LMFDB - Embedded newform 144.2.x.b.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(13,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 4]))

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

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

chi := DirichletCharacter("144.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.x (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:	$1.14984578911$
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			85.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	144.85
Dual form			144.2.x.b.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-3.73205 + 1.00000i) q^{5} +(0.633975 + 2.36603i) q^{6} +(-0.633975 + 0.366025i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-3.73205 + 1.00000i) q^{5} +(0.633975 + 2.36603i) q^{6} +(-0.633975 + 0.366025i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +5.46410i q^{10} +(-0.767949 + 2.86603i) q^{11} +3.46410 q^{12} +(-1.63397 - 6.09808i) q^{13} +(0.267949 + 1.00000i) q^{14} +(4.73205 - 4.73205i) q^{15} +(2.00000 + 3.46410i) q^{16} -2.26795 q^{17} +(-3.00000 - 3.00000i) q^{18} +(-0.633975 + 0.633975i) q^{19} +(7.46410 + 2.00000i) q^{20} +(0.633975 - 1.09808i) q^{21} +(3.63397 + 2.09808i) q^{22} +(-1.09808 - 0.633975i) q^{23} +(1.26795 - 4.73205i) q^{24} +(8.59808 - 4.96410i) q^{25} -8.92820 q^{26} +5.19615i q^{27} +1.46410 q^{28} +(-2.36603 - 0.633975i) q^{29} +(-4.73205 - 8.19615i) q^{30} +(-3.73205 + 6.46410i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-1.33013 - 4.96410i) q^{33} +(-0.830127 + 3.09808i) q^{34} +(2.00000 - 2.00000i) q^{35} +(-5.19615 + 3.00000i) q^{36} +(1.26795 + 1.26795i) q^{37} +(0.633975 + 1.09808i) q^{38} +(7.73205 + 7.73205i) q^{39} +(5.46410 - 9.46410i) q^{40} +(-2.59808 - 1.50000i) q^{41} +(-1.26795 - 1.26795i) q^{42} +(0.330127 - 1.23205i) q^{43} +(4.19615 - 4.19615i) q^{44} +(-3.00000 + 11.1962i) q^{45} +(-1.26795 + 1.26795i) q^{46} +(-4.83013 - 8.36603i) q^{47} +(-6.00000 - 3.46410i) q^{48} +(-3.23205 + 5.59808i) q^{49} +(-3.63397 - 13.5622i) q^{50} +(3.40192 - 1.96410i) q^{51} +(-3.26795 + 12.1962i) q^{52} +(-0.535898 - 0.535898i) q^{53} +(7.09808 + 1.90192i) q^{54} -11.4641i q^{55} +(0.535898 - 2.00000i) q^{56} +(0.401924 - 1.50000i) q^{57} +(-1.73205 + 3.00000i) q^{58} +(4.96410 - 1.33013i) q^{59} +(-12.9282 + 3.46410i) q^{60} +(-3.00000 - 0.803848i) q^{61} +(7.46410 + 7.46410i) q^{62} +2.19615i q^{63} -8.00000i q^{64} +(12.1962 + 21.1244i) q^{65} -7.26795 q^{66} +(1.40192 + 5.23205i) q^{67} +(3.92820 + 2.26795i) q^{68} +2.19615 q^{69} +(-2.00000 - 3.46410i) q^{70} +10.9282i q^{71} +(2.19615 + 8.19615i) q^{72} +9.73205i q^{73} +(2.19615 - 1.26795i) q^{74} +(-8.59808 + 14.8923i) q^{75} +(1.73205 - 0.464102i) q^{76} +(-0.562178 - 2.09808i) q^{77} +(13.3923 - 7.73205i) q^{78} +(-6.00000 - 10.3923i) q^{79} +(-10.9282 - 10.9282i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-3.00000 + 3.00000i) q^{82} +(-1.36603 - 0.366025i) q^{83} +(-2.19615 + 1.26795i) q^{84} +(8.46410 - 2.26795i) q^{85} +(-1.56218 - 0.901924i) q^{86} +(4.09808 - 1.09808i) q^{87} +(-4.19615 - 7.26795i) q^{88} +2.00000i q^{89} +(14.1962 + 8.19615i) q^{90} +(3.26795 + 3.26795i) q^{91} +(1.26795 + 2.19615i) q^{92} -12.9282i q^{93} +(-13.1962 + 3.53590i) q^{94} +(1.73205 - 3.00000i) q^{95} +(-6.92820 + 6.92820i) q^{96} +(-4.13397 - 7.16025i) q^{97} +(6.46410 + 6.46410i) q^{98} +(6.29423 + 6.29423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{3} - 8 q^{5} + 6 q^{6} - 6 q^{7} - 8 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^3 - 8 * q^5 + 6 * q^6 - 6 * q^7 - 8 * q^8 + 6 * q^9	$ 4 q - 2 q^{2} - 6 q^{3} - 8 q^{5} + 6 q^{6} - 6 q^{7} - 8 q^{8} + 6 q^{9} - 10 q^{11} - 10 q^{13} + 8 q^{14} + 12 q^{15} + 8 q^{16} - 16 q^{17} - 12 q^{18} - 6 q^{19} + 16 q^{20} + 6 q^{21} + 18 q^{22} + 6 q^{23} + 12 q^{24} + 24 q^{25} - 8 q^{26} - 8 q^{28} - 6 q^{29} - 12 q^{30} - 8 q^{31} + 8 q^{32} + 12 q^{33} + 14 q^{34} + 8 q^{35} + 12 q^{37} + 6 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{42} - 16 q^{43} - 4 q^{44} - 12 q^{45} - 12 q^{46} - 2 q^{47} - 24 q^{48} - 6 q^{49} - 18 q^{50} + 24 q^{51} - 20 q^{52} - 16 q^{53} + 18 q^{54} + 16 q^{56} + 12 q^{57} + 6 q^{59} - 24 q^{60} - 12 q^{61} + 16 q^{62} + 28 q^{65} - 36 q^{66} + 16 q^{67} - 12 q^{68} - 12 q^{69} - 8 q^{70} - 12 q^{72} - 12 q^{74} - 24 q^{75} + 22 q^{77} + 12 q^{78} - 24 q^{79} - 16 q^{80} - 18 q^{81} - 12 q^{82} - 2 q^{83} + 12 q^{84} + 20 q^{85} + 18 q^{86} + 6 q^{87} + 4 q^{88} + 36 q^{90} + 20 q^{91} + 12 q^{92} - 32 q^{94} - 20 q^{97} + 12 q^{98} - 6 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^3 - 8 * q^5 + 6 * q^6 - 6 * q^7 - 8 * q^8 + 6 * q^9 - 10 * q^11 - 10 * q^13 + 8 * q^14 + 12 * q^15 + 8 * q^16 - 16 * q^17 - 12 * q^18 - 6 * q^19 + 16 * q^20 + 6 * q^21 + 18 * q^22 + 6 * q^23 + 12 * q^24 + 24 * q^25 - 8 * q^26 - 8 * q^28 - 6 * q^29 - 12 * q^30 - 8 * q^31 + 8 * q^32 + 12 * q^33 + 14 * q^34 + 8 * q^35 + 12 * q^37 + 6 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^42 - 16 * q^43 - 4 * q^44 - 12 * q^45 - 12 * q^46 - 2 * q^47 - 24 * q^48 - 6 * q^49 - 18 * q^50 + 24 * q^51 - 20 * q^52 - 16 * q^53 + 18 * q^54 + 16 * q^56 + 12 * q^57 + 6 * q^59 - 24 * q^60 - 12 * q^61 + 16 * q^62 + 28 * q^65 - 36 * q^66 + 16 * q^67 - 12 * q^68 - 12 * q^69 - 8 * q^70 - 12 * q^72 - 12 * q^74 - 24 * q^75 + 22 * q^77 + 12 * q^78 - 24 * q^79 - 16 * q^80 - 18 * q^81 - 12 * q^82 - 2 * q^83 + 12 * q^84 + 20 * q^85 + 18 * q^86 + 6 * q^87 + 4 * q^88 + 36 * q^90 + 20 * q^91 + 12 * q^92 - 32 * q^94 - 20 * q^97 + 12 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$	−3.73205	+	1.00000i	−1.66902	+	0.447214i	−0.964847	−	0.262811i	$-0.915350\pi$
$5$	−3.73205	+	1.00000i	−1.66902	+	0.447214i	−0.704177	+	0.710025i	$0.748684\pi$
$6$	0.633975	+	2.36603i	0.258819	+	0.965926i
$7$	−0.633975	+	0.366025i	−0.239620	+	0.138345i	−0.615002	−	0.788526i	$-0.710845\pi$
$7$	−0.633975	+	0.366025i	−0.239620	+	0.138345i	0.375382	+	0.926870i	$0.377511\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$			5.46410i			1.72790i
$11$	−0.767949	+	2.86603i	−0.231545	+	0.864139i	0.748130	+	0.663552i	$0.230952\pi$
$11$	−0.767949	+	2.86603i	−0.231545	+	0.864139i	−0.979676	+	0.200587i	$0.935715\pi$
$12$	3.46410			1.00000
