LMFDB - Embedded newform 360.2.br.a.293.1

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:	$1$
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			293.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	360.293
Dual form			360.2.br.a.317.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-0.866025 + 1.50000i) q^{3} -2.00000i q^{4} +(1.23205 + 1.86603i) q^{5} +(-0.633975 - 2.36603i) q^{6} +(-4.23205 - 1.13397i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-0.866025 + 1.50000i) q^{3} -2.00000i q^{4} +(1.23205 + 1.86603i) q^{5} +(-0.633975 - 2.36603i) q^{6} +(-4.23205 - 1.13397i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.09808 - 0.633975i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(3.00000 + 1.73205i) q^{12} +(0.464102 + 1.73205i) q^{13} +(5.36603 - 3.09808i) q^{14} +(-3.86603 + 0.232051i) q^{15} -4.00000 q^{16} +(-3.00000 - 3.00000i) q^{17} +(4.09808 + 1.09808i) q^{18} -4.73205 q^{19} +(3.73205 - 2.46410i) q^{20} +(5.36603 - 5.36603i) q^{21} +(2.73205 + 0.732051i) q^{22} +(0.232051 + 0.866025i) q^{23} +(-4.73205 + 1.26795i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(-2.19615 - 1.26795i) q^{26} +5.19615 q^{27} +(-2.26795 + 8.46410i) q^{28} +(2.76795 - 1.59808i) q^{29} +(3.63397 - 4.09808i) q^{30} +(4.09808 - 7.09808i) q^{31} +(4.00000 - 4.00000i) q^{32} +3.46410 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} +(-1.26795 + 6.19615i) q^{40} +(-5.59808 - 3.23205i) q^{41} +10.7321i q^{42} +(-8.83013 - 2.36603i) q^{43} +(-3.46410 + 2.00000i) q^{44} +(3.00000 - 6.00000i) q^{45} +(-1.09808 - 0.633975i) q^{46} +(-0.401924 + 1.50000i) q^{47} +(3.46410 - 6.00000i) q^{48} +(10.5622 + 6.09808i) q^{49} +(-2.63397 - 6.56218i) q^{50} +(7.09808 - 1.90192i) q^{51} +(3.46410 - 0.928203i) 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} +(4.09808 - 7.09808i) q^{57} +(-1.16987 + 4.36603i) q^{58} +(1.56218 + 0.901924i) q^{59} +(0.464102 + 7.73205i) q^{60} +(-12.6962 + 7.33013i) q^{61} +(3.00000 + 11.1962i) q^{62} +(3.40192 + 12.6962i) q^{63} +8.00000i q^{64} +(-2.66025 + 3.00000i) q^{65} +(-3.46410 + 3.46410i) q^{66} +(-7.33013 + 1.96410i) q^{67} +(-6.00000 + 6.00000i) q^{68} +(-1.50000 - 0.401924i) q^{69} +(12.3923 + 6.19615i) q^{70} +12.0000i q^{71} +(2.19615 - 8.19615i) q^{72} +(-10.1962 - 10.1962i) q^{73} +0.928203 q^{74} +(-5.19615 - 6.92820i) q^{75} +9.46410i q^{76} +(2.26795 + 8.46410i) q^{77} +(3.80385 - 2.19615i) q^{78} +(-1.90192 + 1.09808i) q^{79} +(-4.92820 - 7.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(8.83013 - 2.36603i) q^{82} +(-3.03590 + 11.3301i) q^{83} +(-10.7321 - 10.7321i) q^{84} +(1.90192 - 9.29423i) q^{85} +(11.1962 - 6.46410i) q^{86} +5.53590i q^{87} +(1.46410 - 5.46410i) q^{88} -2.66025 q^{89} +(3.00000 + 9.00000i) q^{90} -7.85641i q^{91} +(1.73205 - 0.464102i) q^{92} +(7.09808 + 12.2942i) q^{93} +(-1.09808 - 1.90192i) q^{94} +(-5.83013 - 8.83013i) q^{95} +(2.53590 + 9.46410i) q^{96} +(-6.83013 - 1.83013i) q^{97} +(-16.6603 + 4.46410i) q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 2 q^{5} - 6 q^{6} - 10 q^{7} + 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 2 * q^5 - 6 * q^6 - 10 * q^7 + 8 * q^8 - 6 * q^9	$ 4 q - 4 q^{2} - 2 q^{5} - 6 q^{6} - 10 q^{7} + 8 q^{8} - 6 q^{9} - 2 q^{10} - 4 q^{11} + 12 q^{12} - 12 q^{13} + 18 q^{14} - 12 q^{15} - 16 q^{16} - 12 q^{17} + 6 q^{18} - 12 q^{19} + 8 q^{20} + 18 q^{21} + 4 q^{22} - 6 q^{23} - 12 q^{24} + 6 q^{25} + 12 q^{26} - 16 q^{28} + 18 q^{29} + 18 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} - 18 q^{43} + 12 q^{45} + 6 q^{46} - 12 q^{47} + 18 q^{49} - 14 q^{50} + 18 q^{51} + 8 q^{55} - 4 q^{56} + 6 q^{57} - 22 q^{58} - 18 q^{59} - 12 q^{60} - 30 q^{61} + 12 q^{62} + 24 q^{63} + 24 q^{65} - 12 q^{67} - 24 q^{68} - 6 q^{69} + 8 q^{70} - 12 q^{72} - 20 q^{73} - 24 q^{74} + 16 q^{77} + 36 q^{78} - 18 q^{79} + 8 q^{80} - 18 q^{81} + 18 q^{82} - 26 q^{83} - 36 q^{84} + 18 q^{85} + 24 q^{86} - 8 q^{88} + 24 q^{89} + 12 q^{90} + 18 q^{93} + 6 q^{94} - 6 q^{95} + 24 q^{96} - 10 q^{97} - 32 q^{98} - 12 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 2 * q^5 - 6 * q^6 - 10 * q^7 + 8 * q^8 - 6 * q^9 - 2 * q^10 - 4 * q^11 + 12 * q^12 - 12 * q^13 + 18 * q^14 - 12 * q^15 - 16 * q^16 - 12 * q^17 + 6 * q^18 - 12 * q^19 + 8 * q^20 + 18 * q^21 + 4 * q^22 - 6 * q^23 - 12 * q^24 + 6 * q^25 + 12 * q^26 - 16 * q^28 + 18 * q^29 + 18 * 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 - 18 * q^43 + 12 * q^45 + 6 * q^46 - 12 * q^47 + 18 * q^49 - 14 * q^50 + 18 * q^51 + 8 * q^55 - 4 * q^56 + 6 * q^57 - 22 * q^58 - 18 * q^59 - 12 * q^60 - 30 * q^61 + 12 * q^62 + 24 * q^63 + 24 * q^65 - 12 * q^67 - 24 * q^68 - 6 * q^69 + 8 * q^70 - 12 * q^72 - 20 * q^73 - 24 * q^74 + 16 * q^77 + 36 * q^78 - 18 * q^79 + 8 * q^80 - 18 * q^81 + 18 * q^82 - 26 * q^83 - 36 * q^84 + 18 * q^85 + 24 * q^86 - 8 * q^88 + 24 * q^89 + 12 * q^90 + 18 * q^93 + 6 * q^94 - 6 * q^95 + 24 * q^96 - 10 * q^97 - 32 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$4$		−	2.00000i		−	1.00000i
$5$	1.23205	+	1.86603i	0.550990	+	0.834512i
$5$	1.23205	+	1.86603i	0.550990	+	0.834512i
$6$	−0.633975	−	2.36603i	−0.258819	−	0.965926i
$7$	−4.23205	−	1.13397i	−1.59956	−	0.428602i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$	−4.23205	−	1.13397i	−1.59956	−	0.428602i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	−3.09808	−	0.633975i	−0.979698	−	0.200480i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	3.00000	+	1.73205i	0.866025	+	0.500000i
$13$	0.464102	+	1.73205i	0.128719	+	0.480384i	0.999945	−	0.0104972i	$-0.00334142\pi$
$13$	0.464102	+	1.73205i	0.128719	+	0.480384i	−0.871226	+	0.490882i	$0.836675\pi$
$14$	5.36603	−	3.09808i	1.43413	−	0.827996i
$15$	−3.86603	+	0.232051i	−0.998203	+	0.0599153i
$16$	−4.00000			−1.00000
$17$	−3.00000	−	3.00000i	−0.727607	−	0.727607i	0.242536	−	0.970143i	$-0.422021\pi$
$17$	−3.00000	−	3.00000i	−0.727607	−	0.727607i	−0.970143	+	0.242536i	$0.922021\pi$
$18$	4.09808	+	1.09808i	0.965926	+	0.258819i
$19$	−4.73205			−1.08561			−0.542803	−	0.839860i	$-0.682637\pi$
$19$	−4.73205			−1.08561			−0.542803	+	0.839860i	$0.682637\pi$
$20$	3.73205	−	2.46410i	0.834512	−	0.550990i
$21$	5.36603	−	5.36603i	1.17096	−	1.17096i
$22$	2.73205	+	0.732051i	0.582475	+	0.156074i
$23$	0.232051	+	0.866025i	0.0483859	+	0.180579i	0.985890	−	0.167396i	$-0.0535360\pi$
$23$	0.232051	+	0.866025i	0.0483859	+	0.180579i	−0.937504	+	0.347975i	$0.886869\pi$
$24$	−4.73205	+	1.26795i	−0.965926	+	0.258819i
$25$	−1.96410	+	4.59808i	−0.392820	+	0.919615i
$26$	−2.19615	−	1.26795i	−0.430701	−	0.248665i
$27$	5.19615			1.00000
$28$	−2.26795	+	8.46410i	−0.428602	+	1.59956i
$29$	2.76795	−	1.59808i	0.513995	−	0.296755i	−0.220479	−	0.975392i	$-0.570762\pi$
$29$	2.76795	−	1.59808i	0.513995	−	0.296755i	0.734474	+	0.678636i	$0.237429\pi$
$30$	3.63397	−	4.09808i	0.663470	−	0.748203i
$31$	4.09808	−	7.09808i	0.736036	−	1.27485i	−0.218231	−	0.975897i	$-0.570029\pi$
$31$	4.09808	−	7.09808i	0.736036	−	1.27485i	0.954267	−	0.298955i	$-0.0966380\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	3.46410			0.603023
$34$	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	0.667928	−	0.744226i	$-0.267181\pi$
$37$	−0.464102	−	0.464102i	−0.0762978	−	0.0762978i	−0.744226	+	0.667928i	$0.767181\pi$
$38$	4.73205	−	4.73205i	0.767640	−	0.767640i
$39$	−3.00000	−	0.803848i	−0.480384	−	0.128719i
$40$	−1.26795	+	6.19615i	−0.200480	+	0.979698i
$41$	−5.59808	−	3.23205i	−0.874273	−	0.504762i	−0.00550690	−	0.999985i	$-0.501753\pi$
$41$	−5.59808	−	3.23205i	−0.874273	−	0.504762i	−0.868766	+	0.495223i	$0.835086\pi$
$42$			10.7321i			1.65599i
$43$	−8.83013	−	2.36603i	−1.34658	−	0.360815i	−0.487710	−	0.873006i	$-0.662168\pi$
$43$	−8.83013	−	2.36603i	−1.34658	−	0.360815i	−0.858872	+	0.512190i	$0.828834\pi$
$44$	−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
$47$	−0.401924	+	1.50000i	−0.0586266	+	0.218797i	−0.989024	−	0.147755i	$-0.952795\pi$
$47$	−0.401924	+	1.50000i	−0.0586266	+	0.218797i	0.930397	+	0.366552i	$0.119462\pi$
$48$	3.46410	−	6.00000i	0.500000	−	0.866025i
$49$	10.5622	+	6.09808i	1.50888	+	0.871154i
$50$	−2.63397	−	6.56218i	−0.372500	−	0.928032i
$51$	7.09808	−	1.90192i	0.993929	−	0.266323i
$52$	3.46410	−	0.928203i	0.480384	−	0.128719i
$53$	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
