$		−	12.4641i		−	0.535874i	−0.963436	−	0.267937i	$-0.913658\pi$
$541$		−	12.4641i		−	0.535874i	0.963436	−	0.267937i	$-0.0863418\pi$
$542$	−4.58846	+	4.58846i	−0.197091	+	0.197091i
$543$	2.59808	+	4.50000i	0.111494	+	0.193113i
$544$	24.0000			1.02899
$545$	19.3301	−	1.16025i	0.828012	−	0.0496998i
$546$	−18.5885	−	4.98076i	−0.795513	−	0.213157i
$547$	26.5526	−	7.11474i	1.13531	−	0.304204i	0.358243	−	0.933628i	$-0.383376\pi$
$547$	26.5526	−	7.11474i	1.13531	−	0.304204i	0.777062	+	0.629424i	$0.216709\pi$
$548$	−6.92820	−	25.8564i	−0.295958	−	1.10453i
$549$	−38.0885	+	21.9904i	−1.62558	+	0.938527i
$550$	−5.26795	−	13.1244i	−0.224626	−	0.559624i
$551$	−13.0981	−	7.56218i	−0.557997	−	0.322160i
$552$	3.80385	+	2.19615i	0.161903	+	0.0934745i
$553$	−2.49038	+	9.29423i	−0.105902	+	0.395231i
$554$	6.46410	−	11.1962i	0.274633	−	0.475679i
$555$	−2.49038	−	0.509619i	−0.105711	−	0.0216321i
$556$	12.0000	−	6.92820i	0.508913	−	0.293821i
$557$	−0.803848	+	0.803848i	−0.0340601	+	0.0340601i	−0.723932	−	0.689872i	$-0.757667\pi$
$557$	−0.803848	+	0.803848i	−0.0340601	+	0.0340601i	0.689872	+	0.723932i	$0.257667\pi$
$558$	−24.5885	+	24.5885i	−1.04091	+	1.04091i
$559$		−	16.3923i		−	0.693321i
$560$	12.3923	+	37.1769i	0.523670	+	1.57101i
$561$	−10.3923	+	10.3923i	−0.438763	+	0.438763i
$562$	2.83013	−	0.758330i	0.119382	−	0.0319882i
$563$	8.59808	−	32.0885i	0.362366	−	1.35237i	−0.508591	−	0.861008i	$-0.669834\pi$
$563$	8.59808	−	32.0885i	0.362366	−	1.35237i	0.870957	−	0.491359i	$-0.163500\pi$
$564$	3.80385	+	3.80385i	0.160171	+	0.160171i
$565$	−3.92820	−	0.803848i	−0.165261	−	0.0338181i
$566$	−5.70577	+	3.29423i	−0.239831	+	0.138467i
$567$	27.8827	−	27.8827i	1.17096	−	1.17096i
$568$	24.0000	−	24.0000i	1.00702	−	1.00702i
$569$	−1.26795	+	2.19615i	−0.0531552	+	0.0920675i	−0.891379	−	0.453259i	$-0.850261\pi$
$569$	−1.26795	+	2.19615i	−0.0531552	+	0.0920675i	0.838223	+	0.545327i	$0.183594\pi$
$570$	5.19615	−	25.3923i	0.217643	−	1.06357i
$571$	−3.00000	+	1.73205i	−0.125546	+	0.0724841i	−0.561458	−	0.827505i	$-0.689759\pi$
$571$	−3.00000	+	1.73205i	−0.125546	+	0.0724841i	0.435912	+	0.899989i	$0.356426\pi$
$572$	5.07180	+	5.07180i	0.212062	+	0.212062i
$573$	−32.1962			−1.34501
$574$	40.0526			1.67176
$575$	4.43782	+	0.633975i	0.185070	+	0.0264386i
$576$	20.7846	+	12.0000i	0.866025	+	0.500000i
$577$	5.39230	−	5.39230i	0.224485	−	0.224485i	−0.585899	−	0.810384i	$-0.699259\pi$
$577$	5.39230	−	5.39230i	0.224485	−	0.224485i	0.810384	+	0.585899i	$0.199259\pi$
$578$	−1.00000	−	1.00000i	−0.0415945	−	0.0415945i
$579$	6.33975	+	23.6603i	0.263471	+	0.983287i
$580$	6.39230	−	12.7846i	0.265426	−	0.530852i
$581$	25.6962	+	44.5070i	1.06606	+	1.84646i
$582$	−17.3205			−0.717958
$583$	−14.1962	+	3.80385i	−0.587945	+	0.157539i
$584$		−	40.7846i		−	1.68768i
$585$	−7.98076	+	9.00000i	−0.329964	+	0.372104i
$586$	0.803848	+	1.39230i	0.0332066	+	0.0575156i
$587$	8.74871	+	32.6506i	0.361098	+	1.34764i	0.872634	+	0.488374i	$0.162410\pi$
$587$	8.74871	+	32.6506i	0.361098	+	1.34764i	−0.511536	+	0.859262i	$0.670923\pi$
$588$	36.5885	+	21.1244i	1.50888	+	0.871154i
$589$	19.3923	+	33.5885i	0.799046	+	1.38399i
$590$	−1.14359	+	5.58846i	−0.0470810	+	0.230073i
$591$	−7.60770	+	28.3923i	−0.312939	+	1.16790i
$592$	−1.85641	−	1.85641i	−0.0762978	−	0.0762978i
$593$	−14.6603	+	14.6603i	−0.602024	+	0.602024i	−0.940849	−	0.338825i	$-0.889971\pi$
$593$	−14.6603	+	14.6603i	−0.602024	+	0.602024i	0.338825	+	0.940849i	$0.389971\pi$
$594$	−14.1962	+	3.80385i	−0.582475	+	0.156074i
$595$	18.5885	−	37.1769i	0.762052	−	1.52410i
$596$	−7.00000	−	12.1244i	−0.286731	−	0.496633i
$597$	−3.63397	−	6.29423i	−0.148729	−	0.257606i
$598$	−2.19615	+	0.588457i	−0.0898074	+	0.0240638i
$599$	15.2942	+	26.4904i	0.624905	+	1.08237i	0.988559	+	0.150834i	$0.0481957\pi$
$599$	15.2942	+	26.4904i	0.624905	+	1.08237i	−0.363654	+	0.931534i	$0.618471\pi$
$600$	24.2487	+	3.46410i	0.989949	+	0.141421i
$601$	−21.1962	+	36.7128i	−0.864609	+	1.49755i	0.00282571	+	0.999996i	$0.499101\pi$
$601$	−21.1962	+	36.7128i	−0.864609	+	1.49755i	−0.867435	+	0.497551i	$0.834233\pi$
$602$	−14.6603	+	54.7128i	−0.597507	+	2.22993i
$603$	16.0981	+	16.0981i	0.655564	+	0.655564i
$604$	−27.7128	−	16.0000i	−1.12762	−	0.651031i
$605$	−8.62436	−	13.0622i	−0.350630	−	0.531053i
$606$	3.46410	+	3.46410i	0.140720	+	0.140720i