$13$	−1.63397	−	6.09808i	−0.453183	−	1.69130i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−1.63397	−	6.09808i	−0.453183	−	1.69130i	0.240192	−	0.970725i	$-0.422790\pi$
$14$	0.267949	+	1.00000i	0.0716124	+	0.267261i
$15$	4.73205	−	4.73205i	1.22181	−	1.22181i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−2.26795			−0.550058			−0.275029	−	0.961436i	$-0.588688\pi$
$17$	−2.26795			−0.550058			−0.275029	+	0.961436i	$0.588688\pi$
$18$	−3.00000	−	3.00000i	−0.707107	−	0.707107i
$19$	−0.633975	+	0.633975i	−0.145444	+	0.145444i	−0.776079	−	0.630635i	$-0.782794\pi$
$19$	−0.633975	+	0.633975i	−0.145444	+	0.145444i	0.630635	+	0.776079i	$0.282794\pi$
$20$	7.46410	+	2.00000i	1.66902	+	0.447214i
$21$	0.633975	−	1.09808i	0.138345	−	0.239620i
$22$	3.63397	+	2.09808i	0.774766	+	0.447311i
$23$	−1.09808	−	0.633975i	−0.228965	−	0.132193i	0.381130	−	0.924522i	$-0.375535\pi$
$23$	−1.09808	−	0.633975i	−0.228965	−	0.132193i	−0.610094	+	0.792329i	$0.708868\pi$
$24$	1.26795	−	4.73205i	0.258819	−	0.965926i
$25$	8.59808	−	4.96410i	1.71962	−	0.992820i
$26$	−8.92820			−1.75096
$27$			5.19615i			1.00000i
$28$	1.46410			0.276689
$29$	−2.36603	−	0.633975i	−0.439360	−	0.117726i	0.0323566	−	0.999476i	$-0.489699\pi$
$29$	−2.36603	−	0.633975i	−0.439360	−	0.117726i	−0.471717	+	0.881750i	$0.656365\pi$
$30$	−4.73205	−	8.19615i	−0.863950	−	1.49641i
$31$	−3.73205	+	6.46410i	−0.670296	+	1.16099i	0.307524	+	0.951540i	$0.400500\pi$
$31$	−3.73205	+	6.46410i	−0.670296	+	1.16099i	−0.977820	+	0.209447i	$0.932834\pi$
$32$	5.46410	−	1.46410i	0.965926	−	0.258819i
$33$	−1.33013	−	4.96410i	−0.231545	−	0.864139i
$34$	−0.830127	+	3.09808i	−0.142366	+	0.531316i
$35$	2.00000	−	2.00000i	0.338062	−	0.338062i
$36$	−5.19615	+	3.00000i	−0.866025	+	0.500000i
$37$	1.26795	+	1.26795i	0.208450	+	0.208450i	0.803608	−	0.595159i	$-0.202911\pi$
$37$	1.26795	+	1.26795i	0.208450	+	0.208450i	−0.595159	+	0.803608i	$0.702911\pi$
$38$	0.633975	+	1.09808i	0.102844	+	0.178131i
$39$	7.73205	+	7.73205i	1.23812	+	1.23812i
$40$	5.46410	−	9.46410i	0.863950	−	1.49641i
$41$	−2.59808	−	1.50000i	−0.405751	−	0.234261i	0.283211	−	0.959058i	$-0.408600\pi$
$41$	−2.59808	−	1.50000i	−0.405751	−	0.234261i	−0.688963	+	0.724797i	$0.741934\pi$
$42$	−1.26795	−	1.26795i	−0.195649	−	0.195649i
$43$	0.330127	−	1.23205i	0.0503439	−	0.187886i	−0.936175	−	0.351535i	$-0.885660\pi$
$43$	0.330127	−	1.23205i	0.0503439	−	0.187886i	0.986519	+	0.163649i	$0.0523265\pi$
$44$	4.19615	−	4.19615i	0.632594	−	0.632594i
$45$	−3.00000	+	11.1962i	−0.447214	+	1.66902i
$46$	−1.26795	+	1.26795i	−0.186949	+	0.186949i
$47$	−4.83013	−	8.36603i	−0.704546	−	1.22031i	−0.966855	−	0.255326i	$-0.917817\pi$
$47$	−4.83013	−	8.36603i	−0.704546	−	1.22031i	0.262309	−	0.964984i	$-0.415516\pi$
$48$	−6.00000	−	3.46410i	−0.866025	−	0.500000i
$49$	−3.23205	+	5.59808i	−0.461722	+	0.799725i
$50$	−3.63397	−	13.5622i	−0.513922	−	1.91798i
$51$	3.40192	−	1.96410i	0.476365	−	0.275029i
$52$	−3.26795	+	12.1962i	−0.453183	+	1.69130i
$53$	−0.535898	−	0.535898i	−0.0736113	−	0.0736113i	0.669343	−	0.742954i	$-0.266576\pi$
$53$	−0.535898	−	0.535898i	−0.0736113	−	0.0736113i	−0.742954	+	0.669343i	$0.766576\pi$
$54$	7.09808	+	1.90192i	0.965926	+	0.258819i