$57$	4.09808	−	7.09808i	0.542803	−	0.940163i
$58$	−1.16987	+	4.36603i	−0.153612	+	0.573287i
$59$	1.56218	+	0.901924i	0.203378	+	0.117420i	0.598230	−	0.801324i	$-0.295871\pi$
$59$	1.56218	+	0.901924i	0.203378	+	0.117420i	−0.394852	+	0.918745i	$0.629204\pi$
$60$	0.464102	+	7.73205i	0.0599153	+	0.998203i
$61$	−12.6962	+	7.33013i	−1.62558	+	0.938527i	−0.640184	+	0.768221i	$0.721142\pi$
$61$	−12.6962	+	7.33013i	−1.62558	+	0.938527i	−0.985391	+	0.170305i	$0.945525\pi$
$62$	3.00000	+	11.1962i	0.381000	+	1.42191i
$63$	3.40192	+	12.6962i	0.428602	+	1.59956i
$64$			8.00000i			1.00000i
$65$	−2.66025	+	3.00000i	−0.329964	+	0.372104i
$66$	−3.46410	+	3.46410i	−0.426401	+	0.426401i
$67$	−7.33013	+	1.96410i	−0.895518	+	0.239953i	−0.677090	−	0.735900i	$-0.736759\pi$
$67$	−7.33013	+	1.96410i	−0.895518	+	0.239953i	−0.218427	+	0.975853i	$0.570093\pi$
$68$	−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	$0.252242\pi$
$71$			12.0000i			1.42414i	−0.702109	+	0.712069i	$0.747758\pi$
$72$	2.19615	−	8.19615i	0.258819	−	0.965926i
$73$	−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
$75$	−5.19615	−	6.92820i	−0.600000	−	0.800000i
$76$			9.46410i			1.08561i
$77$	2.26795	+	8.46410i	0.258457	+	0.964574i
$78$	3.80385	−	2.19615i	0.430701	−	0.248665i
$79$	−1.90192	+	1.09808i	−0.213983	+	0.123543i	−0.603161	−	0.797619i	$-0.706092\pi$
$79$	−1.90192	+	1.09808i	−0.213983	+	0.123543i	0.389178	+	0.921163i	$0.372759\pi$
$80$	−4.92820	−	7.46410i	−0.550990	−	0.834512i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	8.83013	−	2.36603i	0.975124	−	0.261284i
$83$	−3.03590	+	11.3301i	−0.333233	+	1.24364i	0.572539	+	0.819878i	$0.305959\pi$
$83$	−3.03590	+	11.3301i	−0.333233	+	1.24364i	−0.905772	+	0.423765i	$0.860708\pi$
$84$	−10.7321	−	10.7321i	−1.17096	−	1.17096i
$85$	1.90192	−	9.29423i	0.206293	−	1.00810i
$86$	11.1962	−	6.46410i	1.20731	−	0.697042i
$87$			5.53590i			0.593511i
$88$	1.46410	−	5.46410i	0.156074	−	0.582475i
$89$	−2.66025			−0.281986			−0.140993	−	0.990011i	$-0.545030\pi$
$89$	−2.66025			−0.281986			−0.140993	+	0.990011i	$0.545030\pi$
$90$	3.00000	+	9.00000i	0.316228	+	0.948683i
$91$		−	7.85641i		−	0.823575i
$92$	1.73205	−	0.464102i	0.180579	−	0.0483859i
$93$	7.09808	+	12.2942i	0.736036	+	1.27485i
$94$	−1.09808	−	1.90192i	−0.113258	−	0.196168i
$95$	−5.83013	−	8.83013i	−0.598158	−	0.905952i
$96$	2.53590	+	9.46410i	0.258819	+	0.965926i
$97$	−6.83013	−	1.83013i	−0.693494	−	0.185821i	−0.105180	−	0.994453i	$-0.533542\pi$
$97$	−6.83013	−	1.83013i	−0.693494	−	0.185821i	−0.588315	+	0.808632i	$0.700208\pi$
$98$	−16.6603	+	4.46410i	−1.68294	+	0.450942i
$99$	−3.00000	+	5.19615i	−0.301511	+	0.522233i
$100$	9.19615	+	3.92820i	0.919615	+	0.392820i
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$	−5.19615	+	9.00000i	−0.514496	+	0.891133i
$103$	−15.5622	+	4.16987i	−1.53339	+	0.410870i	−0.924122	−	0.382097i	$-0.875202\pi$
$103$	−15.5622	+	4.16987i	−1.53339	+	0.410870i	−0.609265	+	0.792967i	$0.708535\pi$
$104$	−2.53590	+	4.39230i	−0.248665	+	0.430701i
$105$	16.6244	+	3.40192i	1.62237	+	0.331994i
$106$	−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	$0.113132\pi$
$108$		−	10.3923i		−	1.00000i
$109$	8.66025			0.829502			0.414751	−	0.909935i	$-0.363869\pi$
$109$	8.66025			0.829502			0.414751	+	0.909935i	$0.363869\pi$
$110$	2.00000	+	6.00000i	0.190693	+	0.572078i
$111$	1.09808	−	0.294229i	0.104225	−	0.0279269i
$112$	16.9282	+	4.53590i	1.59956	+	0.428602i
$113$	0.464102	+	1.73205i	0.0436590	+	0.162938i	0.984314	−	0.176428i	$-0.0564543\pi$
$113$	0.464102	+	1.73205i	0.0436590	+	0.162938i	−0.940655	+	0.339366i	$0.889788\pi$
$114$	3.00000	+	11.1962i	0.280976	+	1.04862i
$115$	−1.33013	+	1.50000i	−0.124035	+	0.139876i
$116$	−3.19615	−	5.53590i	−0.296755	−	0.513995i
$117$	3.80385	−	3.80385i	0.351666	−	0.351666i
$118$	−2.46410	+	0.660254i	−0.226839	+	0.0607813i
$119$	9.29423	+	16.0981i	0.852001	+	1.47571i
$120$	−8.19615	−	7.26795i	−0.748203	−	0.663470i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	5.36603	−	20.0263i	0.485817	−	1.81309i
$123$	9.69615	−	5.59808i	0.874273	−	0.504762i
$124$	−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
$130$	−0.339746	−	5.66025i	−0.0297977	−	0.496437i
$131$	−3.90192	+	6.75833i	−0.340913	+	0.590478i	−0.984602	−	0.174808i	$-0.944069\pi$
$131$	−3.90192	+	6.75833i	−0.340913	+	0.590478i	0.643690	+	0.765287i	$0.277403\pi$
$132$		−	6.92820i		−	0.603023i
$133$	20.0263	+	5.36603i	1.73650	+	0.465293i
$134$	5.36603	−	9.29423i	0.463554	−	0.802899i
$135$	6.40192	+	9.69615i	0.550990	+	0.834512i
$136$		−	12.0000i		−	1.02899i
$137$	3.46410	−	12.9282i	0.295958	−	1.10453i	−0.644495	−	0.764608i	$-0.722932\pi$
$137$	3.46410	−	12.9282i	0.295958	−	1.10453i	0.940453	−	0.339923i	$-0.110401\pi$
$138$	1.90192	−	1.09808i	0.161903	−	0.0934745i
$139$	−3.46410	+	6.00000i	−0.293821	+	0.508913i	−0.974710	−	0.223474i	$-0.928260\pi$
$139$	−3.46410	+	6.00000i	−0.293821	+	0.508913i	0.680889	+	0.732387i	$0.261594\pi$
$140$	−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
$147$	−18.2942	+	10.5622i	−1.50888	+	0.871154i
$148$	−0.928203	+	0.928203i	−0.0762978	+	0.0762978i
$149$	−6.06218	−	3.50000i	−0.496633	−	0.286731i	0.230689	−	0.973028i	$-0.425902\pi$
$149$	−6.06218	−	3.50000i	−0.496633	−	0.286731i	−0.727322	+	0.686296i	$0.759235\pi$
$150$	12.1244	+	1.73205i	0.989949	+	0.141421i
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$	−9.46410	−	9.46410i	−0.767640	−	0.767640i
$153$	−3.29423	+	12.2942i	−0.266323	+	0.993929i
$154$	−10.7321	−	6.19615i	−0.864813	−	0.499300i
$155$	18.2942	−	1.09808i	1.46943	−	0.0881996i
$156$	−1.60770	+	6.00000i	−0.128719	+	0.480384i
$157$	−12.2942	+	3.29423i	−0.981186	+	0.262908i	−0.713544	−	0.700610i	$-0.752911\pi$
$157$	−12.2942	+	3.29423i	−0.981186	+	0.262908i	−0.267642	+	0.963518i	$0.586244\pi$
$158$	0.803848	−	3.00000i	0.0639507	−	0.238667i
$159$	−12.2942	+	3.29423i	−0.974996	+	0.261249i
$160$	12.3923	+	2.53590i	0.979698	+	0.200480i
$161$		−	3.92820i		−	0.309586i
$162$	−3.29423	−	12.2942i	−0.258819	−	0.965926i
$163$	6.46410	−	6.46410i	0.506308	−	0.506308i	−0.407083	−	0.913391i	$-0.633454\pi$
$163$	6.46410	−	6.46410i	0.506308	−	0.506308i	0.913391	+	0.407083i	$0.133454\pi$
$164$	−6.46410	+	11.1962i	−0.504762	+	0.874273i
$165$	4.26795	+	6.46410i	0.332259	+	0.503230i
$166$	−8.29423	−	14.3660i	−0.643757	−	1.11502i
$167$	17.8923	−	4.79423i	1.38455	−	0.370989i	0.511777	−	0.859118i	$-0.328987\pi$
$167$	17.8923	−	4.79423i	1.38455	−	0.370989i	0.872771	+	0.488130i	$0.162321\pi$
$168$	21.4641			1.65599
$169$	8.47372	−	4.89230i	0.651825	−	0.376331i
$170$	7.39230	+	11.1962i	0.566964	+	0.858706i
$171$	7.09808	+	12.2942i	0.542803	+	0.940163i
$172$	−4.73205	+	17.6603i	−0.360815	+	1.34658i
$173$	0.732051	−	2.73205i	0.0556568	−	0.207714i	−0.932498	−	0.361176i	$-0.882375\pi$
$173$	0.732051	−	2.73205i	0.0556568	−	0.207714i	0.988155	+	0.153462i	$0.0490422\pi$
$174$	−5.53590	−	5.53590i	−0.419675	−	0.419675i
$175$	13.5263	−	17.2321i	1.02249	−	1.30262i
$176$	4.00000	+	6.92820i	0.301511	+	0.522233i
$177$	−2.70577	+	1.56218i	−0.203378	+	0.117420i
$178$	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	$-0.964436\pi$
$181$		−	3.00000i		−	0.222988i	0.993765	−	0.111494i	$-0.0355636\pi$
$182$	7.85641	+	7.85641i	0.582356	+	0.582356i
$183$		−	25.3923i		−	1.87705i
$184$	−1.26795	+	2.19615i	−0.0934745	+	0.161903i
$185$	0.294229	−	1.43782i	0.0216321	−	0.105711i
$186$	−19.3923	−	5.19615i	−1.42191	−	0.381000i
$187$	−2.19615	+	8.19615i	−0.160599	+	0.599362i
$188$	3.00000	+	0.803848i	0.218797	+	0.0586266i
$189$	−21.9904	−	5.89230i	−1.59956	−	0.428602i
$190$	14.6603	+	3.00000i	1.06357	+	0.217643i
$191$	−16.0981	+	9.29423i	−1.16482	+	0.672507i	−0.952453	−	0.304684i	$-0.901449\pi$
$191$	−16.0981	+	9.29423i	−1.16482	+	0.672507i	−0.212362	+	0.977191i	$0.568116\pi$
$192$	−12.0000	−	6.92820i	−0.866025	−	0.500000i
$193$	13.6603	−	3.66025i	0.983287	−	0.263471i	0.268858	−	0.963180i	$-0.413354\pi$
$193$	13.6603	−	3.66025i	0.983287	−	0.263471i	0.714428	+	0.699709i	$0.246687\pi$
$194$	8.66025	−	5.00000i	0.621770	−	0.358979i
$195$	−2.19615	−	6.58846i	−0.157270	−	0.471809i
$196$	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	$0.456648\pi$
$198$	−2.19615	−	8.19615i	−0.156074	−	0.582475i
$199$		−	4.19615i		−	0.297457i	−0.988878	−	0.148729i	$-0.952482\pi$