$607$	−28.2583	−	7.57180i	−1.14697	−	0.307330i	−0.365220	−	0.930921i	$-0.619006\pi$
$607$	−28.2583	−	7.57180i	−1.14697	−	0.307330i	−0.781750	+	0.623592i	$0.785673\pi$
$608$	18.9282	−	18.9282i	0.767640	−	0.767640i
$609$	−6.27757	−	23.4282i	−0.254380	−	0.949359i
$610$	−43.9808	+	14.6603i	−1.78073	+	0.593576i
$611$	−2.78461			−0.112653
$612$	−6.58846	−	24.5885i	−0.266323	−	0.993929i
$613$	23.7846	−	23.7846i	0.960651	−	0.960651i	−0.0386033	−	0.999255i	$-0.512291\pi$
$613$	23.7846	−	23.7846i	0.960651	−	0.960651i	0.999255	+	0.0386033i	$0.0122909\pi$
$614$	−28.7321			−1.15953
$615$	11.1962	−	22.3923i	0.451472	−	0.902945i
$616$	−12.3923	−	21.4641i	−0.499300	−	0.864813i
$617$	7.51666	−	28.0526i	0.302609	−	1.12935i	−0.632374	−	0.774663i	$-0.717920\pi$
$617$	7.51666	−	28.0526i	0.302609	−	1.12935i	0.934984	−	0.354691i	$-0.115414\pi$
$618$	34.1769	+	19.7321i	1.37480	+	0.793739i
$619$	−1.90192	+	3.29423i	−0.0764448	+	0.132406i	−0.901714	−	0.432334i	$-0.857690\pi$
$619$	−1.90192	+	3.29423i	−0.0764448	+	0.132406i	0.825269	+	0.564740i	$0.191024\pi$
$620$	−30.5885	+	20.1962i	−1.22846	+	0.811097i
$621$	1.20577	−	4.50000i	0.0483859	−	0.180579i
$622$	−5.19615	+	19.3923i	−0.208347	+	0.777561i
$623$	3.01666	+	11.2583i	0.120860	+	0.451055i
$624$	−12.0000	+	3.21539i	−0.480384	+	0.128719i
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	−10.5885	+	18.3397i	−0.423200	+	0.733004i
$627$			16.3923i			0.654646i
$628$	24.5885	+	6.58846i	0.981186	+	0.262908i
$629$			2.78461i			0.111030i
$630$	34.6865	−	22.9019i	1.38194	−	0.912434i
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$	1.60770	+	6.00000i	0.0639507	+	0.238667i
$633$		0			0
$634$	17.3205	+	10.0000i	0.687885	+	0.397151i
$635$	−12.3827	+	13.9641i	−0.491392	+	0.554148i
$636$	6.58846	−	24.5885i	0.261249	−	0.974996i
$637$	−21.1244	+	5.66025i	−0.836977	+	0.224267i
$638$	−2.33975	+	8.73205i	−0.0926314	+	0.345705i
$639$	−31.1769	−	18.0000i	−1.23334	−	0.712069i
$640$	18.9282	+	16.7846i	0.748203	+	0.663470i
$641$	−36.1865	−	20.8923i	−1.42928	−	0.825196i	−0.432218	−	0.901769i	$-0.642269\pi$
$641$	−36.1865	−	20.8923i	−1.42928	−	0.825196i	−0.997064	+	0.0765727i	$0.975602\pi$
$642$	10.5622	+	18.2942i	0.416856	+	0.722016i
$643$	−25.7942	−	6.91154i	−1.01723	−	0.272565i	−0.288580	−	0.957456i	$-0.593183\pi$
$643$	−25.7942	−	6.91154i	−1.01723	−	0.272565i	−0.728645	+	0.684891i	$0.759850\pi$
$644$	7.85641			0.309586
$645$	26.4904	+	23.4904i	1.04306	+	0.924933i
$646$	−28.3923			−1.11708
$647$	19.6865	+	19.6865i	0.773957	+	0.773957i	0.978796	−	0.204838i	$-0.0656669\pi$
$647$	19.6865	+	19.6865i	0.773957	+	0.773957i	−0.204838	+	0.978796i	$0.565667\pi$
$648$	6.58846	−	24.5885i	0.258819	−	0.965926i
$649$		−	3.60770i		−	0.141614i
$650$	−10.1436	+	7.60770i	−0.397864	+	0.298398i
$651$	−16.0981	+	60.0788i	−0.630933	+	2.35468i
$652$	12.9282	+	12.9282i	0.506308	+	0.506308i
$653$	−7.83013	+	29.2224i	−0.306417	+	1.14356i	0.625303	+	0.780382i	$0.284976\pi$
$653$	−7.83013	+	29.2224i	−0.306417	+	1.14356i	−0.931719	+	0.363180i	$0.881691\pi$
$654$	5.49038	−	20.4904i	0.214691	−	0.801237i
$655$	9.61474	+	14.5622i	0.375679	+	0.568991i
$656$	22.3923	−	12.9282i	0.874273	−	0.504762i
$657$	−41.7846	+	11.1962i	−1.63017	+	0.436804i
$658$	9.29423	+	2.49038i	0.362327	+	0.0970852i
$659$	10.7321	+	6.19615i	0.418061	+	0.241368i	0.694248	−	0.719736i	$-0.255737\pi$
$659$	10.7321	+	6.19615i	0.418061	+	0.241368i	−0.276186	+	0.961104i	$0.589071\pi$
$660$	−15.4641	+	0.928203i	−0.601939	+	0.0361303i
$661$	6.00000	−	3.46410i	0.233373	−	0.134738i	−0.378754	−	0.925497i	$-0.623647\pi$
$661$	6.00000	−	3.46410i	0.233373	−	0.134738i	0.612127	+	0.790759i	$0.290314\pi$
$662$	0.803848	−	0.215390i	0.0312424	−	0.00837138i
$663$	11.4115	+	6.58846i	0.443188	+	0.255874i
$664$	28.7321	+	16.5885i	1.11502	+	0.643757i
$665$	−14.6603	−	43.9808i	−0.568500	−	1.70550i
$666$	−1.39230	+	2.41154i	−0.0539507	+	0.0934454i
$667$	−2.02628	−	2.02628i	−0.0784579	−	0.0784579i
$668$	−35.7846	−	9.58846i	−1.38455	−	0.370989i
$669$	−20.9545	+	20.9545i	−0.810147	+	0.810147i
$670$	13.2224	+	20.0263i	0.510827	+	0.773683i
$671$	25.3923	−	14.6603i	0.980259	−	0.565953i
$672$	42.9282			1.65599
$673$	4.66025	−	1.24871i	0.179640	−	0.0481343i	−0.167878	−	0.985808i	$-0.553691\pi$
$673$	4.66025	−	1.24871i	0.179640	−	0.0481343i	0.347517	+	0.937674i	$0.387025\pi$