$55$		−	11.4641i		−	1.54582i
$56$	0.535898	−	2.00000i	0.0716124	−	0.267261i
$57$	0.401924	−	1.50000i	0.0532361	−	0.198680i
$58$	−1.73205	+	3.00000i	−0.227429	+	0.393919i
$59$	4.96410	−	1.33013i	0.646271	−	0.173168i	0.0792287	−	0.996856i	$-0.474754\pi$
$59$	4.96410	−	1.33013i	0.646271	−	0.173168i	0.567042	+	0.823689i	$0.308088\pi$
$60$	−12.9282	+	3.46410i	−1.66902	+	0.447214i
$61$	−3.00000	−	0.803848i	−0.384111	−	0.102922i	0.0615961	−	0.998101i	$-0.480381\pi$
$61$	−3.00000	−	0.803848i	−0.384111	−	0.102922i	−0.445707	+	0.895179i	$0.647048\pi$
$62$	7.46410	+	7.46410i	0.947942	+	0.947942i
$63$			2.19615i			0.276689i
$64$		−	8.00000i		−	1.00000i
$65$	12.1962	+	21.1244i	1.51275	+	2.62015i
$66$	−7.26795			−0.894623
$67$	1.40192	+	5.23205i	0.171272	+	0.639197i	0.997157	+	0.0753572i	$0.0240097\pi$
$67$	1.40192	+	5.23205i	0.171272	+	0.639197i	−0.825884	+	0.563840i	$0.809324\pi$
$68$	3.92820	+	2.26795i	0.476365	+	0.275029i
$69$	2.19615			0.264386
$70$	−2.00000	−	3.46410i	−0.239046	−	0.414039i
$71$			10.9282i			1.29694i	0.761241	+	0.648470i	$0.224591\pi$
$71$			10.9282i			1.29694i	−0.761241	+	0.648470i	$0.775409\pi$
$72$	2.19615	+	8.19615i	0.258819	+	0.965926i
$73$			9.73205i			1.13905i	0.821974	+	0.569525i	$0.192873\pi$
$73$			9.73205i			1.13905i	−0.821974	+	0.569525i	$0.807127\pi$
$74$	2.19615	−	1.26795i	0.255298	−	0.147396i
$75$	−8.59808	+	14.8923i	−0.992820	+	1.71962i
$76$	1.73205	−	0.464102i	0.198680	−	0.0532361i
$77$	−0.562178	−	2.09808i	−0.0640661	−	0.239098i
$78$	13.3923	−	7.73205i	1.51638	−	0.875482i
$79$	−6.00000	−	10.3923i	−0.675053	−	1.16923i	−0.976453	−	0.215728i	$-0.930788\pi$
$79$	−6.00000	−	10.3923i	−0.675053	−	1.16923i	0.301401	−	0.953498i	$-0.402546\pi$
$80$	−10.9282	−	10.9282i	−1.22181	−	1.22181i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−3.00000	+	3.00000i	−0.331295	+	0.331295i
$83$	−1.36603	−	0.366025i	−0.149941	−	0.0401765i	0.183068	−	0.983100i	$-0.441397\pi$
$83$	−1.36603	−	0.366025i	−0.149941	−	0.0401765i	−0.333009	+	0.942924i	$0.608064\pi$
$84$	−2.19615	+	1.26795i	−0.239620	+	0.138345i
$85$	8.46410	−	2.26795i	0.918061	−	0.245994i
$86$	−1.56218	−	0.901924i	−0.168454	−	0.0972569i
$87$	4.09808	−	1.09808i	0.439360	−	0.117726i
$88$	−4.19615	−	7.26795i	−0.447311	−	0.774766i
$89$			2.00000i			0.212000i	0.994366	+	0.106000i	$0.0338043\pi$
$89$			2.00000i			0.212000i	−0.994366	+	0.106000i	$0.966196\pi$
$90$	14.1962	+	8.19615i	1.49641	+	0.863950i
$91$	3.26795	+	3.26795i	0.342574	+	0.342574i
$92$	1.26795	+	2.19615i	0.132193	+	0.228965i
$93$		−	12.9282i		−	1.34059i
$94$	−13.1962	+	3.53590i	−1.36108	+	0.364700i
$95$	1.73205	−	3.00000i	0.177705	−	0.307794i
$96$	−6.92820	+	6.92820i	−0.707107	+	0.707107i
$97$	−4.13397	−	7.16025i	−0.419742	−	0.727014i	0.576172	−	0.817329i	$-0.304546\pi$
$97$	−4.13397	−	7.16025i	−0.419742	−	0.727014i	−0.995913	+	0.0903150i	$0.971213\pi$
$98$	6.46410	+	6.46410i	0.652973	+	0.652973i
$99$	6.29423	+	6.29423i	0.632594	+	0.632594i
$100$	−19.8564			−1.98564
$101$	−2.00000	+	7.46410i	−0.199007	+	0.742706i	0.792186	+	0.610280i	$0.208943\pi$
$101$	−2.00000	+	7.46410i	−0.199007	+	0.742706i	−0.991193	+	0.132426i	$0.957723\pi$