$199$		−	4.19615i		−	0.297457i	0.988878	−	0.148729i	$-0.0475181\pi$
$200$	−13.1244	+	5.26795i	−0.928032	+	0.372500i
$201$	3.40192	−	12.6962i	0.239953	−	0.895518i
$202$	−2.73205	−	0.732051i	−0.192226	−	0.0515069i
$203$	−13.5263	+	3.62436i	−0.949359	+	0.254380i
$204$	−3.80385	−	14.1962i	−0.266323	−	0.993929i
$205$	−0.866025	−	14.4282i	−0.0604858	−	1.00771i
$206$	11.3923	−	19.7321i	0.793739	−	1.37480i
$207$	1.90192	−	1.90192i	0.132193	−	0.132193i
$208$	−1.85641	−	6.92820i	−0.128719	−	0.480384i
$209$	4.73205	+	8.19615i	0.327323	+	0.566940i
$210$	−20.0263	+	13.2224i	−1.38194	+	0.912434i
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$	10.3923	−	10.3923i	0.713746	−	0.713746i
$213$	−18.0000	−	10.3923i	−1.23334	−	0.712069i
$214$			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
$222$	−0.803848	+	1.39230i	−0.0539507	+	0.0934454i
$223$	4.42820	−	16.5263i	0.296534	−	1.10668i	−0.643457	−	0.765483i	$-0.722500\pi$
$223$	4.42820	−	16.5263i	0.296534	−	1.10668i	0.939991	−	0.341199i	$-0.110833\pi$
$224$	−21.4641	+	12.3923i	−1.43413	+	0.827996i
$225$	14.8923	−	1.79423i	0.992820	−	0.119615i
$226$	−2.19615	−	1.26795i	−0.146086	−	0.0843427i
$227$	−10.0981	−	2.70577i	−0.670233	−	0.179588i	−0.0923731	−	0.995724i	$-0.529445\pi$
$227$	−10.0981	−	2.70577i	−0.670233	−	0.179588i	−0.577860	+	0.816136i	$0.696112\pi$
$228$	−14.1962	−	8.19615i	−0.940163	−	0.542803i
$229$	5.76795	−	9.99038i	0.381157	−	0.660183i	−0.610071	−	0.792347i	$-0.708859\pi$
$229$	5.76795	−	9.99038i	0.381157	−	0.660183i	0.991228	+	0.132164i	$0.0421925\pi$
$230$	−0.169873	−	2.83013i	−0.0112011	−	0.186613i
$231$	−14.6603	−	3.92820i	−0.964574	−	0.258457i
$232$	8.73205	+	2.33975i	0.573287	+	0.153612i
$233$	−18.1244	+	18.1244i	−1.18737	+	1.18737i	−0.209573	+	0.977793i	$0.567207\pi$
$233$	−18.1244	+	18.1244i	−1.18737	+	1.18737i	−0.977793	+	0.209573i	$0.932793\pi$
$234$			7.60770i			0.497331i
$235$	−3.29423	+	1.09808i	−0.214892	+	0.0716306i
$236$	1.80385	−	3.12436i	0.117420	−	0.203378i
$237$		−	3.80385i		−	0.247086i
$238$	−25.3923	−	6.80385i	−1.64594	−	0.441028i
$239$	9.46410	−	16.3923i	0.612182	−	1.06033i	−0.378690	−	0.925524i	$-0.623625\pi$
$239$	9.46410	−	16.3923i	0.612182	−	1.06033i	0.990872	−	0.134807i	$-0.0430413\pi$
$240$	15.4641	−	0.928203i	0.998203	−	0.0599153i
$241$	9.40192	+	16.2846i	0.605631	+	1.04898i	0.991951	+	0.126619i	$0.0404126\pi$
$241$	9.40192	+	16.2846i	0.605631	+	1.04898i	−0.386320	+	0.922365i	$0.626254\pi$
$242$	2.56218	+	9.56218i	0.164703	+	0.614680i
$243$	−7.79423	−	13.5000i	−0.500000	−	0.866025i
$244$	14.6603	+	25.3923i	0.938527	+	1.62558i
$245$	1.63397	+	27.2224i	0.104391	+	1.73918i
$246$	−4.09808	+	15.2942i	−0.261284	+	0.975124i
$247$	−2.19615	−	8.19615i	−0.139738	−	0.521509i
$248$	22.3923	−	6.00000i	1.42191	−	0.381000i
$249$	−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	$0.183068\pi$
$252$	25.3923	−	6.80385i	1.59956	−	0.428602i
$253$	1.26795	−	1.26795i	0.0797153	−	0.0797153i
$254$			11.8038i			0.740639i
$255$	12.2942	+	10.9019i	0.769894	+	0.682705i
$256$	16.0000			1.00000
$257$	−15.7583	+	4.22243i	−0.982978	+	0.263388i	−0.714298	−	0.699842i	$-0.753254\pi$
$257$	−15.7583	+	4.22243i	−0.982978	+	0.263388i	−0.268680	+	0.963230i	$0.586587\pi$
$258$			22.3923i			1.39408i
$259$	1.43782	+	2.49038i	0.0893419	+	0.154745i
$260$	6.00000	+	5.32051i	0.372104	+	0.329964i
$261$	−8.30385	−	4.79423i	−0.513995	−	0.296755i
$262$	−2.85641	−	10.6603i	−0.176469	−	0.658593i
$263$	13.5622	+	3.63397i	0.836280	+	0.224080i	0.651451	−	0.758690i	$-0.274160\pi$
$263$	13.5622	+	3.63397i	0.836280	+	0.224080i	0.184828	+	0.982771i	$0.440827\pi$
$264$	6.92820	+	6.92820i	0.426401	+	0.426401i
$265$	−3.29423	+	16.0981i	−0.202363	+	0.988897i
$266$	−25.3923	+	14.6603i	−1.55690	+	0.898878i
$267$	2.30385	−	3.99038i	0.140993	−	0.244207i
$268$	3.92820	+	14.6603i	0.239953	+	0.895518i
$269$		−	1.00000i		−	0.0609711i	−0.999535	−	0.0304855i	$-0.990295\pi$
$269$		−	1.00000i		−	0.0609711i	0.999535	−	0.0304855i	$-0.00970535\pi$
$270$	−16.0981	−	3.29423i	−0.979698	−	0.200480i
$271$	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
$273$	11.7846	+	6.80385i	0.713237	+	0.411788i
$274$	9.46410	+	16.3923i	0.571747	+	0.990295i
$275$	9.92820	−	1.19615i	0.598693	−	0.0721307i
$276$	−0.803848	+	3.00000i	−0.0483859	+	0.180579i
$277$	−2.36603	+	8.83013i	−0.142161	+	0.530551i	0.857705	+	0.514143i	$0.171890\pi$
$277$	−2.36603	+	8.83013i	−0.142161	+	0.530551i	−0.999865	+	0.0164083i	$0.994777\pi$
$278$	−2.53590	−	9.46410i	−0.152093	−	0.567619i
$279$	−24.5885			−1.47207
$280$	12.3923	−	24.7846i	0.740582	−	1.48116i
$281$	−1.79423	+	1.03590i	−0.107035	+	0.0617965i	−0.552562	−	0.833472i	$-0.686350\pi$
$281$	−1.79423	+	1.03590i	−0.107035	+	0.0617965i	0.445527	+	0.895268i	$0.353016\pi$
$282$	3.80385			0.226516
$283$	1.20577	+	4.50000i	0.0716757	+	0.267497i	0.992459	−	0.122577i	$-0.0391159\pi$
$283$	1.20577	+	4.50000i	0.0716757	+	0.267497i	−0.920783	+	0.390074i	$0.872449\pi$
$284$	24.0000			1.42414
$285$	18.2942	−	1.09808i	1.08366	−	0.0650444i
$286$			5.07180i			0.299902i
$287$	20.0263	+	20.0263i	1.18211	+	1.18211i
$288$	−16.3923	−	4.39230i	−0.965926	−	0.258819i
$289$			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
$293$	−1.09808	+	0.294229i	−0.0641503	+	0.0171890i	−0.290751	−	0.956799i	$-0.593905\pi$
$293$	−1.09808	+	0.294229i	−0.0641503	+	0.0171890i	0.226601	+	0.973988i	$0.427239\pi$
$294$	7.73205	−	28.8564i	0.450942	−	1.68294i
$295$	0.241670	+	4.02628i	0.0140706	+	0.234419i
$296$		−	1.85641i		−	0.107901i
$297$	−5.19615	−	9.00000i	−0.301511	−	0.522233i
$298$	9.56218	−	2.56218i	0.553922	−	0.148423i
$299$	−1.39230	+	0.803848i	−0.0805191	+	0.0464877i
$300$	−13.8564	+	10.3923i	−0.800000	+	0.600000i
$301$	34.6865	+	20.0263i	1.99930	+	1.15430i
$302$	−21.8564	−	5.85641i	−1.25769	−	0.336998i
$303$	−3.46410			−0.199007
$304$	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	0.166183	−	0.986095i	$-0.446856\pi$
$307$	−14.3660	−	14.3660i	−0.819912	−	0.819912i	−0.986095	+	0.166183i	$0.946856\pi$
$308$	16.9282	−	4.53590i	0.964574	−	0.258457i
$309$	7.22243	−	26.9545i	0.410870	−	1.53339i
$310$	−17.1962	+	19.3923i	−0.976676	+	1.10141i
$311$	12.2942	+	7.09808i	0.697142	+	0.402495i	0.806282	−	0.591531i	$-0.201476\pi$
$311$	12.2942	+	7.09808i	0.697142	+	0.402495i	−0.109140	+	0.994026i	$0.534810\pi$
$312$	−4.39230	−	7.60770i	−0.248665	−	0.430701i
$313$	−3.87564	+	14.4641i	−0.219064	+	0.817559i	0.765632	+	0.643279i	$0.222427\pi$
$313$	−3.87564	+	14.4641i	−0.219064	+	0.817559i	−0.984696	+	0.174280i	$0.944240\pi$
$314$	9.00000	−	15.5885i	0.507899	−	0.879708i
$315$	−19.5000	+	21.9904i	−1.09870	+	1.23902i
$316$	2.19615	+	3.80385i	0.123543	+	0.213983i
$317$	13.6603	+	3.66025i	0.767236	+	0.205580i	0.621150	−	0.783692i	$-0.286666\pi$
$317$	13.6603	+	3.66025i	0.767236	+	0.205580i	0.146086	+	0.989272i	$0.453332\pi$
$318$	9.00000	−	15.5885i	0.504695	−	0.874157i
$319$	−5.53590	−	3.19615i	−0.309951	−	0.178950i
$320$	−14.9282	+	9.85641i	−0.834512	+	0.550990i
$321$	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
$327$	−7.50000	+	12.9904i	−0.414751	+	0.718370i
$328$	−4.73205	−	17.6603i	−0.261284	−	0.975124i
$329$	3.40192	−	5.89230i	0.187554	−	0.324853i
$330$	−10.7321	−	2.19615i	−0.590780	−	0.120894i
$331$	−0.509619	+	0.294229i	−0.0280112	+	0.0161723i	−0.513940	−	0.857826i	$-0.671815\pi$
$331$	−0.509619	+	0.294229i	−0.0280112	+	0.0161723i	0.485929	+	0.873998i	$0.338481\pi$
$332$	22.6603	+	6.07180i	1.24364	+	0.333233i
$333$	−0.509619	+	1.90192i	−0.0279269	+	0.104225i
$334$	−13.0981	+	22.6865i	−0.716695	+	1.24135i
$335$	−12.6962	−	11.2583i	−0.693665	−	0.615108i
$336$	−21.4641	+	21.4641i	−1.17096	+	1.17096i
$337$	0.0717968	+	0.267949i	0.00391102	+	0.0145961i	0.967854	−	0.251514i	$-0.0809283\pi$
$337$	0.0717968	+	0.267949i	0.00391102	+	0.0145961i	−0.963943	+	0.266110i	$0.914262\pi$
$338$	−3.58142	+	13.3660i	−0.194803	+	0.727016i
$339$	−3.00000	−	0.803848i	−0.162938	−	0.0436590i
$340$	−18.5885	−	3.80385i	−1.00810	−	0.206293i
$341$	−16.3923			−0.887693
$342$	−19.3923	−	5.19615i	−1.04862	−	0.280976i
$343$	−16.0981	−	16.0981i	−0.869214	−	0.869214i
$344$	−12.9282	−	22.3923i	−0.697042	−	1.20731i
$345$	−1.09808	−	3.29423i	−0.0591184	−	0.177355i
$346$	2.00000	+	3.46410i	0.107521	+	0.186231i
$347$	−1.90192	−	7.09808i	−0.102101	−	0.381045i	0.895899	−	0.444257i	$-0.146532\pi$