$674$	0.339746	−	0.196152i	0.0130865	−	0.00755551i
$675$	−3.10770	−	25.7942i	−0.119615	−	0.992820i
$676$	−9.78461	+	16.9474i	−0.376331	+	0.651825i
$677$	−10.5359	−	39.3205i	−0.404927	−	1.51121i	−0.804189	−	0.594373i	$-0.797400\pi$
$677$	−10.5359	−	39.3205i	−0.404927	−	1.51121i	0.399262	−	0.916837i	$-0.369266\pi$
$678$	−2.19615	+	3.80385i	−0.0843427	+	0.146086i
$679$	−26.8301	+	15.4904i	−1.02965	+	0.594466i
$680$	−1.60770	−	26.7846i	−0.0616523	−	1.02714i
$681$	12.8038	+	12.8038i	0.490645	+	0.490645i
$682$	16.3923	−	16.3923i	0.627694	−	0.627694i
$683$	7.00000	+	7.00000i	0.267848	+	0.267848i	0.828232	−	0.560385i	$-0.189347\pi$
$683$	7.00000	+	7.00000i	0.267848	+	0.267848i	−0.560385	+	0.828232i	$0.689347\pi$
$684$	−24.5885	−	14.1962i	−0.940163	−	0.542803i
$685$	−28.3923	+	9.46410i	−1.08481	+	0.361605i
$686$	32.1962			1.22925
$687$	−17.3038	−	9.99038i	−0.660183	−	0.381157i
$688$	9.46410	+	35.3205i	0.360815	+	1.34658i
$689$	6.58846	+	11.4115i	0.251000	+	0.434745i
$690$	2.19615	−	4.39230i	0.0836061	−	0.167212i
$691$	−40.4711	−	23.3660i	−1.53959	−	0.888885i	−0.998862	−	0.0476910i	$-0.984814\pi$
$691$	−40.4711	−	23.3660i	−1.53959	−	0.888885i	−0.540733	−	0.841194i	$-0.681853\pi$
$692$	1.46410	+	5.46410i	0.0556568	+	0.207714i
$693$	−18.5885	+	18.5885i	−0.706117	+	0.706117i
$694$	−9.00000	+	5.19615i	−0.341635	+	0.197243i
$695$	−8.53590	−	12.9282i	−0.323785	−	0.490395i
$696$	−11.0718	−	11.0718i	−0.419675	−	0.419675i
$697$	−26.4904	−	7.09808i	−1.00339	−	0.268859i
$698$	13.3468	+	49.8109i	0.505183	+	1.88537i
$699$	11.4904	−	42.8827i	0.434606	−	1.62197i
$700$	40.6603	−	16.3205i	1.53681	−	0.616857i
$701$	−50.1769			−1.89516			−0.947578	−	0.319525i	$-0.896477\pi$
$701$	−50.1769			−1.89516			−0.947578	+	0.319525i	$0.896477\pi$
$702$	6.58846	+	11.4115i	0.248665	+	0.430701i
$703$	2.19615	+	2.19615i	0.0828295	+	0.0828295i
$704$	−13.8564	−	8.00000i	−0.522233	−	0.301511i
$705$	3.99038	−	4.50000i	0.150286	−	0.169480i
$706$	−16.3923	−	9.46410i	−0.616933	−	0.356186i
$707$	8.46410	+	2.26795i	0.318325	+	0.0852950i
$708$	5.41154	+	3.12436i	0.203378	+	0.117420i
$709$	−9.57180	+	16.5788i	−0.359476	+	0.622631i	−0.987873	−	0.155261i	$-0.950378\pi$
$709$	−9.57180	+	16.5788i	−0.359476	+	0.622631i	0.628397	+	0.777893i	$0.283711\pi$
$710$	−28.3923	−	25.1769i	−1.06554	−	0.944873i
$711$	5.70577	−	3.29423i	0.213983	−	0.123543i
$712$	5.32051	+	5.32051i	0.199394	+	0.199394i
$713$	1.90192	+	7.09808i	0.0712276	+	0.265825i
$714$	−32.1962	−	32.1962i	−1.20491	−	1.20491i
$715$	5.32051	−	6.00000i	0.198976	−	0.224387i
$716$	12.7846			0.477783
$717$	−28.3923	−	16.3923i	−1.06033	−	0.612182i
$718$	2.19615	−	2.19615i	0.0819597	−	0.0819597i
$719$	−1.51666			−0.0565619			−0.0282809	−	0.999600i	$-0.509003\pi$
$719$	−1.51666			−0.0565619			−0.0282809	+	0.999600i	$0.509003\pi$
$720$	12.0000	−	24.0000i	0.447214	−	0.894427i
$721$	70.5885			2.62885
$722$	−3.39230	+	3.39230i	−0.126249	+	0.126249i
$723$		−	32.5692i		−	1.21126i
$724$	6.00000			0.222988
$725$	−14.6962	−	6.27757i	−0.545801	−	0.233143i
$726$	−16.5622	+	4.43782i	−0.614680	+	0.164703i
$727$	−0.767949	−	2.86603i	−0.0284817	−	0.106295i	0.950222	−	0.311574i	$-0.100856\pi$
$727$	−0.767949	−	2.86603i	−0.0284817	−	0.106295i	−0.978703	+	0.205279i	$0.934190\pi$
$728$	−15.7128	+	15.7128i	−0.582356	+	0.582356i
$729$	−27.0000			−1.00000
$730$	−45.5167	+	2.73205i	−1.68465	+	0.101118i
$731$	19.3923	−	33.5885i	0.717250	−	1.24231i
$732$			50.7846i			1.87705i
$733$	−10.5622	−	2.83013i	−0.390123	−	0.104533i	0.0584252	−	0.998292i	$-0.481392\pi$
$733$	−10.5622	−	2.83013i	−0.390123	−	0.104533i	−0.448548	+	0.893759i	$0.648059\pi$
$734$	−12.1244	−	7.00000i	−0.447518	−	0.258375i
$735$	21.1244	−	42.2487i	0.779184	−	1.55837i
$736$	4.39230	−	2.53590i	0.161903	−	0.0934745i
$737$	−10.7321	−	10.7321i	−0.395320	−	0.395320i
$738$	−19.3923	−	19.3923i	−0.713841	−	0.713841i
$739$	22.7321			0.836212			0.418106	−	0.908398i	$-0.362694\pi$
$739$	22.7321			0.836212			0.418106	+	0.908398i	$0.362694\pi$
$740$	−1.94744	+	2.19615i	−0.0715894	+	0.0807322i
$741$	14.1962	−	3.80385i	0.521509	−	0.139738i
$742$	−11.7846	−	43.9808i	−0.432627	−	1.61458i
$743$	−25.4545	−	6.82051i	−0.933834	−	0.250220i	−0.240345	−	0.970687i	$-0.577261\pi$
$743$	−25.4545	−	6.82051i	−0.933834	−	0.250220i	−0.693489	+	0.720467i	$0.743927\pi$