$102$	−1.43782	−	5.36603i	−0.142366	−	0.531316i
$103$	−7.90192	−	4.56218i	−0.778600	−	0.449525i	0.0573341	−	0.998355i	$-0.481740\pi$
$103$	−7.90192	−	4.56218i	−0.778600	−	0.449525i	−0.835934	+	0.548830i	$0.815073\pi$
$104$	15.4641	+	8.92820i	1.51638	+	0.875482i
$105$	−1.26795	+	4.73205i	−0.123739	+	0.461801i
$106$	−0.928203	+	0.535898i	−0.0901551	+	0.0520511i
$107$	−13.4904	−	13.4904i	−1.30416	−	1.30416i	−0.925558	−	0.378607i	$-0.876403\pi$
$107$	−13.4904	−	13.4904i	−1.30416	−	1.30416i	−0.378607	−	0.925558i	$-0.623597\pi$
$108$	5.19615	−	9.00000i	0.500000	−	0.866025i
$109$	7.26795	−	7.26795i	0.696143	−	0.696143i	−0.267433	−	0.963576i	$-0.586175\pi$
$109$	7.26795	−	7.26795i	0.696143	−	0.696143i	0.963576	+	0.267433i	$0.0861754\pi$
$110$	−15.6603	−	4.19615i	−1.49315	−	0.400087i
$111$	−3.00000	−	0.803848i	−0.284747	−	0.0762978i
$112$	−2.53590	−	1.46410i	−0.239620	−	0.138345i
$113$	6.92820	−	12.0000i	0.651751	−	1.12887i	−0.330947	−	0.943649i	$-0.607368\pi$
$113$	6.92820	−	12.0000i	0.651751	−	1.12887i	0.982698	−	0.185216i	$-0.0592984\pi$
$114$	−1.90192	−	1.09808i	−0.178131	−	0.102844i
$115$	4.73205	+	1.26795i	0.441266	+	0.118237i
$116$	3.46410	+	3.46410i	0.321634	+	0.321634i
$117$	−18.2942	−	4.90192i	−1.69130	−	0.453183i
$118$		−	7.26795i		−	0.669069i
$119$	1.43782	−	0.830127i	0.131805	−	0.0760976i
$120$			18.9282i			1.72790i
$121$	1.90192	+	1.09808i	0.172902	+	0.0998251i
$122$	−2.19615	+	3.80385i	−0.198830	+	0.344384i
$123$	5.19615			0.468521
$124$	12.9282	−	7.46410i	1.16099	−	0.670296i
$125$	−13.4641	+	13.4641i	−1.20427	+	1.20427i
$126$	3.00000	+	0.803848i	0.267261	+	0.0716124i
$127$	−6.19615			−0.549820			−0.274910	−	0.961470i	$-0.588648\pi$
$127$	−6.19615			−0.549820			−0.274910	+	0.961470i	$0.588648\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$	0.571797	+	2.13397i	0.0503439	+	0.187886i
$130$	33.3205	−	8.92820i	2.92240	−	0.783055i
$131$	0.830127	+	3.09808i	0.0725285	+	0.270680i	0.992662	−	0.120926i	$-0.0385863\pi$
$131$	0.830127	+	3.09808i	0.0725285	+	0.270680i	−0.920133	+	0.391606i	$0.871920\pi$
$132$	−2.66025	+	9.92820i	−0.231545	+	0.864139i
$133$	0.169873	−	0.633975i	0.0147299	−	0.0549726i
$134$	7.66025			0.661745
$135$	−5.19615	−	19.3923i	−0.447214	−	1.66902i
$136$	4.53590	−	4.53590i	0.388950	−	0.388950i
$137$	14.2583	−	8.23205i	1.21817	−	0.703312i	0.253645	−	0.967297i	$-0.418371\pi$
$137$	14.2583	−	8.23205i	1.21817	−	0.703312i	0.964527	+	0.263986i	$0.0850372\pi$
$138$	0.803848	−	3.00000i	0.0684280	−	0.255377i
$139$	−9.06218	+	2.42820i	−0.768644	+	0.205958i	−0.621772	−	0.783198i	$-0.713587\pi$
$139$	−9.06218	+	2.42820i	−0.768644	+	0.205958i	−0.146872	+	0.989156i	$0.546920\pi$
$140$	−5.46410	+	1.46410i	−0.461801	+	0.123739i
$141$	14.4904	+	8.36603i	1.22031	+	0.704546i
$142$	14.9282	+	4.00000i	1.25275	+	0.335673i
$143$	18.7321			1.56645
$144$	12.0000			1.00000
$145$	9.46410			0.785951
$146$	13.2942	+	3.56218i	1.10024	+	0.294808i
$147$		−	11.1962i		−	0.923443i
$148$	−0.928203	−	3.46410i	−0.0762978	−	0.284747i
$149$	3.09808	−	0.830127i	0.253804	−	0.0680067i	−0.129674	−	0.991557i	$-0.541393\pi$
$149$	3.09808	−	0.830127i	0.253804	−	0.0680067i	0.383478	+	0.923550i	$0.374726\pi$