$347$	−1.90192	−	7.09808i	−0.102101	−	0.381045i	−0.998000	+	0.0632121i	$0.979866\pi$
$348$	11.0718			0.593511
$349$	−18.2321	−	31.5788i	−0.975939	−	1.69038i	−0.676800	−	0.736167i	$-0.736634\pi$
$349$	−18.2321	−	31.5788i	−0.975939	−	1.69038i	−0.299139	−	0.954209i	$-0.596700\pi$
$350$	3.70577	+	30.7583i	0.198082	+	1.64410i
$351$	2.41154	+	9.00000i	0.128719	+	0.480384i
$352$	−10.9282	−	2.92820i	−0.582475	−	0.156074i
$353$	12.9282	+	3.46410i	0.688099	+	0.184376i	0.585894	−	0.810388i	$-0.300744\pi$
$353$	12.9282	+	3.46410i	0.688099	+	0.184376i	0.102205	+	0.994763i	$0.467410\pi$
$354$	1.14359	−	4.26795i	0.0607813	−	0.226839i
$355$	−22.3923	+	14.7846i	−1.18846	+	0.784686i
$356$			5.32051i			0.281986i
$357$	−32.1962			−1.70400
$358$	−6.39230	−	6.39230i	−0.337844	−	0.337844i
$359$	2.19615			0.115908			0.0579542	−	0.998319i	$-0.481542\pi$
$359$	2.19615			0.115908			0.0579542	+	0.998319i	$0.481542\pi$
$360$	18.0000	−	6.00000i	0.948683	−	0.316228i
$361$	3.39230			0.178542
$362$	3.00000	+	3.00000i	0.157676	+	0.157676i
$363$	6.06218	+	10.5000i	0.318182	+	0.551107i
$364$	−15.7128			−0.823575
$365$	6.46410	−	31.5885i	0.338347	−	1.65342i
$366$	25.3923	+	25.3923i	1.32728	+	1.32728i
$367$	−9.56218	−	2.56218i	−0.499142	−	0.133745i	0.000459976	−	1.00000i	$-0.499854\pi$
$367$	−9.56218	−	2.56218i	−0.499142	−	0.133745i	−0.499602	+	0.866255i	$0.666520\pi$
$368$	−0.928203	−	3.46410i	−0.0483859	−	0.180579i
$369$			19.3923i			1.00952i
$370$	1.14359	+	1.73205i	0.0594526	+	0.0900450i
$371$	−16.0981	−	27.8827i	−0.835770	−	1.44760i
$372$	24.5885	−	14.1962i	1.27485	−	0.736036i
$373$	0.973721	+	3.63397i	0.0504173	+	0.188160i	0.986542	−	0.163508i	$-0.0522811\pi$
$373$	0.973721	+	3.63397i	0.0504173	+	0.188160i	−0.936125	+	0.351669i	$0.885614\pi$
$374$	−6.00000	−	10.3923i	−0.310253	−	0.537373i
$375$	6.52628	−	18.2321i	0.337016	−	0.941499i
$376$	−3.80385	+	2.19615i	−0.196168	+	0.113258i
$377$	4.05256	+	4.05256i	0.208717	+	0.208717i
$378$	27.8827	−	16.0981i	1.43413	−	0.827996i
$379$	33.1244			1.70148			0.850742	−	0.525584i	$-0.176153\pi$
$379$	33.1244			1.70148			0.850742	+	0.525584i	$0.176153\pi$
$380$	−17.6603	+	11.6603i	−0.905952	+	0.598158i
$381$	3.74167	+	13.9641i	0.191692	+	0.715403i
$382$	6.80385	−	25.3923i	0.348115	−	1.29918i
$383$	7.43782	+	27.7583i	0.380055	+	1.41838i	0.845816	+	0.533474i	$0.179114\pi$
$383$	7.43782	+	27.7583i	0.380055	+	1.41838i	−0.465761	+	0.884910i	$0.654220\pi$
$384$	18.9282	−	5.07180i	0.965926	−	0.258819i
$385$	−13.0000	+	14.6603i	−0.662541	+	0.747156i
$386$	−10.0000	+	17.3205i	−0.508987	+	0.881591i
$387$	7.09808	+	26.4904i	0.360815	+	1.34658i
$388$	−3.66025	+	13.6603i	−0.185821	+	0.693494i
$389$	−15.0622	+	8.69615i	−0.763683	+	0.440912i	−0.830616	−	0.556845i	$-0.812012\pi$
$389$	−15.0622	+	8.69615i	−0.763683	+	0.440912i	0.0669337	+	0.997757i	$0.478678\pi$
$390$	8.78461	+	4.39230i	0.444826	+	0.222413i
$391$	1.90192	−	3.29423i	0.0961844	−	0.166596i
$392$	8.92820	+	33.3205i	0.450942	+	1.68294i
$393$	−6.75833	−	11.7058i	−0.340913	−	0.590478i
$394$		−	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	0.726991	−	0.686647i	$-0.240918\pi$
$397$	0.803848	+	0.803848i	0.0403440	+	0.0403440i	−0.686647	+	0.726991i	$0.740918\pi$
$398$	4.19615	+	4.19615i	0.210334	+	0.210334i
$399$	−25.3923	+	25.3923i	−1.27121	+	1.27121i
$400$	7.85641	−	18.3923i	0.392820	−	0.919615i
$401$	−31.3923	−	18.1244i	−1.56766	−	0.905087i	−0.996442	−	0.0842869i	$-0.973139\pi$
$401$	−31.3923	−	18.1244i	−1.56766	−	0.905087i	−0.571215	−	0.820800i	$-0.693528\pi$
$402$	9.29423	+	16.0981i	0.463554	+	0.802899i
$403$	14.1962	+	3.80385i	0.707161	+	0.189483i
$404$	3.46410	−	2.00000i	0.172345	−	0.0995037i
$405$	−20.0885	+	1.20577i	−0.998203	+	0.0599153i
$406$	9.90192	−	17.1506i	0.491424	−	0.851172i
$407$	−0.339746	+	1.26795i	−0.0168406	+	0.0628499i
$408$	18.0000	+	10.3923i	0.891133	+	0.514496i
$409$	−5.19615	−	3.00000i	−0.256933	−	0.148340i	0.366002	−	0.930614i	$-0.380726\pi$
$409$	−5.19615	−	3.00000i	−0.256933	−	0.148340i	−0.622935	+	0.782274i	$0.714060\pi$
$410$	15.2942	+	13.5622i	0.755328	+	0.669788i
$411$	16.3923	+	16.3923i	0.808573	+	0.808573i
$412$	8.33975	+	31.1244i	0.410870	+	1.53339i
$413$	−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
$417$	−6.00000	−	10.3923i	−0.293821	−	0.508913i
$418$	−12.9282	−	3.46410i	−0.632339	−	0.169435i
$419$	10.7321	+	6.19615i	0.524295	+	0.302702i	0.738690	−	0.674045i	$-0.235445\pi$
$419$	10.7321	+	6.19615i	0.524295	+	0.302702i	−0.214395	+	0.976747i	$0.568778\pi$
$420$	6.80385	−	33.2487i	0.331994	−	1.62237i
$421$	−4.60770	+	2.66025i	−0.224565	+	0.129653i	−0.608062	−	0.793889i	$-0.708053\pi$
$421$	−4.60770	+	2.66025i	−0.224565	+	0.129653i	0.383497	+	0.923542i	$0.374720\pi$
$422$		0			0
$423$	4.50000	−	1.20577i	0.218797	−	0.0586266i
$424$			20.7846i			1.00939i
$425$	19.6865	−	7.90192i	0.954937	−	0.383300i
$426$	28.3923	−	7.60770i	1.37561	−	0.368594i
$427$	62.0429	−	16.6244i	3.00247	−	0.804509i
$428$	−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	$-0.821772\pi$
$431$		−	22.0526i		−	1.06223i	0.847298	−	0.531117i	$-0.178228\pi$
$432$	−20.7846			−1.00000
$433$	−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
$435$	−10.3301	+	6.82051i	−0.495292	+	0.327018i
$436$		−	17.3205i		−	0.829502i
$437$	−1.09808	−	4.09808i	−0.0525281	−	0.196038i
$438$	−17.6603	+	30.5885i	−0.843840	+	1.46157i
$439$	−16.2679	+	9.39230i	−0.776427	+	0.448270i	−0.835162	−	0.550003i	$-0.814626\pi$
$439$	−16.2679	+	9.39230i	−0.776427	+	0.448270i	0.0587356	+	0.998274i	$0.481293\pi$
$440$	12.0000	−	4.00000i	0.572078	−	0.190693i
$441$		−	36.5885i		−	1.74231i
$442$	2.78461	+	10.3923i	0.132450	+	0.494312i
$443$	9.99038	−	37.2846i	0.474657	−	1.77145i	−0.148039	−	0.988982i	$-0.547296\pi$
$443$	9.99038	−	37.2846i	0.474657	−	1.77145i	0.622696	−	0.782464i	$-0.286037\pi$
$444$	−0.588457	−	2.19615i	−0.0279269	−	0.104225i
$445$	−3.27757	−	4.96410i	−0.155372	−	0.235321i
$446$	12.0981	+	20.9545i	0.572861	+	0.992224i
$447$	10.5000	−	6.06218i	0.496633	−	0.286731i
$448$	9.07180	−	33.8564i	0.428602	−	1.59956i
$449$	32.7846			1.54720			0.773601	−	0.633673i	$-0.218454\pi$
$449$	32.7846			1.54720			0.773601	+	0.633673i	$0.218454\pi$
$450$	−13.0981	+	16.6865i	−0.617449	+	0.786611i
$451$			12.9282i			0.608765i
$452$	3.46410	−	0.928203i	0.162938	−	0.0436590i
$453$	−27.7128			−1.30206
$454$	12.8038	−	7.39230i	0.600914	−	0.346938i
$455$	14.6603	−	9.67949i	0.687283	−	0.453782i
$456$	22.3923	−	6.00000i	1.04862	−	0.280976i
$457$	9.83013	+	2.63397i	0.459834	+	0.123212i	0.481297	−	0.876558i	$-0.340166\pi$
$457$	9.83013	+	2.63397i	0.459834	+	0.123212i	−0.0214632	+	0.999770i	$0.506832\pi$
$458$	4.22243	+	15.7583i	0.197301	+	0.736338i
$459$	−15.5885	−	15.5885i	−0.727607	−	0.727607i
$460$	3.00000	+	2.66025i	0.139876	+	0.124035i
$461$	−6.79423	−	11.7679i	−0.316439	−	0.548088i	0.663304	−	0.748350i	$-0.269154\pi$
$461$	−6.79423	−	11.7679i	−0.316439	−	0.548088i	−0.979742	+	0.200262i	$0.935821\pi$
$462$	18.5885	−	10.7321i	0.864813	−	0.499300i
$463$	6.56218	−	1.75833i	0.304970	−	0.0817165i	−0.103089	−	0.994672i	$-0.532873\pi$
$463$	6.56218	−	1.75833i	0.304970	−	0.0817165i	0.408059	+	0.912956i	$0.366206\pi$
$464$	−11.0718	+	6.39230i	−0.513995	+	0.296755i
$465$	−14.1962	+	28.3923i	−0.658331	+	1.31666i
$466$		−	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
$472$	1.32051	+	4.92820i	0.0607813	+	0.226839i
$473$	4.73205	+	17.6603i	0.217580	+	0.812019i
$474$	3.80385	+	3.80385i	0.174717	+	0.174717i
$475$	9.29423	−	21.7583i	0.426448	−	0.998341i
$476$	32.1962	−	18.5885i	1.47571	−	0.852001i
$477$	5.70577	−	21.2942i	0.261249	−	0.974996i
$478$	6.92820	+	25.8564i	0.316889	+	1.18264i
$479$	−10.5622	−	18.2942i	−0.482598	−	0.835885i	0.517202	−	0.855863i	$-0.326974\pi$
$479$	−10.5622	−	18.2942i	−0.482598	−	0.835885i	−0.999800	+	0.0199786i	$0.993640\pi$
$480$	−14.5359	+	16.3923i	−0.663470	+	0.748203i
$481$	0.588457	−	1.01924i	0.0268313	−	0.0464732i
$482$	−25.6865	−	6.88269i	−1.16999	−	0.313498i
$483$	5.89230	+	3.40192i	0.268109	+	0.154793i
$484$	−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	$0.215332\pi$
$488$	−40.0526	−	10.7321i	−1.81309	−	0.485817i
$489$	4.09808	+	15.2942i	0.185321	+	0.691629i
$490$	−28.8564	−	25.5885i	−1.30360	−	1.15597i
$491$	−12.3923	+	21.4641i	−0.559257	+	0.968661i	0.438302	+	0.898828i	$0.355580\pi$