$744$	10.3923	+	38.7846i	0.381000	+	1.42191i
$745$	−13.0622	+	8.62436i	−0.478561	+	0.315972i
$746$	−4.60770	+	2.66025i	−0.168700	+	0.0973988i
$747$	9.10770	−	33.9904i	0.333233	−	1.24364i
$748$	4.39230	+	16.3923i	0.160599	+	0.599362i
$749$	32.7224	+	18.8923i	1.19565	+	0.690310i
$750$	2.24167	−	27.2942i	0.0818542	−	0.996644i
$751$	−6.80385	−	11.7846i	−0.248276	−	0.430027i	0.714772	−	0.699358i	$-0.246531\pi$
$751$	−6.80385	−	11.7846i	−0.248276	−	0.430027i	−0.963048	+	0.269331i	$0.913197\pi$
$752$	6.00000	−	1.60770i	0.218797	−	0.0586266i
$753$	39.8827	−	23.0263i	1.45341	−	0.839124i
$754$	8.10512			0.295171
$755$	−16.0000	+	32.0000i	−0.582300	+	1.16460i
$756$	−11.7846	−	43.9808i	−0.428602	−	1.59956i
$757$	34.0526	+	34.0526i	1.23766	+	1.23766i	0.960954	+	0.276707i	$0.0892431\pi$
$757$	34.0526	+	34.0526i	1.23766	+	1.23766i	0.276707	+	0.960954i	$0.410757\pi$
$758$	33.1244	−	33.1244i	1.20313	−	1.20313i
$759$	−0.803848	+	3.00000i	−0.0291778	+	0.108893i
$760$	−22.3923	−	19.8564i	−0.812254	−	0.720268i
$761$	21.4808	−	12.4019i	0.778677	−	0.449569i	−0.0572842	−	0.998358i	$-0.518244\pi$
$761$	21.4808	−	12.4019i	0.778677	−	0.449569i	0.835961	+	0.548789i	$0.184911\pi$
$762$	10.2224	+	17.7058i	0.370320	+	0.641412i
$763$	−9.82051	−	36.6506i	−0.355526	−	1.32684i
$764$	−18.5885	+	32.1962i	−0.672507	+	1.16482i
$765$	−27.0000	+	9.00000i	−0.976187	+	0.325396i
$766$	−35.1962	+	20.3205i	−1.27169	+	0.734210i
$767$	−3.12436	+	0.837169i	−0.112814	+	0.0302284i
$768$	24.0000	−	13.8564i	0.866025	−	0.500000i
$769$	29.9378	−	17.2846i	1.07959	−	0.623299i	0.148801	−	0.988867i	$-0.452459\pi$
$769$	29.9378	−	17.2846i	1.07959	−	0.623299i	0.930785	+	0.365568i	$0.119125\pi$
$770$	−23.1244	+	15.2679i	−0.833344	+	0.550219i
$771$	7.31347	+	27.2942i	0.263388	+	0.982978i
$772$	27.3205	+	7.32051i	0.983287	+	0.263471i
$773$	16.1962	+	16.1962i	0.582535	+	0.582535i	0.935599	−	0.353064i	$-0.114860\pi$
$773$	16.1962	+	16.1962i	0.582535	+	0.582535i	−0.353064	+	0.935599i	$0.614860\pi$
$774$	33.5885	−	19.3923i	1.20731	−	0.697042i
$775$	24.5885	+	32.7846i	0.883243	+	1.17766i
$776$	−10.0000	+	17.3205i	−0.358979	+	0.621770i
$777$			4.98076i			0.178684i
$778$	−23.7583	+	6.36603i	−0.851777	+	0.228233i
$779$	−26.4904	+	15.2942i	−0.949116	+	0.547973i
$780$	4.39230	+	13.1769i	0.157270	+	0.471809i
$781$	20.7846	+	12.0000i	0.743732	+	0.429394i
$782$	−5.19615	−	1.39230i	−0.185814	−	0.0497887i
$783$	−8.30385	+	14.3827i	−0.296755	+	0.513995i
$784$	42.2487	−	24.3923i	1.50888	−	0.871154i
$785$	5.70577	−	27.8827i	0.203648	−	0.995176i
$786$	18.4641	−	4.94744i	0.658593	−	0.176469i
$787$	10.4378	−	38.9545i	0.372068	−	1.38858i	−0.485513	−	0.874229i	$-0.661367\pi$
$787$	10.4378	−	38.9545i	0.372068	−	1.38858i	0.857582	−	0.514348i	$-0.171966\pi$
$788$	24.0000	+	24.0000i	0.854965	+	0.854965i
$789$	17.1962	+	17.1962i	0.612199	+	0.612199i
$790$	6.58846	−	2.19615i	0.234407	−	0.0781356i
$791$			7.85641i			0.279342i
$792$	−4.39230	+	16.3923i	−0.156074	+	0.582475i
$793$	−18.5885	−	18.5885i	−0.660095	−	0.660095i
$794$	1.60770			0.0570550
$795$	−27.8827	−	5.70577i	−0.988897	−	0.202363i
$796$	−8.39230			−0.297457
$797$	−22.1244	−	5.92820i	−0.783685	−	0.209988i	−0.155276	−	0.987871i	$-0.549627\pi$
$797$	−22.1244	−	5.92820i	−0.783685	−	0.209988i	−0.628409	+	0.777883i	$0.716293\pi$
$798$	−50.7846			−1.79776
$799$	−5.70577	−	3.29423i	−0.201856	−	0.116541i
$800$	17.4641	−	22.2487i	0.617449	−	0.786611i
$801$	3.99038	−	6.91154i	0.140993	−	0.244207i
$802$	13.2679	−	49.5167i	0.468508	−	1.74849i
$803$	27.8564	−	7.46410i	0.983031	−	0.263402i
$804$	25.3923	−	6.80385i	0.895518	−	0.239953i
$805$	−0.526279	−	8.76795i	−0.0185489	−	0.309030i
$806$	−18.0000	−	10.3923i	−0.634023	−	0.366053i
$807$	−0.866025	−	1.50000i	−0.0304855	−	0.0528025i
$808$	5.46410	−	1.46410i	0.192226	−	0.0515069i
$809$	−45.7128			−1.60718			−0.803588	−	0.595185i	$-0.797079\pi$
$809$	−45.7128			−1.60718			−0.803588	+	0.595185i	$0.797079\pi$
$810$	−27.8827	−	5.70577i	−0.979698	−	0.200480i
$811$		−	16.7321i		−	0.587542i	−0.955876	−	0.293771i	$-0.905090\pi$
$811$		−	16.7321i		−	0.587542i	0.955876	−	0.293771i	$-0.0949103\pi$
$812$	−27.0526	−	7.24871i	−0.949359	−	0.254380i
$813$	6.88269	−	3.97372i	0.241386	−	0.139364i
$814$	0.928203	−	1.60770i	0.0325335	−	0.0563497i
$815$	13.5622	−	15.2942i	0.475062	−	0.535733i