$150$	17.1962	+	17.1962i	1.40406	+	1.40406i
$151$	−2.36603	+	1.36603i	−0.192544	+	0.111166i	−0.593173	−	0.805075i	$-0.702125\pi$
$151$	−2.36603	+	1.36603i	−0.192544	+	0.111166i	0.400629	+	0.916240i	$0.368792\pi$
$152$		−	2.53590i		−	0.205689i
$153$	−3.40192	+	5.89230i	−0.275029	+	0.476365i
$154$	−3.07180			−0.247532
$155$	7.46410	−	27.8564i	0.599531	−	2.23748i
$156$	−5.66025	−	21.1244i	−0.453183	−	1.69130i
$157$	−1.26795	−	4.73205i	−0.101193	−	0.377659i	0.896692	−	0.442655i	$-0.145963\pi$
$157$	−1.26795	−	4.73205i	−0.101193	−	0.377659i	−0.997886	+	0.0649959i	$0.979297\pi$
$158$	−16.3923	+	4.39230i	−1.30410	+	0.349433i
$159$	1.26795	+	0.339746i	0.100555	+	0.0269436i
$160$	−18.9282	+	10.9282i	−1.49641	+	0.863950i
$161$	0.928203			0.0731527
$162$	−12.2942	+	3.29423i	−0.965926	+	0.258819i
$163$	−7.00000	+	7.00000i	−0.548282	+	0.548282i	−0.925944	−	0.377661i	$-0.876728\pi$
$163$	−7.00000	+	7.00000i	−0.548282	+	0.548282i	0.377661	+	0.925944i	$0.376728\pi$
$164$	3.00000	+	5.19615i	0.234261	+	0.405751i
$165$	9.92820	+	17.1962i	0.772910	+	1.33872i
$166$	−1.00000	+	1.73205i	−0.0776151	+	0.134433i
$167$	0.464102	+	0.267949i	0.0359133	+	0.0207345i	0.517849	−	0.855472i	$-0.326733\pi$
$167$	0.464102	+	0.267949i	0.0359133	+	0.0207345i	−0.481936	+	0.876206i	$0.660066\pi$
$168$	0.928203	+	3.46410i	0.0716124	+	0.267261i
$169$	−23.2583	+	13.4282i	−1.78910	+	1.03294i
$170$		−	12.3923i		−	0.950446i
$171$	0.696152	+	2.59808i	0.0532361	+	0.198680i
$172$	−1.80385	+	1.80385i	−0.137542	+	0.137542i
$173$	−12.5622	−	3.36603i	−0.955085	−	0.255914i	−0.252566	−	0.967580i	$-0.581275\pi$
$173$	−12.5622	−	3.36603i	−0.955085	−	0.255914i	−0.702519	+	0.711665i	$0.747941\pi$
$174$		−	6.00000i		−	0.454859i
$175$	−3.63397	+	6.29423i	−0.274703	+	0.475799i
$176$	−11.4641	+	3.07180i	−0.864139	+	0.231545i
$177$	−6.29423	+	6.29423i	−0.473103	+	0.473103i
$178$	2.73205	+	0.732051i	0.204776	+	0.0548695i
$179$	11.9282	−	11.9282i	0.891556	−	0.891556i	−0.103114	−	0.994670i	$-0.532881\pi$
$179$	11.9282	−	11.9282i	0.891556	−	0.891556i	0.994670	+	0.103114i	$0.0328806\pi$
$180$	16.3923	−	16.3923i	1.22181	−	1.22181i
$181$	13.3923	+	13.3923i	0.995442	+	0.995442i	0.999990	−	0.00454748i	$-0.00144751\pi$
$181$	13.3923	+	13.3923i	0.995442	+	0.995442i	−0.00454748	+	0.999990i	$0.501448\pi$
$182$	5.66025	−	3.26795i	0.419566	−	0.242237i
$183$	5.19615	−	1.39230i	0.384111	−	0.102922i
$184$	3.46410	−	0.928203i	0.255377	−	0.0684280i
$185$	−6.00000	−	3.46410i	−0.441129	−	0.254686i
$186$	−17.6603	−	4.73205i	−1.29491	−	0.346971i
$187$	1.74167	−	6.50000i	0.127364	−	0.475327i
$188$			19.3205i			1.40909i
$189$	−1.90192	−	3.29423i	−0.138345	−	0.239620i
$190$	−3.46410	−	3.46410i	−0.251312	−	0.251312i
$191$	7.02628	+	12.1699i	0.508404	+	0.880581i	0.999953	+	0.00973114i	$0.00309757\pi$
$191$	7.02628	+	12.1699i	0.508404	+	0.880581i	−0.491549	+	0.870850i	$0.663569\pi$
$192$	6.92820	+	12.0000i	0.500000	+	0.866025i
$193$	−9.13397	+	15.8205i	−0.657478	+	1.13879i	0.323789	+	0.946129i	$0.395043\pi$
$193$	−9.13397	+	15.8205i	−0.657478	+	1.13879i	−0.981266	+	0.192656i	$0.938290\pi$
$194$	−11.2942	+	3.02628i	−0.810878	+	0.217274i