$491$	−12.3923	+	21.4641i	−0.559257	+	0.968661i	−0.997559	+	0.0698335i	$0.977753\pi$
$492$	−11.1962	−	19.3923i	−0.504762	−	0.874273i
$493$	−13.0981	−	3.50962i	−0.589908	−	0.158065i
$494$	10.3923	+	6.00000i	0.467572	+	0.269953i
$495$	−13.3923	+	0.803848i	−0.601939	+	0.0361303i
$496$	−16.3923	+	28.3923i	−0.736036	+	1.27485i
$497$	13.6077	−	50.7846i	0.610389	−	2.27800i
$498$	28.7321			1.28751
$499$	−13.3923	+	23.1962i	−0.599522	+	1.03840i	0.393370	+	0.919380i	$0.371309\pi$
$499$	−13.3923	+	23.1962i	−0.599522	+	1.03840i	−0.992892	+	0.119022i	$0.962024\pi$
$500$	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	−0.612946	−	0.790125i	$-0.710016\pi$
$503$	3.97372	−	3.97372i	0.177179	−	0.177179i	0.790125	+	0.612946i	$0.210016\pi$
$504$	−18.5885	+	32.1962i	−0.827996	+	1.43413i
$505$	−2.00000	+	4.00000i	−0.0889988	+	0.177998i
$506$			2.53590i			0.112734i
$507$			16.9474i			0.752662i
$508$	−11.8038	−	11.8038i	−0.523711	−	0.523711i
$509$	−6.57180	−	3.79423i	−0.291290	−	0.168176i	0.347234	−	0.937779i	$-0.387121\pi$
$509$	−6.57180	−	3.79423i	−0.291290	−	0.168176i	−0.638523	+	0.769602i	$0.720454\pi$
$510$	−23.1962	+	1.39230i	−1.02714	+	0.0616523i
$511$	31.5885	+	54.7128i	1.39739	+	2.42035i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−24.5885			−1.08561
$514$	11.5359	−	19.9808i	0.508827	−	0.881314i
$515$	−26.9545	−	23.9019i	−1.18776	−	1.05324i
$516$	−22.3923	−	22.3923i	−0.985766	−	0.985766i
$517$	3.00000	−	0.803848i	0.131940	−	0.0353532i
$518$	−3.92820	−	1.05256i	−0.172595	−	0.0462468i
$519$	3.46410	+	3.46410i	0.152057	+	0.152057i
$520$	−11.3205	+	0.679492i	−0.496437	+	0.0297977i
$521$			14.6603i			0.642277i	0.947032	+	0.321139i	$0.104066\pi$
$521$			14.6603i			0.642277i	−0.947032	+	0.321139i	$0.895934\pi$
$522$	13.0981	−	3.50962i	0.573287	−	0.153612i
$523$	1.56218	−	1.56218i	0.0683093	−	0.0683093i	−0.672127	−	0.740436i	$-0.734619\pi$
$523$	1.56218	−	1.56218i	0.0683093	−	0.0683093i	0.740436	+	0.672127i	$0.234619\pi$
$524$	13.5167	+	7.80385i	0.590478	+	0.340913i
$525$	14.1340	+	35.2128i	0.616857	+	1.53681i
$526$	−17.1962	+	9.92820i	−0.749788	+	0.432890i
$527$	−33.5885	+	9.00000i	−1.46314	+	0.392046i
$528$	−13.8564			−0.603023
$529$	19.2224	−	11.0981i	0.835758	−	0.482525i
$530$	−12.8038	−	19.3923i	−0.556164	−	0.842348i
$531$		−	5.41154i		−	0.234841i
$532$	10.7321	−	40.0526i	0.465293	−	1.73650i
$533$	3.00000	−	11.1962i	0.129944	−	0.484959i
$534$	1.68653	+	6.29423i	0.0729834	+	0.272378i
$535$	18.8923	+	3.86603i	0.816786	+	0.167143i
$536$	−18.5885	−	10.7321i	−0.802899	−	0.463554i
$537$	−9.58846	−	5.53590i	−0.413772	−	0.238892i
$538$	1.00000	+	1.00000i	0.0431131	+	0.0431131i
$539$		−	24.3923i		−	1.05065i
$540$	19.3923	−	12.8038i	0.834512	−	0.550990i
$541$			12.4641i			0.535874i	0.963436	+	0.267937i	$0.0863418\pi$
$541$			12.4641i			0.535874i	−0.963436	+	0.267937i	$0.913658\pi$
$542$	−4.58846	+	4.58846i	−0.197091	+	0.197091i
$543$	4.50000	+	2.59808i	0.193113	+	0.111494i
$544$	−24.0000			−1.02899
$545$	10.6699	+	16.1603i	0.457047	+	0.692229i
$546$	−18.5885	+	4.98076i	−0.795513	+	0.213157i
$547$	7.11474	−	26.5526i	0.304204	−	1.13531i	−0.629424	−	0.777062i	$-0.716709\pi$
$547$	7.11474	−	26.5526i	0.304204	−	1.13531i	0.933628	−	0.358243i	$-0.116624\pi$
$548$	−25.8564	−	6.92820i	−1.10453	−	0.295958i
$549$	38.0885	+	21.9904i	1.62558	+	0.938527i
$550$	−8.73205	+	11.1244i	−0.372336	+	0.474344i
$551$	−13.0981	+	7.56218i	−0.557997	+	0.322160i
$552$	−2.19615	−	3.80385i	−0.0934745	−	0.161903i
$553$	9.29423	−	2.49038i	0.395231	−	0.105902i
$554$	−6.46410	−	11.1962i	−0.274633	−	0.475679i
$555$	1.90192	+	1.68653i	0.0807322	+	0.0715894i
$556$	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
$562$	0.758330	−	2.83013i	0.0319882	−	0.119382i
$563$	−32.0885	+	8.59808i	−1.35237	+	0.362366i	−0.861008	−	0.508591i	$-0.830166\pi$
$563$	−32.0885	+	8.59808i	−1.35237	+	0.362366i	−0.491359	+	0.870957i	$0.663500\pi$
$564$	−3.80385	+	3.80385i	−0.160171	+	0.160171i
$565$	−2.66025	+	3.00000i	−0.111918	+	0.126211i
$566$	−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	$-0.149739\pi$
$569$	1.26795	+	2.19615i	0.0531552	+	0.0920675i	−0.838223	+	0.545327i	$0.816406\pi$
$570$	−17.1962	+	19.3923i	−0.720268	+	0.812254i
$571$	−3.00000	−	1.73205i	−0.125546	−	0.0724841i	0.435912	−	0.899989i	$-0.356426\pi$
$571$	−3.00000	−	1.73205i	−0.125546	−	0.0724841i	−0.561458	+	0.827505i	$0.689759\pi$
$572$	−5.07180	−	5.07180i	−0.212062	−	0.212062i
$573$		−	32.1962i		−	1.34501i
$574$	−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
$582$			17.3205i			0.717958i
$583$	3.80385	−	14.1962i	0.157539	−	0.587945i
$584$		−	40.7846i		−	1.68768i
$585$	11.7846	+	2.41154i	0.487234	+	0.0997050i
$586$	0.803848	−	1.39230i	0.0332066	−	0.0575156i
$587$	−32.6506	−	8.74871i	−1.34764	−	0.361098i	−0.488374	−	0.872634i	$-0.662410\pi$
$587$	−32.6506	−	8.74871i	−1.34764	−	0.361098i	−0.859262	+	0.511536i	$0.829077\pi$
$588$	21.1244	+	36.5885i	0.871154	+	1.50888i
$589$	−19.3923	+	33.5885i	−0.799046	+	1.38399i
$590$	−4.26795	−	3.78461i	−0.175709	−	0.155810i
$591$	−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	−0.338825	−	0.940849i	$-0.610029\pi$
$593$	14.6603	−	14.6603i	0.602024	−	0.602024i	0.940849	+	0.338825i	$0.110029\pi$
$594$	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
$597$	6.29423	+	3.63397i	0.257606	+	0.148729i
$598$	0.588457	−	2.19615i	0.0240638	−	0.0898074i
$599$	−15.2942	+	26.4904i	−0.624905	+	1.08237i	0.363654	+	0.931534i	$0.381529\pi$
$599$	−15.2942	+	26.4904i	−0.624905	+	1.08237i	−0.988559	+	0.150834i	$0.951804\pi$
$600$	3.46410	−	24.2487i	0.141421	−	0.989949i
$601$	−21.1962	−	36.7128i	−0.864609	−	1.49755i	−0.867435	−	0.497551i	$-0.834233\pi$
$601$	−21.1962	−	36.7128i	−0.864609	−	1.49755i	0.00282571	−	0.999996i	$-0.499101\pi$
$602$	−54.7128	+	14.6603i	−2.22993	+	0.597507i
$603$	16.0981	+	16.0981i	0.655564	+	0.655564i
$604$	27.7128	−	16.0000i	1.12762	−	0.651031i
$605$	15.6244	−	0.937822i	0.635220	−	0.0381279i
$606$	3.46410	−	3.46410i	0.140720	−	0.140720i
$607$	7.57180	+	28.2583i	0.307330	+	1.14697i	0.930921	+	0.365220i	$0.119006\pi$
$607$	7.57180	+	28.2583i	0.307330	+	1.14697i	−0.623592	+	0.781750i	$0.714327\pi$
$608$	−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
$612$	24.5885	+	6.58846i	0.993929	+	0.266323i
$613$	−23.7846	+	23.7846i	−0.960651	+	0.960651i	−0.999255	−	0.0386033i	$-0.987709\pi$
$613$	−23.7846	+	23.7846i	−0.960651	+	0.960651i	0.0386033	+	0.999255i	$0.487709\pi$
$614$	28.7321			1.15953
$615$	22.3923	+	11.1962i	0.902945	+	0.451472i
$616$	−12.3923	+	21.4641i	−0.499300	+	0.864813i
$617$	28.0526	−	7.51666i	1.12935	−	0.302609i	0.354691	−	0.934984i	$-0.384586\pi$
$617$	28.0526	−	7.51666i	1.12935	−	0.302609i	0.774663	+	0.632374i	$0.217920\pi$
$618$	19.7321	+	34.1769i	0.793739	+	1.37480i
$619$	1.90192	+	3.29423i	0.0764448	+	0.132406i	0.901714	−	0.432334i	$-0.142310\pi$
$619$	1.90192	+	3.29423i	0.0764448	+	0.132406i	−0.825269	+	0.564740i	$0.808976\pi$
$620$	−2.19615	−	36.5885i	−0.0881996	−	1.46943i
$621$	1.20577	+	4.50000i	0.0483859	+	0.180579i
$622$	−19.3923	+	5.19615i	−0.777561	+	0.208347i
$623$	11.2583	+	3.01666i	0.451055	+	0.120860i
$624$	12.0000	+	3.21539i	0.480384	+	0.128719i
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	−10.5885	−	18.3397i	−0.423200	−	0.733004i
$627$	−16.3923			−0.654646
$628$	6.58846	+	24.5885i	0.262908	+	0.981186i
$629$			2.78461i			0.111030i
$630$	−2.49038	−	41.4904i	−0.0992192	−	1.65302i
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$	−6.00000	−	1.60770i	−0.238667	−	0.0639507i
$633$		0			0
$634$	−17.3205	+	10.0000i	−0.687885	+	0.397151i
$635$	18.2846	+	3.74167i	0.725603	+	0.148484i
$636$	6.58846	+	24.5885i	0.261249	+	0.974996i
$637$	−5.66025	+	21.1244i	−0.224267	+	0.836977i
$638$	8.73205	−	2.33975i	0.345705	−	0.0926314i
$639$	31.1769	−	18.0000i	1.23334	−	0.712069i
$640$	5.07180	−	24.7846i	0.200480	−	0.979698i
$641$	−36.1865	+	20.8923i	−1.42928	+	0.825196i	−0.997064	−	0.0765727i	$-0.975602\pi$
$641$	−36.1865	+	20.8923i	−1.42928	+	0.825196i	−0.432218	+	0.901769i	$0.642269\pi$
$642$	−18.2942	−	10.5622i	−0.722016	−	0.416856i
$643$	−6.91154	−	25.7942i	−0.272565	−	1.01723i	−0.957456	−	0.288580i	$-0.906817\pi$
$643$	−6.91154	−	25.7942i	−0.272565	−	1.01723i	0.684891	−	0.728645i	$-0.259850\pi$
$644$	−7.85641			−0.309586