$816$	−28.3923	−	7.60770i	−0.993929	−	0.266323i
$817$	−11.1962	−	41.7846i	−0.391704	−	1.46186i
$818$	−2.19615	+	8.19615i	−0.0767867	+	0.286572i
$819$	20.4115	+	11.7846i	0.713237	+	0.411788i
$820$	−15.9282	−	24.1244i	−0.556237	−	0.842459i
$821$	−14.2846	+	24.7417i	−0.498536	+	0.863490i	−0.999999	−	0.00168929i	$-0.999462\pi$
$821$	−14.2846	+	24.7417i	−0.498536	+	0.863490i	0.501462	+	0.865180i	$0.332796\pi$
$822$			32.7846i			1.14349i
$823$	2.96410	−	11.0622i	0.103322	−	0.385603i	−0.894827	−	0.446412i	$-0.852701\pi$
$823$	2.96410	−	11.0622i	0.103322	−	0.385603i	0.998149	+	0.0608092i	$0.0193681\pi$
$824$	39.4641	−	22.7846i	1.37480	−	0.793739i
$825$	2.07180	+	17.1962i	0.0721307	+	0.598693i
$826$	11.1769			0.388895
$827$	9.29423	−	9.29423i	0.323192	−	0.323192i	−0.526798	−	0.849990i	$-0.676608\pi$
$827$	9.29423	−	9.29423i	0.323192	−	0.323192i	0.849990	+	0.526798i	$0.176608\pi$
$828$	−3.80385	−	3.80385i	−0.132193	−	0.132193i
$829$	25.0526			0.870111			0.435056	−	0.900404i	$-0.356729\pi$
$829$	25.0526			0.870111			0.435056	+	0.900404i	$0.356729\pi$
$830$	16.5885	−	33.1769i	0.575794	−	1.15159i
$831$	−11.1962	+	11.1962i	−0.388390	+	0.388390i
$832$	−3.71281	+	13.8564i	−0.128719	+	0.480384i
$833$	−49.9808	−	13.3923i	−1.73173	−	0.464016i
$834$	−16.3923	+	4.39230i	−0.567619	+	0.152093i
$835$	−8.30385	+	40.5788i	−0.287366	+	1.40429i
$836$	16.3923	+	9.46410i	0.566940	+	0.327323i
$837$	36.8827	−	21.2942i	1.27485	−	0.736036i
$838$	4.53590	−	16.9282i	0.156690	−	0.584775i
$839$	14.0263	−	24.2942i	0.484241	−	0.838730i	−0.515595	−	0.856832i	$-0.672429\pi$
$839$	14.0263	−	24.2942i	0.484241	−	0.838730i	0.999836	+	0.0181024i	$0.00576248\pi$
$840$	−2.87564	−	47.9090i	−0.0992192	−	1.65302i
$841$	−9.39230	−	16.2679i	−0.323873	−	0.560964i
$842$	7.26795	−	1.94744i	0.250470	−	0.0671133i
$843$	−3.58846			−0.123593
$844$		0			0
$845$	19.5692	+	9.78461i	0.673202	+	0.336601i
$846$	−3.29423	−	5.70577i	−0.113258	−	0.196168i
$847$	−21.6865	+	21.6865i	−0.745158	+	0.745158i
$848$	−20.7846	−	20.7846i	−0.713746	−	0.713746i
$849$	7.79423	−	2.08846i	0.267497	−	0.0716757i
$850$	−29.7846	+	3.58846i	−1.02160	+	0.123083i
$851$	0.294229	+	0.509619i	0.0100860	+	0.0174695i
$852$	−36.0000	+	20.7846i	−1.23334	+	0.712069i
$853$	12.0000	+	44.7846i	0.410872	+	1.53340i	0.792962	+	0.609271i	$0.208538\pi$
$853$	12.0000	+	44.7846i	0.410872	+	1.53340i	−0.382090	+	0.924125i	$0.624796\pi$
$854$	45.4186	+	78.6673i	1.55419	+	2.69194i
$855$	−14.1962	+	28.3923i	−0.485498	+	0.970996i
$856$	24.3923			0.833712
$857$	−27.9282	+	7.48334i	−0.954009	+	0.255626i	−0.702063	−	0.712115i	$-0.747737\pi$
$857$	−27.9282	+	7.48334i	−0.954009	+	0.255626i	−0.251947	+	0.967741i	$0.581071\pi$
$858$	−4.39230	−	7.60770i	−0.149951	−	0.259722i
$859$	8.66025	+	15.0000i	0.295484	+	0.511793i	0.975097	−	0.221777i	$-0.0711857\pi$
$859$	8.66025	+	15.0000i	0.295484	+	0.511793i	−0.679613	+	0.733571i	$0.737852\pi$
$860$	38.7846	−	12.9282i	1.32254	−	0.440848i
$861$	−47.3827	−	12.6962i	−1.61480	−	0.432684i
$862$	−22.0526	−	22.0526i	−0.751113	−	0.751113i
$863$	−12.4186	+	12.4186i	−0.422734	+	0.422734i	−0.886144	−	0.463410i	$-0.846626\pi$
$863$	−12.4186	+	12.4186i	−0.422734	+	0.422734i	0.463410	+	0.886144i	$0.346626\pi$
$864$	−20.7846	−	20.7846i	−0.707107	−	0.707107i
$865$	6.00000	−	2.00000i	0.204006	−	0.0680020i
$866$	30.7846			1.04610
$867$	0.866025	+	1.50000i	0.0294118	+	0.0509427i
$868$	50.7846	+	50.7846i	1.72374	+	1.72374i
$869$	−3.80385	+	2.19615i	−0.129037	+	0.0744994i
$870$	−11.6147	+	13.0981i	−0.393776	+	0.444066i
$871$	−6.80385	+	11.7846i	−0.230540	+	0.399306i
$872$	−17.3205	−	17.3205i	−0.586546	−	0.586546i
$873$	20.4904	+	5.49038i	0.693494	+	0.185821i
$874$	−5.19615	+	3.00000i	−0.175762	+	0.101477i
$875$	−20.9378	−	44.2846i	−0.707828	−	1.49709i
$876$	−12.9282	+	48.2487i	−0.436804	+	1.63017i
$877$	−6.46410	+	24.1244i	−0.218277	+	0.814622i	0.766710	+	0.641994i	$0.221892\pi$
$877$	−6.46410	+	24.1244i	−0.218277	+	0.814622i	−0.984987	+	0.172628i	$0.944774\pi$
$878$	−25.6603	+	6.87564i	−0.865992	+	0.232042i
$879$	−0.509619	−	1.90192i	−0.0171890	−	0.0641503i
$880$	−8.00000	+	16.0000i	−0.269680	+	0.539360i
$881$		−	2.07180i		−	0.0698006i	−0.999391	−	0.0349003i	$-0.988889\pi$
$881$		−	2.07180i		−	0.0698006i	0.999391	−	0.0349003i	$-0.0111114\pi$
$882$	−36.5885	−	36.5885i	−1.23200	−	1.23200i