$195$	−36.5885	−	21.1244i	−2.62015	−	1.51275i
$196$	11.1962	−	6.46410i	0.799725	−	0.461722i
$197$	−3.66025	−	3.66025i	−0.260782	−	0.260782i	0.564590	−	0.825372i	$-0.309034\pi$
$197$	−3.66025	−	3.66025i	−0.260782	−	0.260782i	−0.825372	+	0.564590i	$0.809034\pi$
$198$	10.9019	−	6.29423i	0.774766	−	0.447311i
$199$		−	0.875644i		−	0.0620728i	−0.999518	−	0.0310364i	$-0.990119\pi$
$199$		−	0.875644i		−	0.0620728i	0.999518	−	0.0310364i	$-0.00988078\pi$
$200$	−7.26795	+	27.1244i	−0.513922	+	1.91798i
$201$	−6.63397	−	6.63397i	−0.467924	−	0.467924i
$202$	9.46410	+	5.46410i	0.665892	+	0.384453i
$203$	1.73205	−	0.464102i	0.121566	−	0.0325735i
$204$	−7.85641			−0.550058
$205$	11.1962	+	3.00000i	0.781973	+	0.209529i
$206$	−9.12436	+	9.12436i	−0.635724	+	0.635724i
$207$	−3.29423	+	1.90192i	−0.228965	+	0.132193i
$208$	17.8564	−	17.8564i	1.23812	−	1.23812i
$209$	−1.33013	−	2.30385i	−0.0920068	−	0.159360i
$210$	6.00000	+	3.46410i	0.414039	+	0.239046i
$211$	−1.09808	−	4.09808i	−0.0755947	−	0.282123i	0.917773	−	0.397106i	$-0.129985\pi$
$211$	−1.09808	−	4.09808i	−0.0755947	−	0.282123i	−0.993367	+	0.114983i	$0.963319\pi$
$212$	0.392305	+	1.46410i	0.0269436	+	0.100555i
$213$	−9.46410	−	16.3923i	−0.648470	−	1.12318i
$214$	−23.3660	+	13.4904i	−1.59727	+	0.922183i
$215$			4.92820i			0.336101i
$216$	−10.3923	−	10.3923i	−0.707107	−	0.707107i
$217$		−	5.46410i		−	0.370927i
$218$	−7.26795	−	12.5885i	−0.492248	−	0.852598i
$219$	−8.42820	−	14.5981i	−0.569525	−	0.986447i
$220$	−11.4641	+	19.8564i	−0.772910	+	1.33872i
$221$	3.70577	+	13.8301i	0.249277	+	0.930315i
$222$	−2.19615	+	3.80385i	−0.147396	+	0.255298i
$223$	11.0263	+	19.0981i	0.738374	+	1.27890i	0.953227	+	0.302255i	$0.0977395\pi$
$223$	11.0263	+	19.0981i	0.738374	+	1.27890i	−0.214853	+	0.976646i	$0.568927\pi$
$224$	−2.92820	+	2.92820i	−0.195649	+	0.195649i
$225$		−	29.7846i		−	1.98564i
$226$	−13.8564	−	13.8564i	−0.921714	−	0.921714i
$227$	−14.4282	−	3.86603i	−0.957633	−	0.256597i	−0.254035	−	0.967195i	$-0.581758\pi$
$227$	−14.4282	−	3.86603i	−0.957633	−	0.256597i	−0.703598	+	0.710598i	$0.748425\pi$
$228$	−2.19615	+	2.19615i	−0.145444	+	0.145444i
$229$	6.83013	−	1.83013i	0.451347	−	0.120938i	−0.0259823	−	0.999662i	$-0.508271\pi$
$229$	6.83013	−	1.83013i	0.451347	−	0.120938i	0.477330	+	0.878724i	$0.341605\pi$
$230$	3.46410	−	6.00000i	0.228416	−	0.395628i
$231$	2.66025	+	2.66025i	0.175032	+	0.175032i
$232$	6.00000	−	3.46410i	0.393919	−	0.227429i
$233$		−	7.19615i		−	0.471436i	−0.971822	−	0.235718i	$-0.924256\pi$
$233$		−	7.19615i		−	0.471436i	0.971822	−	0.235718i	$-0.0757441\pi$
$234$	−13.3923	+	23.1962i	−0.875482	+	1.51638i
$235$	26.3923	+	26.3923i	1.72164	+	1.72164i
$236$	−9.92820	−	2.66025i	−0.646271	−	0.173168i
$237$	18.0000	+	10.3923i	1.16923	+	0.675053i
$238$	−0.607695	−	2.26795i	−0.0393910	−	0.147009i
$239$	−13.0981	+	22.6865i	−0.847244	+	1.46747i	0.0364139	+	0.999337i	$0.488407\pi$
$239$	−13.0981	+	22.6865i	−0.847244	+	1.46747i	−0.883658	+	0.468133i	$0.844927\pi$
$240$	25.8564	+	6.92820i	1.66902	+	0.447214i
$241$	−6.40192	−	11.0885i	−0.412384	−	0.714270i	0.582766	−	0.812640i	$-0.301971\pi$