$645$	34.6865	+	7.09808i	1.36578	+	0.279486i
$646$	−28.3923			−1.11708
$647$	−19.6865	−	19.6865i	−0.773957	−	0.773957i	0.204838	−	0.978796i	$-0.434333\pi$
$647$	−19.6865	−	19.6865i	−0.773957	−	0.773957i	−0.978796	+	0.204838i	$0.934333\pi$
$648$	−24.5885	+	6.58846i	−0.965926	+	0.258819i
$649$		−	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
$653$	29.2224	−	7.83013i	1.14356	−	0.306417i	0.363180	−	0.931719i	$-0.381691\pi$
$653$	29.2224	−	7.83013i	1.14356	−	0.306417i	0.780382	+	0.625303i	$0.215024\pi$
$654$	−5.49038	−	20.4904i	−0.214691	−	0.801237i
$655$	−17.4186	+	1.04552i	−0.680600	+	0.0408517i
$656$	22.3923	+	12.9282i	0.874273	+	0.504762i
$657$	−11.1962	+	41.7846i	−0.436804	+	1.63017i
$658$	2.49038	+	9.29423i	0.0970852	+	0.362327i
$659$	−10.7321	+	6.19615i	−0.418061	+	0.241368i	−0.694248	−	0.719736i	$-0.744263\pi$
$659$	−10.7321	+	6.19615i	−0.418061	+	0.241368i	0.276186	+	0.961104i	$0.410929\pi$
$660$	12.9282	−	8.53590i	0.503230	−	0.332259i
$661$	6.00000	+	3.46410i	0.233373	+	0.134738i	0.612127	−	0.790759i	$-0.290314\pi$
$661$	6.00000	+	3.46410i	0.233373	+	0.134738i	−0.378754	+	0.925497i	$0.623647\pi$
$662$	0.215390	−	0.803848i	0.00837138	−	0.0312424i
$663$	6.58846	+	11.4115i	0.255874	+	0.443188i
$664$	−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
$668$	−9.58846	−	35.7846i	−0.370989	−	1.38455i
$669$	20.9545	+	20.9545i	0.810147	+	0.810147i
$670$	23.9545	−	1.43782i	0.925442	−	0.0555479i
$671$	25.3923	+	14.6603i	0.980259	+	0.565953i
$672$		−	42.9282i		−	1.65599i
$673$	−1.24871	+	4.66025i	−0.0481343	+	0.179640i	−0.985808	−	0.167878i	$-0.946309\pi$
$673$	−1.24871	+	4.66025i	−0.0481343	+	0.179640i	0.937674	+	0.347517i	$0.112975\pi$
$674$	−0.339746	−	0.196152i	−0.0130865	−	0.00755551i
$675$	−10.2058	+	23.8923i	−0.392820	+	0.919615i
$676$	−9.78461	−	16.9474i	−0.376331	−	0.651825i
$677$	39.3205	+	10.5359i	1.51121	+	0.404927i	0.916837	−	0.399262i	$-0.130734\pi$
$677$	39.3205	+	10.5359i	1.51121	+	0.404927i	0.594373	+	0.804189i	$0.297400\pi$
$678$	3.80385	−	2.19615i	0.146086	−	0.0843427i
$679$	26.8301	+	15.4904i	1.02965	+	0.594466i
$680$	22.3923	−	14.7846i	0.858706	−	0.566964i
$681$	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
$687$	9.99038	+	17.3038i	0.381157	+	0.660183i
$688$	35.3205	+	9.46410i	1.34658	+	0.360815i
$689$	−6.58846	+	11.4115i	−0.251000	+	0.434745i
$690$	4.39230	+	2.19615i	0.167212	+	0.0836061i
$691$	−40.4711	+	23.3660i	−1.53959	+	0.888885i	−0.540733	+	0.841194i	$0.681853\pi$
$691$	−40.4711	+	23.3660i	−1.53959	+	0.888885i	−0.998862	+	0.0476910i	$0.984814\pi$
$692$	−5.46410	−	1.46410i	−0.207714	−	0.0556568i
$693$	18.5885	−	18.5885i	0.706117	−	0.706117i
$694$	9.00000	+	5.19615i	0.341635	+	0.197243i
$695$	−15.4641	+	0.928203i	−0.586587	+	0.0352088i
$696$	−11.0718	+	11.0718i	−0.419675	+	0.419675i
$697$	7.09808	+	26.4904i	0.268859	+	1.00339i
$698$	49.8109	+	13.3468i	1.88537	+	0.505183i
$699$	−11.4904	−	42.8827i	−0.434606	−	1.62197i
$700$	−34.4641	−	27.0526i	−1.30262	−	1.02249i
$701$	−50.1769			−1.89516			−0.947578	−	0.319525i	$-0.896477\pi$
$701$	−50.1769			−1.89516			−0.947578	+	0.319525i	$0.896477\pi$
$702$	−11.4115	−	6.58846i	−0.430701	−	0.248665i
$703$	2.19615	+	2.19615i	0.0828295	+	0.0828295i
$704$	13.8564	−	8.00000i	0.522233	−	0.301511i
$705$	1.20577	−	5.89230i	0.0454120	−	0.221917i
$706$	−16.3923	+	9.46410i	−0.616933	+	0.356186i
$707$	−2.26795	−	8.46410i	−0.0852950	−	0.318325i
$708$	3.12436	+	5.41154i	0.117420	+	0.203378i
$709$	9.57180	+	16.5788i	0.359476	+	0.622631i	0.987873	−	0.155261i	$-0.0496220\pi$
$709$	9.57180	+	16.5788i	0.359476	+	0.622631i	−0.628397	+	0.777893i	$0.716289\pi$
$710$	7.60770	−	37.1769i	0.285512	−	1.39522i
$711$	5.70577	+	3.29423i	0.213983	+	0.123543i
$712$	−5.32051	−	5.32051i	−0.199394	−	0.199394i
$713$	7.09808	+	1.90192i	0.265825	+	0.0712276i
$714$	32.1962	−	32.1962i	1.20491	−	1.20491i
$715$	7.85641	+	1.60770i	0.293813	+	0.0601244i
$716$	12.7846			0.477783
$717$	16.3923	+	28.3923i	0.612182	+	1.06033i
$718$	−2.19615	+	2.19615i	−0.0819597	+	0.0819597i
$719$	1.51666			0.0565619			0.0282809	−	0.999600i	$-0.490997\pi$
$719$	1.51666			0.0565619			0.0282809	+	0.999600i	$0.490997\pi$
$720$	−12.0000	+	24.0000i	−0.447214	+	0.894427i
$721$	70.5885			2.62885
$722$	−3.39230	+	3.39230i	−0.126249	+	0.126249i
$723$	−32.5692			−1.21126
$724$	−6.00000			−0.222988
$725$	1.91154	+	15.8660i	0.0709929	+	0.589249i
$726$	−16.5622	−	4.43782i	−0.614680	−	0.164703i
$727$	2.86603	+	0.767949i	0.106295	+	0.0284817i	0.311574	−	0.950222i	$-0.399144\pi$
$727$	2.86603	+	0.767949i	0.106295	+	0.0284817i	−0.205279	+	0.978703i	$0.565810\pi$
$728$	15.7128	−	15.7128i	0.582356	−	0.582356i
$729$	27.0000			1.00000
$730$	25.1244	+	38.0526i	0.929894	+	1.40839i
$731$	19.3923	+	33.5885i	0.717250	+	1.24231i
$732$	−50.7846			−1.87705
$733$	−2.83013	−	10.5622i	−0.104533	−	0.390123i	0.893759	−	0.448548i	$-0.148059\pi$
$733$	−2.83013	−	10.5622i	−0.104533	−	0.390123i	−0.998292	+	0.0584252i	$0.981392\pi$
$734$	12.1244	−	7.00000i	0.447518	−	0.258375i
$735$	−42.2487	−	21.1244i	−1.55837	−	0.779184i
$736$	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	$-0.637306\pi$
$739$	−22.7321			−0.836212			−0.418106	+	0.908398i	$0.637306\pi$
$740$	−2.87564	−	0.588457i	−0.105711	−	0.0216321i
$741$	14.1962	+	3.80385i	0.521509	+	0.139738i
$742$	43.9808	+	11.7846i	1.61458	+	0.432627i
$743$	−6.82051	−	25.4545i	−0.250220	−	0.933834i	−0.970687	−	0.240345i	$-0.922739\pi$
$743$	−6.82051	−	25.4545i	−0.250220	−	0.933834i	0.720467	−	0.693489i	$-0.243927\pi$
$744$	−10.3923	+	38.7846i	−0.381000	+	1.42191i
$745$	−0.937822	−	15.6244i	−0.0343591	−	0.572432i
$746$	−4.60770	−	2.66025i	−0.168700	−	0.0973988i
$747$	33.9904	−	9.10770i	1.24364	−	0.333233i
$748$	16.3923	+	4.39230i	0.599362	+	0.160599i
$749$	−32.7224	+	18.8923i	−1.19565	+	0.690310i
$750$	11.7058	+	24.7583i	0.427434	+	0.904046i
$751$	−6.80385	+	11.7846i	−0.248276	+	0.430027i	−0.963048	−	0.269331i	$-0.913197\pi$
$751$	−6.80385	+	11.7846i	−0.248276	+	0.430027i	0.714772	+	0.699358i	$0.246531\pi$
$752$	1.60770	−	6.00000i	0.0586266	−	0.218797i
$753$	−23.0263	+	39.8827i	−0.839124	+	1.45341i
$754$	−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	$-0.910757\pi$
$757$	−34.0526	−	34.0526i	−1.23766	−	1.23766i	−0.276707	−	0.960954i	$-0.589243\pi$
$758$	−33.1244	+	33.1244i	−1.20313	+	1.20313i
$759$	0.803848	+	3.00000i	0.0291778	+	0.108893i
$760$	6.00000	−	29.3205i	0.217643	−	1.06357i
$761$	21.4808	+	12.4019i	0.778677	+	0.449569i	0.835961	−	0.548789i	$-0.184911\pi$
$761$	21.4808	+	12.4019i	0.778677	+	0.449569i	−0.0572842	+	0.998358i	$0.518244\pi$
$762$	−17.7058	−	10.2224i	−0.641412	−	0.370320i
$763$	−36.6506	−	9.82051i	−1.32684	−	0.355526i
$764$	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
$767$	−0.837169	+	3.12436i	−0.0302284	+	0.112814i
$768$	−13.8564	+	24.0000i	−0.500000	+	0.866025i
$769$	−29.9378	−	17.2846i	−1.07959	−	0.623299i	−0.148801	−	0.988867i	$-0.547541\pi$
$769$	−29.9378	−	17.2846i	−1.07959	−	0.623299i	−0.930785	+	0.365568i	$0.880875\pi$
$770$	−1.66025	−	27.6603i	−0.0598314	−	0.996806i
$771$	7.31347	−	27.2942i	0.263388	−	0.982978i
$772$	−7.32051	−	27.3205i	−0.263471	−	0.983287i
$773$	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
$777$	−4.98076			−0.178684
$778$	6.36603	−	23.7583i	0.228233	−	0.851777i
$779$	26.4904	+	15.2942i	0.949116	+	0.547973i
$780$	−13.1769	+	4.39230i	−0.471809	+	0.157270i
$781$	20.7846	−	12.0000i	0.743732	−	0.429394i
$782$	1.39230	+	5.19615i	0.0497887	+	0.185814i
$783$	14.3827	−	8.30385i	0.513995	−	0.296755i
$784$	−42.2487	−	24.3923i	−1.50888	−	0.871154i
$785$	−21.2942	−	18.8827i	−0.760024	−	0.673952i
$786$	18.4641	+	4.94744i	0.658593	+	0.176469i
$787$	38.9545	−	10.4378i	1.38858	−	0.372068i	0.514348	−	0.857582i	$-0.328034\pi$
$787$	38.9545	−	10.4378i	1.38858	−	0.372068i	0.874229	+	0.485513i	$0.161367\pi$
$788$	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
$792$	−16.3923	+	4.39230i	−0.582475	+	0.156074i
$793$	−18.5885	−	18.5885i	−0.660095	−	0.660095i
$794$	−1.60770			−0.0570550
$795$	−21.2942	−	18.8827i	−0.755228	−	0.669700i
$796$	−8.39230			−0.297457
$797$	5.92820	+	22.1244i	0.209988	+	0.783685i	0.987871	+	0.155276i	$0.0496268\pi$
$797$	5.92820	+	22.1244i	0.209988	+	0.783685i	−0.777883	+	0.628409i	$0.783707\pi$
$798$		−	50.7846i		−	1.79776i
$799$	5.70577	−	3.29423i	0.201856	−	0.116541i