$883$	−27.4186	+	27.4186i	−0.922709	+	0.922709i	−0.997220	−	0.0745113i	$-0.976260\pi$
$883$	−27.4186	+	27.4186i	−0.922709	+	0.922709i	0.0745113	+	0.997220i	$0.476260\pi$
$884$	13.1769	−	7.60770i	0.443188	−	0.255874i
$885$	3.12436	−	6.24871i	0.105024	−	0.210048i
$886$	27.2942	−	47.2750i	0.916968	−	1.58823i
$887$	−0.418584	+	1.56218i	−0.0140547	+	0.0524528i	−0.972597	−	0.232497i	$-0.925310\pi$
$887$	−0.418584	+	1.56218i	−0.0140547	+	0.0524528i	0.958542	+	0.284950i	$0.0919770\pi$
$888$	1.60770	+	2.78461i	0.0539507	+	0.0934454i
$889$	31.6699	+	18.2846i	1.06217	+	0.613246i
$890$	5.58142	−	6.29423i	0.187089	−	0.210983i
$891$	18.0000			0.603023
$892$	8.85641	+	33.0526i	0.296534	+	1.10668i
$893$	−7.09808	+	1.90192i	−0.237528	+	0.0636455i
$894$	4.43782	+	16.5622i	0.148423	+	0.553922i
$895$	−0.856406	−	14.2679i	−0.0286265	−	0.476925i
$896$	24.7846	−	42.9282i	0.827996	−	1.43413i
$897$	2.78461			0.0929754
$898$	32.7846	−	32.7846i	1.09404	−	1.09404i
$899$		−	26.1962i		−	0.873691i
$900$	−27.5885	−	11.7846i	−0.919615	−	0.392820i
$901$			31.1769i			1.03865i
$902$	12.9282	+	12.9282i	0.430462	+	0.430462i
$903$	34.6865	−	60.0788i	1.15430	−	1.99930i
$904$	2.53590	+	4.39230i	0.0843427	+	0.146086i
$905$	−0.401924	−	6.69615i	−0.0133604	−	0.222588i
$906$	27.7128	+	27.7128i	0.920697	+	0.920697i
$907$	3.52628	−	0.944864i	0.117088	−	0.0313737i	−0.199799	−	0.979837i	$-0.564029\pi$
$907$	3.52628	−	0.944864i	0.117088	−	0.0313737i	0.316887	+	0.948463i	$0.397362\pi$
$908$	20.1962	−	5.41154i	0.670233	−	0.179588i
$909$	−3.00000	−	5.19615i	−0.0995037	−	0.172345i
$910$	18.5885	+	16.4833i	0.616201	+	0.546417i
$911$	23.4904	+	13.5622i	0.778271	+	0.449335i	0.835817	−	0.549008i	$-0.184994\pi$
$911$	23.4904	+	13.5622i	0.778271	+	0.449335i	−0.0575461	+	0.998343i	$0.518328\pi$
$912$	−28.3923	+	16.3923i	−0.940163	+	0.542803i
$913$	−6.07180	+	22.6603i	−0.200947	+	0.749945i
$914$	12.4641	+	7.19615i	0.412276	+	0.238028i
$915$	56.6769	−	3.40192i	1.87368	−	0.112464i
$916$	−19.9808	+	11.5359i	−0.660183	+	0.381157i
$917$	24.1769	−	24.1769i	0.798392	−	0.798392i
$918$			31.1769i			1.02899i
$919$			20.1962i			0.666210i	0.942890	+	0.333105i	$0.108096\pi$
$919$			20.1962i			0.666210i	−0.942890	+	0.333105i	$0.891904\pi$
$920$	−3.12436	−	4.73205i	−0.103007	−	0.156011i
$921$	33.9904	+	9.10770i	1.12002	+	0.300109i
$922$	−4.97372	−	18.5622i	−0.163801	−	0.611313i
$923$	5.56922	−	20.7846i	0.183313	−	0.684134i
$924$	7.85641	+	29.3205i	0.258457	+	0.964574i
$925$	2.58142	+	2.02628i	0.0848764	+	0.0666237i
$926$	−4.80385	−	8.32051i	−0.157864	−	0.273429i
$927$	−34.1769	−	34.1769i	−1.12252	−	1.12252i
$928$	−17.4641	+	4.67949i	−0.573287	+	0.153612i
$929$	2.19615	−	3.80385i	0.0720534	−	0.124800i	−0.827748	−	0.561100i	$-0.810378\pi$
$929$	2.19615	−	3.80385i	0.0720534	−	0.124800i	0.899801	+	0.436300i	$0.143711\pi$
$930$	42.5885	−	14.1962i	1.39653	−	0.465510i
$931$	−49.9808	+	28.8564i	−1.63805	+	0.945731i
$932$	−36.2487	−	36.2487i	−1.18737	−	1.18737i
$933$	12.2942	−	21.2942i	0.402495	−	0.697142i
$934$			17.2154i			0.563305i
$935$	18.0000	−	6.00000i	0.588663	−	0.196221i
$936$	15.2154			0.497331
$937$	−4.58846	+	4.58846i	−0.149898	+	0.149898i	−0.778073	−	0.628174i	$-0.783802\pi$
$937$	−4.58846	+	4.58846i	−0.149898	+	0.149898i	0.628174	+	0.778073i	$0.283802\pi$
$938$	33.2487	−	33.2487i	1.08561	−	1.08561i
$939$	18.3397	−	18.3397i	0.598495	−	0.598495i
$940$	−2.19615	−	6.58846i	−0.0716306	−	0.214892i
$941$	−4.40192	−	7.62436i	−0.143499	−	0.248547i	0.785313	−	0.619099i	$-0.212502\pi$
$941$	−4.40192	−	7.62436i	−0.143499	−	0.248547i	−0.928812	+	0.370552i	$0.879169\pi$
$942$	−27.0000	−	15.5885i	−0.879708	−	0.507899i
$943$	−5.59808	+	1.50000i	−0.182298	+	0.0488467i
$944$	6.24871	−	3.60770i	0.203378	−	0.117420i
$945$	−48.2942	+	16.0981i	−1.57101	+	0.523670i
$946$	−22.3923	+	12.9282i	−0.728037	+	0.420332i
$947$	6.18653	+	23.0885i	0.201035	+	0.750274i	0.990622	+	0.136634i	$0.0436286\pi$
$947$	6.18653	+	23.0885i	0.201035	+	0.750274i	−0.789586	+	0.613640i	$0.789705\pi$
$948$		−	7.60770i		−	0.247086i
$949$	−12.9282	−	22.3923i	−0.419667	−	0.726885i
$950$	−20.6603	+	26.3205i	−0.670307	+	0.853950i
$951$	−17.3205	−	17.3205i	−0.561656	−	0.561656i
$952$	−50.7846	+	13.6077i	−1.64594	+	0.441028i
$953$	−24.9282	+	24.9282i	−0.807504	+	0.807504i	−0.984255	−	0.176752i	$-0.943441\pi$
$953$	−24.9282	+	24.9282i	−0.807504	+	0.807504i	0.176752	+	0.984255i	$0.443441\pi$
$954$	−15.5885	+	27.0000i	−0.504695	+	0.874157i
$955$	37.1769	+	18.5885i	1.20302	+	0.601508i
$956$	−32.7846	+	18.9282i	−1.06033	+	0.612182i
$957$	5.53590	−	9.58846i	0.178950	−	0.309951i
$958$	7.73205	+	28.8564i	0.249811	+	0.932308i
$959$	29.3205	+	50.7846i	0.946809	+	1.63992i
$960$	−17.0718	−	25.8564i	−0.550990	−	0.834512i
$961$	−18.0885	+	31.3301i	−0.583499	+	1.01065i
$962$	−1.60770	−	0.430781i	−0.0518342	−	0.0138889i
$963$	−6.69615	−	24.9904i	−0.215780	−	0.805304i
$964$	−32.5692	−	18.8038i	−1.04898	−	0.605631i
$965$	6.33975	−	30.9808i	0.204084	−	0.997306i
$966$	−9.29423	−	2.49038i	−0.299037	−	0.0801267i
$967$	15.9641	+	4.27757i	0.513371	+	0.137557i	0.506199	−	0.862417i	$-0.331050\pi$
$967$	15.9641	+	4.27757i	0.513371	+	0.137557i	0.00717234	+	0.999974i	$0.497717\pi$
$968$	−5.12436	+	19.1244i	−0.164703	+	0.614680i
$969$	33.5885	+	9.00000i	1.07902	+	0.289122i
$970$	20.0000	+	10.0000i	0.642161	+	0.321081i
$971$	−29.8038			−0.956451			−0.478225	−	0.878237i	$-0.658720\pi$
$971$	−29.8038			−0.956451			−0.478225	+	0.878237i	$0.658720\pi$
$972$	−15.5885	+	27.0000i	−0.500000	+	0.866025i
$973$	−21.4641	+	21.4641i	−0.688108	+	0.688108i
$974$			6.78461i			0.217393i
$975$	14.4115	−	5.78461i	0.461539	−	0.185256i
$976$	50.7846	+	29.3205i	1.62558	+	0.938527i
$977$	−10.7321	+	40.0526i	−0.343349	+	1.28139i	0.551181	+	0.834386i	$0.314177\pi$
$977$	−10.7321	+	40.0526i	−0.343349	+	1.28139i	−0.894529	+	0.447009i	$0.852489\pi$
$978$	−11.1962	−	19.3923i	−0.358013	−	0.620098i
$979$	−2.66025	+	4.60770i	−0.0850221	+	0.147263i
$980$	−30.0526	−	45.5167i	−0.959994	−	1.45398i
$981$	−12.9904	+	22.5000i	−0.414751	+	0.718370i
$982$	33.8564	+	9.07180i	1.08040	+	0.289493i
$983$	3.57180	+	13.3301i	0.113923	+	0.425165i	0.999204	−	0.0398907i	$-0.0127010\pi$
$983$	3.57180	+	13.3301i	0.113923	+	0.425165i	−0.885281	+	0.465056i	$0.846034\pi$
$984$	−30.5885	+	8.19615i	−0.975124	+	0.261284i
$985$	25.1769	−	28.3923i	0.802203	−	0.904654i
$986$	16.6077	+	9.58846i	0.528897	+	0.305359i
$987$	−10.2058	−	5.89230i	−0.324853	−	0.187554i
$988$	4.39230	−	16.3923i	0.139738	−	0.521509i
$989$		−	8.19615i		−	0.260622i
$990$	18.5885	+	3.80385i	0.590780	+	0.120894i
$991$	10.1962			0.323891			0.161946	−	0.986800i	$-0.448223\pi$
$991$	10.1962			0.323891			0.161946	+	0.986800i	$0.448223\pi$
$992$	44.7846	+	12.0000i	1.42191	+	0.381000i
$993$	−1.01924			−0.0323445
$994$	−37.1769	+	64.3923i	−1.17918	+	2.04240i
$995$	0.562178	+	9.36603i	0.0178222	+	0.296923i
$996$	−28.7321	−	28.7321i	−0.910410	−	0.910410i
$997$	6.63397	−	1.77757i	0.210100	−	0.0562961i	−0.152234	−	0.988345i	$-0.548647\pi$
$997$	6.63397	−	1.77757i	0.210100	−	0.0562961i	0.362334	+	0.932048i	$0.381980\pi$
$998$	−36.5885	−	9.80385i	−1.15819	−	0.310335i
$999$	2.41154	−	2.41154i	0.0762978	−	0.0762978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.br.b.173.1	yes	4
5.2	odd	4		360.2.br.a.317.1	yes	4
8.5	even	2		360.2.br.c.173.1	yes	4
9.5	odd	6		360.2.br.d.293.1	yes	4
40.37	odd	4		360.2.br.d.317.1	yes	4
45.32	even	12		360.2.br.c.77.1	yes	4
72.5	odd	6		360.2.br.a.293.1	✓	4
360.77	even	12	inner	360.2.br.b.77.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.br.a.293.1	✓	4	72.5	odd	6
360.2.br.a.317.1	yes	4	5.2	odd	4
360.2.br.b.77.1	yes	4	360.77	even	12	inner
360.2.br.b.173.1	yes	4	1.1	even	1	trivial
360.2.br.c.77.1	yes	4	45.32	even	12
360.2.br.c.173.1	yes	4	8.5	even	2
360.2.br.d.293.1	yes	4	9.5	odd	6
360.2.br.d.317.1	yes	4	40.37	odd	4

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.50000 - 0.866025i) q^{3} -2.00000i q^{4} +(-2.23205 + 0.133975i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(1.13397 + 4.