$800$	10.5359	+	26.2487i	0.372500	+	0.928032i
$801$	3.99038	+	6.91154i	0.140993	+	0.244207i
$802$	49.5167	−	13.2679i	1.74849	−	0.468508i
$803$	−7.46410	+	27.8564i	−0.263402	+	0.983031i
$804$	−25.3923	−	6.80385i	−0.895518	−	0.239953i
$805$	7.33013	−	4.83975i	0.258353	−	0.170579i
$806$	−18.0000	+	10.3923i	−0.634023	+	0.366053i
$807$	1.50000	+	0.866025i	0.0528025	+	0.0304855i
$808$	−1.46410	+	5.46410i	−0.0515069	+	0.192226i
$809$	45.7128			1.60718			0.803588	−	0.595185i	$-0.202921\pi$
$809$	45.7128			1.60718			0.803588	+	0.595185i	$0.202921\pi$
$810$	18.8827	−	21.2942i	0.663470	−	0.748203i
$811$			16.7321i			0.587542i	0.955876	+	0.293771i	$0.0949103\pi$
$811$			16.7321i			0.587542i	−0.955876	+	0.293771i	$0.905090\pi$
$812$	7.24871	+	27.0526i	0.254380	+	0.949359i
$813$	−3.97372	+	6.88269i	−0.139364	+	0.241386i
$814$	−0.928203	−	1.60770i	−0.0325335	−	0.0563497i
$815$	20.0263	+	4.09808i	0.701490	+	0.143549i
$816$	−28.3923	+	7.60770i	−0.993929	+	0.266323i
$817$	41.7846	+	11.1962i	1.46186	+	0.391704i
$818$	8.19615	−	2.19615i	0.286572	−	0.0767867i
$819$	−20.4115	+	11.7846i	−0.713237	+	0.411788i
$820$	−28.8564	+	1.73205i	−1.00771	+	0.0604858i
$821$	−14.2846	−	24.7417i	−0.498536	−	0.863490i	0.501462	−	0.865180i	$-0.332796\pi$
$821$	−14.2846	−	24.7417i	−0.498536	−	0.863490i	−0.999999	+	0.00168929i	$0.999462\pi$
$822$	−32.7846			−1.14349
$823$	−11.0622	+	2.96410i	−0.385603	+	0.103322i	−0.446412	−	0.894827i	$-0.647299\pi$
$823$	−11.0622	+	2.96410i	−0.385603	+	0.103322i	0.0608092	+	0.998149i	$0.480632\pi$
$824$	−39.4641	−	22.7846i	−1.37480	−	0.793739i
$825$	−6.80385	+	15.9282i	−0.236880	+	0.554549i
$826$	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	$-0.643271\pi$
$829$	−25.0526			−0.870111			−0.435056	+	0.900404i	$0.643271\pi$
$830$	16.5885	−	33.1769i	0.575794	−	1.15159i
$831$	−11.1962	−	11.1962i	−0.388390	−	0.388390i
$832$	−13.8564	+	3.71281i	−0.480384	+	0.128719i
$833$	−13.3923	−	49.9808i	−0.464016	−	1.73173i
$834$	16.3923	+	4.39230i	0.567619	+	0.152093i
$835$	30.9904	+	27.4808i	1.07247	+	0.951011i
$836$	16.3923	−	9.46410i	0.566940	−	0.327323i
$837$	21.2942	−	36.8827i	0.736036	−	1.27485i
$838$	−16.9282	+	4.53590i	−0.584775	+	0.156690i
$839$	−14.0263	−	24.2942i	−0.484241	−	0.838730i	0.515595	−	0.856832i	$-0.327571\pi$
$839$	−14.0263	−	24.2942i	−0.484241	−	0.838730i	−0.999836	+	0.0181024i	$0.994238\pi$
$840$	26.4449	+	40.0526i	0.912434	+	1.38194i
$841$	−9.39230	+	16.2679i	−0.323873	+	0.560964i
$842$	1.94744	−	7.26795i	0.0671133	−	0.250470i
$843$		−	3.58846i		−	0.123593i
$844$		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
$850$	−11.7846	+	27.5885i	−0.404209	+	0.946276i
$851$	0.294229	−	0.509619i	0.0100860	−	0.0174695i
$852$	−20.7846	+	36.0000i	−0.712069	+	1.23334i
$853$	44.7846	+	12.0000i	1.53340	+	0.410872i	0.924125	−	0.382090i	$-0.124796\pi$
$853$	44.7846	+	12.0000i	1.53340	+	0.410872i	0.609271	+	0.792962i	$0.291462\pi$
$854$	−45.4186	+	78.6673i	−1.55419	+	2.69194i
$855$	−14.1962	+	28.3923i	−0.485498	+	0.970996i
$856$	24.3923			0.833712
$857$	−7.48334	+	27.9282i	−0.255626	+	0.954009i	0.712115	+	0.702063i	$0.247737\pi$
$857$	−7.48334	+	27.9282i	−0.255626	+	0.954009i	−0.967741	+	0.251947i	$0.918929\pi$
$858$	−7.60770	−	4.39230i	−0.259722	−	0.149951i
$859$	−8.66025	+	15.0000i	−0.295484	+	0.511793i	−0.975097	−	0.221777i	$-0.928814\pi$
$859$	−8.66025	+	15.0000i	−0.295484	+	0.511793i	0.679613	+	0.733571i	$0.262148\pi$
$860$	−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	−0.463410	−	0.886144i	$-0.653374\pi$
$863$	12.4186	−	12.4186i	0.422734	−	0.422734i	0.886144	+	0.463410i	$0.153374\pi$
$864$	20.7846	−	20.7846i	0.707107	−	0.707107i
$865$	6.00000	−	2.00000i	0.204006	−	0.0680020i
$866$	30.7846			1.04610
$867$	−1.50000	−	0.866025i	−0.0509427	−	0.0294118i
$868$	50.7846	+	50.7846i	1.72374	+	1.72374i
$869$	3.80385	+	2.19615i	0.129037	+	0.0744994i
$870$	3.50962	−	17.1506i	0.118987	−	0.581461i
$871$	−6.80385	−	11.7846i	−0.230540	−	0.399306i
$872$	17.3205	+	17.3205i	0.586546	+	0.586546i
$873$	5.49038	+	20.4904i	0.185821	+	0.693494i
$874$	5.19615	+	3.00000i	0.175762	+	0.101477i
$875$	48.8205	+	4.00962i	1.65043	+	0.135550i
$876$	−12.9282	−	48.2487i	−0.436804	−	1.63017i
$877$	−24.1244	+	6.46410i	−0.814622	+	0.218277i	−0.641994	−	0.766710i	$-0.721892\pi$
$877$	−24.1244	+	6.46410i	−0.814622	+	0.218277i	−0.172628	+	0.984987i	$0.555226\pi$
$878$	6.87564	−	25.6603i	0.232042	−	0.865992i
$879$	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	$0.0111114\pi$
$881$			2.07180i			0.0698006i	−0.999391	+	0.0349003i	$0.988889\pi$
$882$	36.5885	+	36.5885i	1.23200	+	1.23200i
$883$	27.4186	−	27.4186i	0.922709	−	0.922709i	−0.0745113	−	0.997220i	$-0.523740\pi$
$883$	27.4186	−	27.4186i	0.922709	−	0.922709i	0.997220	+	0.0745113i	$0.0237397\pi$
$884$	−13.1769	−	7.60770i	−0.443188	−	0.255874i
$885$	−6.24871	−	3.12436i	−0.210048	−	0.105024i
$886$	27.2942	+	47.2750i	0.916968	+	1.58823i
$887$	−1.56218	+	0.418584i	−0.0524528	+	0.0140547i	−0.284950	−	0.958542i	$-0.591977\pi$
$887$	−1.56218	+	0.418584i	−0.0524528	+	0.0140547i	0.232497	+	0.972597i	$0.425310\pi$
$888$	2.78461	+	1.60770i	0.0934454	+	0.0539507i
$889$	−31.6699	+	18.2846i	−1.06217	+	0.613246i
$890$	8.24167	+	1.68653i	0.276261	+	0.0565327i
$891$	18.0000			0.603023
$892$	−33.0526	−	8.85641i	−1.10668	−	0.296534i
$893$	1.90192	−	7.09808i	0.0636455	−	0.237528i
$894$	−4.43782	+	16.5622i	−0.148423	+	0.553922i
$895$	−11.9282	+	7.87564i	−0.398716	+	0.263254i
$896$	24.7846	+	42.9282i	0.827996	+	1.43413i
$897$		−	2.78461i		−	0.0929754i
$898$	−32.7846	+	32.7846i	−1.09404	+	1.09404i
$899$		−	26.1962i		−	0.873691i
$900$	−3.58846	−	29.7846i	−0.119615	−	0.992820i
$901$		−	31.1769i		−	1.03865i
$902$	−12.9282	−	12.9282i	−0.430462	−	0.430462i
$903$	−60.0788	+	34.6865i	−1.99930	+	1.15430i
$904$	−2.53590	+	4.39230i	−0.0843427	+	0.146086i
$905$	5.59808	−	3.69615i	0.186086	−	0.122864i
$906$	27.7128	−	27.7128i	0.920697	−	0.920697i
$907$	0.944864	−	3.52628i	0.0313737	−	0.117088i	−0.948463	−	0.316887i	$-0.897362\pi$
$907$	0.944864	−	3.52628i	0.0313737	−	0.117088i	0.979837	+	0.199799i	$0.0640290\pi$
$908$	−5.41154	+	20.1962i	−0.179588	+	0.670233i
$909$	3.00000	−	5.19615i	0.0995037	−	0.172345i
$910$	−4.98076	+	24.3397i	−0.165111	+	0.806855i
$911$	23.4904	−	13.5622i	0.778271	−	0.449335i	−0.0575461	−	0.998343i	$-0.518328\pi$
$911$	23.4904	−	13.5622i	0.778271	−	0.449335i	0.835817	+	0.549008i	$0.184994\pi$
$912$	−16.3923	+	28.3923i	−0.542803	+	0.940163i
$913$	22.6603	−	6.07180i	0.749945	−	0.200947i
$914$	−12.4641	+	7.19615i	−0.412276	+	0.238028i
$915$	47.3827	−	31.2846i	1.56642	−	1.03424i
$916$	−19.9808	−	11.5359i	−0.660183	−	0.381157i
$917$	24.1769	−	24.1769i	0.798392	−	0.798392i
$918$	31.1769			1.02899
$919$			20.1962i			0.666210i	0.942890	+	0.333105i	$0.108096\pi$
$919$			20.1962i			0.666210i	−0.942890	+	0.333105i	$0.891904\pi$
$920$	−5.66025	+	0.339746i	−0.186613	+	0.0112011i
$921$	33.9904	−	9.10770i	1.12002	−	0.300109i
$922$	18.5622	+	4.97372i	0.611313	+	0.163801i
$923$	−20.7846	+	5.56922i	−0.684134	+	0.183313i
$924$	−7.85641	+	29.3205i	−0.258457	+	0.964574i
$925$	3.04552	−	1.22243i	0.100136	−	0.0401933i
$926$	−4.80385	+	8.32051i	−0.157864	+	0.273429i
$927$	34.1769	+	34.1769i	1.12252	+	1.12252i
$928$	4.67949	−	17.4641i	0.153612	−	0.573287i
$929$	−2.19615	−	3.80385i	−0.0720534	−	0.124800i	0.827748	−	0.561100i	$-0.189622\pi$
$929$	−2.19615	−	3.80385i	−0.0720534	−	0.124800i	−0.899801	+	0.436300i	$0.856289\pi$
$930$	−14.1962	−	42.5885i	−0.465510	−	1.39653i
$931$	−49.9808	−	28.8564i	−1.63805	−	0.945731i
$932$	36.2487	+	36.2487i	1.18737	+	1.18737i
$933$	−21.2942	+	12.2942i	−0.697142	+	0.402495i
$934$			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	−0.928812	−	0.370552i	$-0.879169\pi$
$941$	−4.40192	+	7.62436i	−0.143499	+	0.248547i	0.785313	+	0.619099i	$0.212502\pi$
$942$	15.5885	+	27.0000i	0.507899	+	0.879708i
$943$	1.50000	−	5.59808i	0.0488467	−	0.182298i
$944$	−6.24871	−	3.60770i	−0.203378	−	0.117420i
$945$	−16.0981	−	48.2942i	−0.523670	−	1.57101i
$946$	−22.3923	−	12.9282i	−0.728037	−	0.420332i
$947$	−23.0885	−	6.18653i	−0.750274	−	0.201035i	−0.136634	−	0.990622i	$-0.543629\pi$
$947$	−23.0885	−	6.18653i	−0.750274	−	0.201035i	−0.613640	+	0.789586i	$0.710295\pi$
$948$	−7.60770			−0.247086
$949$	12.9282	−	22.3923i	0.419667	−	0.726885i