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.50000 - 0.866025i) q^{3} -2.00000i q^{4} +(-2.23205 + 0.133975i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(1.13397 + 4.23205i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +(2.09808 - 2.36603i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-1.73205 - 3.00000i) q^{12} +(1.73205 + 0.464102i) q^{13} +(-5.36603 - 3.09808i) q^{14} +(-3.23205 + 2.13397i) q^{15} -4.00000 q^{16} +(3.00000 + 3.00000i) q^{17} +(1.09808 + 4.09808i) q^{18} +4.73205 q^{19} +(0.267949 + 4.46410i) q^{20} +(5.36603 + 5.36603i) q^{21} +(-0.732051 - 2.73205i) q^{22} +(0.866025 + 0.232051i) q^{23} +(4.73205 + 1.26795i) q^{24} +(4.96410 - 0.598076i) q^{25} +(-2.19615 + 1.26795i) q^{26} -5.19615i q^{27} +(8.46410 - 2.26795i) q^{28} +(-2.76795 - 1.59808i) q^{29} +(1.09808 - 5.36603i) q^{30} +(4.09808 + 7.09808i) q^{31} +(4.00000 - 4.00000i) q^{32} +3.46410i q^{33} -6.00000 q^{34} +(-3.09808 - 9.29423i) q^{35} +(-5.19615 - 3.00000i) q^{36} +(0.464102 + 0.464102i) q^{37} +(-4.73205 + 4.73205i) q^{38} +(3.00000 - 0.803848i) q^{39} +(-4.73205 - 4.19615i) q^{40} +(-5.59808 + 3.23205i) q^{41} -10.7321 q^{42} +(-2.36603 - 8.83013i) q^{43} +(3.46410 + 2.00000i) q^{44} +(-3.00000 + 6.00000i) q^{45} +(-1.09808 + 0.633975i) q^{46} +(-1.50000 + 0.401924i) q^{47} +(-6.00000 + 3.46410i) q^{48} +(-10.5622 + 6.09808i) q^{49} +(-4.36603 + 5.56218i) q^{50} +(7.09808 + 1.90192i) q^{51} +(0.928203 - 3.46410i) q^{52} +(5.19615 + 5.19615i) q^{53} +(5.19615 + 5.19615i) q^{54} +(2.00000 - 4.00000i) q^{55} +(-6.19615 + 10.7321i) q^{56} +(7.09808 - 4.09808i) q^{57} +(4.36603 - 1.16987i) q^{58} +(-1.56218 + 0.901924i) q^{59} +(4.26795 + 6.46410i) q^{60} +(-12.6962 - 7.33013i) q^{61} +(-11.1962 - 3.00000i) q^{62} +(12.6962 + 3.40192i) q^{63} +8.00000i q^{64} +(-3.92820 - 0.803848i) q^{65} +(-3.46410 - 3.46410i) q^{66} +(-1.96410 + 7.33013i) q^{67} +(6.00000 - 6.00000i) q^{68} +(1.50000 - 0.401924i) q^{69} +(12.3923 + 6.19615i) q^{70} -12.0000i q^{71} +(8.19615 - 2.19615i) q^{72} +(-10.1962 - 10.1962i) q^{73} -0.928203 q^{74} +(6.92820 - 5.19615i) q^{75} -9.46410i q^{76} +(-8.46410 - 2.26795i) q^{77} +(-2.19615 + 3.80385i) q^{78} +(1.90192 + 1.09808i) q^{79} +(8.92820 - 0.535898i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.36603 - 8.83013i) q^{82} +(11.3301 - 3.03590i) q^{83} +(10.7321 - 10.7321i) q^{84} +(-7.09808 - 6.29423i) q^{85} +(11.1962 + 6.46410i) q^{86} -5.53590 q^{87} +(-5.46410 + 1.46410i) q^{88} +2.66025 q^{89} +(-3.00000 - 9.00000i) q^{90} +7.85641i q^{91} +(0.464102 - 1.73205i) q^{92} +(12.2942 + 7.09808i) q^{93} +(1.09808 - 1.90192i) q^{94} +(-10.5622 + 0.633975i) q^{95} +(2.53590 - 9.46410i) q^{96} +(1.83013 + 6.83013i) q^{97} +(4.46410 - 16.6603i) q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 8 q^{7} + 8 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 6 * q^3 - 2 * q^5 - 6 * q^6 + 8 * q^7 + 8 * q^8 + 6 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 8 q^{7} + 8 q^{8} + 6 q^{9} - 2 q^{10} - 4 q^{11} - 18 q^{14} - 6 q^{15} - 16 q^{16} + 12 q^{17} - 6 q^{18} + 12 q^{19} + 8 q^{20} + 18 q^{21} + 4 q^{22} + 12 q^{24} + 6 q^{25} + 12 q^{26} + 20 q^{28} - 18 q^{29} - 6 q^{30} + 6 q^{31} + 16 q^{32} - 24 q^{34} - 2 q^{35} - 12 q^{37} - 12 q^{38} + 12 q^{39} - 12 q^{40} - 12 q^{41} - 36 q^{42} - 6 q^{43} - 12 q^{45} + 6 q^{46} - 6 q^{47} - 24 q^{48} - 18 q^{49} - 14 q^{50} + 18 q^{51} - 24 q^{52} + 8 q^{55} - 4 q^{56} + 18 q^{57} + 14 q^{58} + 18 q^{59} + 24 q^{60} - 30 q^{61} - 24 q^{62} + 30 q^{63} + 12 q^{65} + 6 q^{67} + 24 q^{68} + 6 q^{69} + 8 q^{70} + 12 q^{72} - 20 q^{73} + 24 q^{74} - 20 q^{77} + 12 q^{78} + 18 q^{79} + 8 q^{80} - 18 q^{81} + 6 q^{82} + 28 q^{83} + 36 q^{84} - 18 q^{85} + 24 q^{86} - 36 q^{87} - 8 q^{88} - 24 q^{89} - 12 q^{90} - 12 q^{92} + 18 q^{93} - 6 q^{94} - 18 q^{95} + 24 q^{96} - 10 q^{97} + 4 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 2 * q^5 - 6 * q^6 + 8 * q^7 + 8 * q^8 + 6 * q^9 - 2 * q^10 - 4 * q^11 - 18 * q^14 - 6 * q^15 - 16 * q^16 + 12 * q^17 - 6 * q^18 + 12 * q^19 + 8 * q^20 + 18 * q^21 + 4 * q^22 + 12 * q^24 + 6 * q^25 + 12 * q^26 + 20 * q^28 - 18 * q^29 - 6 * q^30 + 6 * q^31 + 16 * q^32 - 24 * q^34 - 2 * q^35 - 12 * q^37 - 12 * q^38 + 12 * q^39 - 12 * q^40 - 12 * q^41 - 36 * q^42 - 6 * q^43 - 12 * q^45 + 6 * q^46 - 6 * q^47 - 24 * q^48 - 18 * q^49 - 14 * q^50 + 18 * q^51 - 24 * q^52 + 8 * q^55 - 4 * q^56 + 18 * q^57 + 14 * q^58 + 18 * q^59 + 24 * q^60 - 30 * q^61 - 24 * q^62 + 30 * q^63 + 12 * q^65 + 6 * q^67 + 24 * q^68 + 6 * q^69 + 8 * q^70 + 12 * q^72 - 20 * q^73 + 24 * q^74 - 20 * q^77 + 12 * q^78 + 18 * q^79 + 8 * q^80 - 18 * q^81 + 6 * q^82 + 28 * q^83 + 36 * q^84 - 18 * q^85 + 24 * q^86 - 36 * q^87 - 8 * q^88 - 24 * q^89 - 12 * q^90 - 12 * q^92 + 18 * q^93 - 6 * q^94 - 18 * q^95 + 24 * q^96 - 10 * q^97 + 4 * q^98 + 12 * q^99

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