$950$	12.4641	+	31.0526i	0.404389	+	1.00748i
$951$	−17.3205	+	17.3205i	−0.561656	+	0.561656i
$952$	−13.6077	+	50.7846i	−0.441028	+	1.64594i
$953$	24.9282	−	24.9282i	0.807504	−	0.807504i	−0.176752	−	0.984255i	$-0.556559\pi$
$953$	24.9282	−	24.9282i	0.807504	−	0.807504i	0.984255	+	0.176752i	$0.0565590\pi$
$954$	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
$957$	9.58846	−	5.53590i	0.309951	−	0.178950i
$958$	28.8564	+	7.73205i	0.932308	+	0.249811i
$959$	−29.3205	+	50.7846i	−0.946809	+	1.63992i
$960$	−1.85641	−	30.9282i	−0.0599153	−	0.998203i
$961$	−18.0885	−	31.3301i	−0.583499	−	1.01065i
$962$	0.430781	+	1.60770i	0.0138889	+	0.0518342i
$963$	−24.9904	−	6.69615i	−0.805304	−	0.215780i
$964$	32.5692	−	18.8038i	1.04898	−	0.605631i
$965$	23.6603	+	20.9808i	0.761651	+	0.675395i
$966$	−9.29423	+	2.49038i	−0.299037	+	0.0801267i
$967$	−4.27757	−	15.9641i	−0.137557	−	0.513371i	−0.999974	−	0.00717234i	$-0.997717\pi$
$967$	−4.27757	−	15.9641i	−0.137557	−	0.513371i	0.862417	−	0.506199i	$-0.168950\pi$
$968$	19.1244	−	5.12436i	0.614680	−	0.164703i
$969$	−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	$0.658720\pi$
$972$	−27.0000	+	15.5885i	−0.866025	+	0.500000i
$973$	21.4641	−	21.4641i	0.688108	−	0.688108i
$974$			6.78461i			0.217393i
$975$	9.58846	−	12.2154i	0.307076	−	0.391206i
$976$	50.7846	−	29.3205i	1.62558	−	0.938527i
$977$	−40.0526	+	10.7321i	−1.28139	+	0.343349i	−0.834386	−	0.551181i	$-0.814177\pi$
$977$	−40.0526	+	10.7321i	−1.28139	+	0.343349i	−0.447009	+	0.894529i	$0.647511\pi$
$978$	−19.3923	−	11.1962i	−0.620098	−	0.358013i
$979$	2.66025	+	4.60770i	0.0850221	+	0.147263i
$980$	54.4449	−	3.26795i	1.73918	−	0.104391i
$981$	−12.9904	−	22.5000i	−0.414751	−	0.718370i
$982$	−9.07180	−	33.8564i	−0.289493	−	1.08040i
$983$	13.3301	+	3.57180i	0.425165	+	0.113923i	0.465056	−	0.885281i	$-0.346034\pi$
$983$	13.3301	+	3.57180i	0.425165	+	0.113923i	−0.0398907	+	0.999204i	$0.512701\pi$
$984$	30.5885	+	8.19615i	0.975124	+	0.261284i
$985$	−37.1769	−	7.60770i	−1.18455	−	0.242401i
$986$	16.6077	−	9.58846i	0.528897	−	0.305359i
$987$	5.89230	+	10.2058i	0.187554	+	0.324853i
$988$	−16.3923	+	4.39230i	−0.521509	+	0.139738i
$989$		−	8.19615i		−	0.260622i
$990$	12.5885	−	14.1962i	0.400087	−	0.451183i
$991$	10.1962			0.323891			0.161946	−	0.986800i	$-0.448223\pi$
$991$	10.1962			0.323891			0.161946	+	0.986800i	$0.448223\pi$
$992$	−12.0000	−	44.7846i	−0.381000	−	1.42191i
$993$		−	1.01924i		−	0.0323445i
$994$	37.1769	+	64.3923i	1.17918	+	2.04240i
$995$	7.83013	−	5.16987i	0.248232	−	0.163896i
$996$	−28.7321	+	28.7321i	−0.910410	+	0.910410i
$997$	1.77757	−	6.63397i	0.0562961	−	0.210100i	−0.932048	−	0.362334i	$-0.881980\pi$
$997$	1.77757	−	6.63397i	0.0562961	−	0.210100i	0.988345	+	0.152234i	$0.0486467\pi$
$998$	−9.80385	−	36.5885i	−0.310335	−	1.15819i
$999$	−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.a.293.1	✓	4
5.2	odd	4		360.2.br.b.77.1	yes	4
8.5	even	2		360.2.br.d.293.1	yes	4
9.2	odd	6		360.2.br.c.173.1	yes	4
40.37	odd	4		360.2.br.c.77.1	yes	4
45.2	even	12		360.2.br.d.317.1	yes	4
72.29	odd	6		360.2.br.b.173.1	yes	4
360.317	even	12	inner	360.2.br.a.317.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.br.a.293.1	✓	4	1.1	even	1	trivial
360.2.br.a.317.1	yes	4	360.317	even	12	inner
360.2.br.b.77.1	yes	4	5.2	odd	4
360.2.br.b.173.1	yes	4	72.29	odd	6
360.2.br.c.77.1	yes	4	40.37	odd	4
360.2.br.c.173.1	yes	4	9.2	odd	6
360.2.br.d.293.1	yes	4	8.5	even	2
360.2.br.d.317.1	yes	4	45.2	even	12

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-0.866025 + 1.50000i) q^{3} -2.00000i q^{4} +(1.23205 + 1.86603i) q^{5} +(-0.633975 - 2.36603i) q^{6} +(-4.23205 - 1.13397i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-0.866025 + 1.50000i) q^{3} -2.00000i q^{4} +(1.23205 + 1.86603i) q^{5} +(-0.633975 - 2.36603i) q^{6} +(-4.23205 - 1.13397i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.09808 - 0.633975i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(3.00000 + 1.73205i) q^{12} +(0.464102 + 1.73205i) q^{13} +(5.36603 - 3.09808i) q^{14} +(-3.86603 + 0.232051i) q^{15} -4.00000 q^{16} +(-3.00000 - 3.00000i) q^{17} +(4.09808 + 1.09808i) q^{18} -4.73205 q^{19} +(3.73205 - 2.46410i) q^{20} +(5.36603 - 5.36603i) q^{21} +(2.73205 + 0.732051i) q^{22} +(0.232051 + 0.866025i) q^{23} +(-4.73205 + 1.26795i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(-2.19615 - 1.26795i) q^{26} +5.19615 q^{27} +(-2.26795 + 8.46410i) q^{28} +(2.76795 - 1.59808i) q^{29} +(3.63397 - 4.09808i) q^{30} +(4.09808 - 7.09808i) q^{31} +(4.00000 - 4.00000i) q^{32} +3.46410 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} +(-1.26795 + 6.19615i) q^{40} +(-5.59808 - 3.23205i) q^{41} +10.7321i q^{42} +(-8.83013 - 2.36603i) q^{43} +(-3.46410 + 2.00000i) q^{44} +(3.00000 - 6.00000i) q^{45} +(-1.09808 - 0.633975i) q^{46} +(-0.401924 + 1.50000i) q^{47} +(3.46410 - 6.00000i) q^{48} +(10.5622 + 6.09808i) q^{49} +(-2.63397 - 6.56218i) q^{50} +(7.09808 - 1.90192i) q^{51} +(3.46410 - 0.928203i) 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} +(4.09808 - 7.09808i) q^{57} +(-1.16987 + 4.36603i) q^{58} +(1.56218 + 0.901924i) q^{59} +(0.464102 + 7.73205i) q^{60} +(-12.6962 + 7.33013i) q^{61} +(3.00000 + 11.1962i) q^{62} +(3.40192 + 12.6962i) q^{63} +8.00000i q^{64} +(-2.66025 + 3.00000i) q^{65} +(-3.46410 + 3.46410i) q^{66} +(-7.33013 + 1.96410i) q^{67} +(-6.00000 + 6.00000i) q^{68} +(-1.50000 - 0.401924i) q^{69} +(12.3923 + 6.19615i) q^{70} +12.0000i q^{71} +(2.19615 - 8.19615i) q^{72} +(-10.1962 - 10.1962i) q^{73} +0.928203 q^{74} +(-5.19615 - 6.92820i) q^{75} +9.46410i q^{76} +(2.26795 + 8.46410i) q^{77} +(3.80385 - 2.19615i) q^{78} +(-1.90192 + 1.09808i) q^{79} +(-4.92820 - 7.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(8.83013 - 2.36603i) q^{82} +(-3.03590 + 11.3301i) q^{83} +(-10.7321 - 10.7321i) q^{84} +(1.90192 - 9.29423i) q^{85} +(11.1962 - 6.46410i) q^{86} +5.53590i q^{87} +(1.46410 - 5.46410i) q^{88} -2.66025 q^{89} +(3.00000 + 9.00000i) q^{90} -7.85641i q^{91} +(1.73205 - 0.464102i) q^{92} +(7.09808 + 12.2942i) q^{93} +(-1.09808 - 1.90192i) q^{94} +(-5.83013 - 8.83013i) q^{95} +(2.53590 + 9.46410i) q^{96} +(-6.83013 - 1.83013i) q^{97} +(-16.6603 + 4.46410i) q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{5} - 6 q^{6} - 10 q^{7} + 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 2 * q^5 - 6 * q^6 - 10 * q^7 + 8 * q^8 - 6 * q^9	\( 4 q - 4 q^{2} - 2 q^{5} - 6 q^{6} - 10 q^{7} + 8 q^{8} - 6 q^{9} - 2 q^{10} - 4 q^{11} + 12 q^{12} - 12 q^{13} + 18 q^{14} - 12 q^{15} - 16 q^{16} - 12 q^{17} + 6 q^{18} - 12 q^{19} + 8 q^{20} + 18 q^{21} + 4 q^{22} - 6 q^{23} - 12 q^{24} + 6 q^{25} + 12 q^{26} - 16 q^{28} + 18 q^{29} + 18 q^{30} + 6 q^{31} + 16 q^{32} + 24 q^{34} - 2 q^{35} + 12 q^{37} + 12 q^{38} - 12 q^{39} - 12 q^{40} - 12 q^{41} - 18 q^{43} + 12 q^{45} + 6 q^{46} - 12 q^{47} + 18 q^{49} - 14 q^{50} + 18 q^{51} + 8 q^{55} - 4 q^{56} + 6 q^{57} - 22 q^{58} - 18 q^{59} - 12 q^{60} - 30 q^{61} + 12 q^{62} + 24 q^{63} + 24 q^{65} - 12 q^{67} - 24 q^{68} - 6 q^{69} + 8 q^{70} - 12 q^{72} - 20 q^{73} - 24 q^{74} + 16 q^{77} + 36 q^{78} - 18 q^{79} + 8 q^{80} - 18 q^{81} + 18 q^{82} - 26 q^{83} - 36 q^{84} + 18 q^{85} + 24 q^{86} - 8 q^{88} + 24 q^{89} + 12 q^{90} + 18 q^{93} + 6 q^{94} - 6 q^{95} + 24 q^{96} - 10 q^{97} - 32 q^{98} - 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^5 - 6 * q^6 - 10 * q^7 + 8 * q^8 - 6 * q^9 - 2 * q^10 - 4 * q^11 + 12 * q^12 - 12 * q^13 + 18 * q^14 - 12 * q^15 - 16 * q^16 - 12 * q^17 + 6 * q^18 - 12 * q^19 + 8 * q^20 + 18 * q^21 + 4 * q^22 - 6 * q^23 - 12 * q^24 + 6 * q^25 + 12 * q^26 - 16 * q^28 + 18 * q^29 + 18 * 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 - 18 * q^43 + 12 * q^45 + 6 * q^46 - 12 * q^47 + 18 * q^49 - 14 * q^50 + 18 * q^51 + 8 * q^55 - 4 * q^56 + 6 * q^57 - 22 * q^58 - 18 * q^59 - 12 * q^60 - 30 * q^61 + 12 * q^62 + 24 * q^63 + 24 * q^65 - 12 * q^67 - 24 * q^68 - 6 * q^69 + 8 * q^70 - 12 * q^72 - 20 * q^73 - 24 * q^74 + 16 * q^77 + 36 * q^78 - 18 * q^79 + 8 * q^80 - 18 * q^81 + 18 * q^82 - 26 * q^83 - 36 * q^84 + 18 * q^85 + 24 * q^86 - 8 * q^88 + 24 * q^89 + 12 * q^90 + 18 * q^93 + 6 * q^94 - 6 * q^95 + 24 * q^96 - 10 * q^97 - 32 * q^98 - 12 * q^99

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