$241$	−6.40192	−	11.0885i	−0.412384	−	0.714270i	−0.995150	+	0.0983699i	$0.968637\pi$
$242$	2.19615	−	2.19615i	0.141174	−	0.141174i
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	4.39230	+	4.39230i	0.281189	+	0.281189i
$245$	6.46410	−	24.1244i	0.412976	−	1.54125i
$246$	1.90192	−	7.09808i	0.121262	−	0.452557i
$247$	4.90192	+	2.83013i	0.311902	+	0.180077i
$248$	−5.46410	−	20.3923i	−0.346971	−	1.29491i
$249$	2.36603	−	0.633975i	0.149941	−	0.0401765i
$250$	13.4641	+	23.3205i	0.851545	+	1.47492i
$251$	2.83013	+	2.83013i	0.178636	+	0.178636i	0.790761	−	0.612125i	$-0.209685\pi$
$251$	2.83013	+	2.83013i	0.178636	+	0.178636i	−0.612125	+	0.790761i	$0.709685\pi$
$252$	2.19615	−	3.80385i	0.138345	−	0.239620i
$253$	2.66025	−	2.66025i	0.167249	−	0.167249i
$254$	−2.26795	+	8.46410i	−0.142304	+	0.531085i
$255$	−10.7321	+	10.7321i	−0.672067	+	0.672067i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−4.42820	+	7.66987i	−0.276224	+	0.478434i	−0.970443	−	0.241330i	$-0.922416\pi$
$257$	−4.42820	+	7.66987i	−0.276224	+	0.478434i	0.694219	+	0.719763i	$0.255750\pi$
$258$	3.12436			0.194514
$259$	−1.26795	−	0.339746i	−0.0787865	−	0.0211108i
$260$		−	48.7846i		−	3.02549i
$261$	−5.19615	+	5.19615i	−0.321634	+	0.321634i
$262$	4.53590			0.280229
$263$	−23.4904	+	13.5622i	−1.44848	+	0.836280i	−0.998391	−	0.0567045i	$-0.981941\pi$
$263$	−23.4904	+	13.5622i	−1.44848	+	0.836280i	−0.450088	+	0.892984i	$0.648607\pi$
$264$	12.5885	+	7.26795i	0.774766	+	0.447311i
$265$	2.53590	+	1.46410i	0.155779	+	0.0899390i
$266$	−0.803848	−	0.464102i	−0.0492871	−	0.0284559i
$267$	−1.73205	−	3.00000i	−0.106000	−	0.183597i
$268$	2.80385	−	10.4641i	0.171272	−	0.639197i
$269$	4.73205	−	4.73205i	0.288518	−	0.288518i	−0.547976	−	0.836494i	$-0.684601\pi$
$269$	4.73205	−	4.73205i	0.288518	−	0.288518i	0.836494	+	0.547976i	$0.184601\pi$
$270$	−28.3923			−1.72790
$271$	20.3923			1.23874			0.619372	−	0.785098i	$-0.287387\pi$
$271$	20.3923			1.23874			0.619372	+	0.785098i	$0.287387\pi$
$272$	−4.53590	−	7.85641i	−0.275029	−	0.476365i
$273$	−7.73205	−	2.07180i	−0.467965	−	0.125391i
$274$	−6.02628	−	22.4904i	−0.364061	−	1.35869i
$275$	7.62436	+	28.4545i	0.459766	+	1.71587i
$276$	−3.80385	−	2.19615i	−0.228965	−	0.132193i
$277$	−4.22243	+	15.7583i	−0.253701	+	0.946826i	0.715107	+	0.699015i	$0.246378\pi$
$277$	−4.22243	+	15.7583i	−0.253701	+	0.946826i	−0.968808	+	0.247811i	$0.920289\pi$
$278$			13.2679i			0.795759i
$279$	11.1962	+	19.3923i	0.670296	+	1.16099i
$280$			8.00000i			0.478091i
$281$	−8.66025	+	5.00000i	−0.516627	+	0.298275i	−0.735554	−	0.677466i	$-0.763078\pi$
$281$	−8.66025	+	5.00000i	−0.516627	+	0.298275i	0.218926	+	0.975741i	$0.429745\pi$
$282$	16.7321	−	16.7321i	0.996379	−	0.996379i
$283$	27.7583	−	7.43782i	1.65006	−	0.442133i	0.690431	−	0.723398i	$-0.257421\pi$
$283$	27.7583	−	7.43782i	1.65006	−	0.442133i	0.959630	+	0.281265i	$0.0907541\pi$
$284$	10.9282	−	18.9282i	0.648470	−	1.12318i
$285$			6.00000i			0.355409i
$286$	6.85641	−	25.5885i	0.405428	−	1.51308i
$287$	2.19615			0.129635
$288$	4.39230	−	16.3923i	0.258819	−	0.965926i
$289$	−11.8564			−0.697436
$290$	3.46410	−	12.9282i	0.203419	−	0.759170i
$291$	12.4019	+	7.16025i	0.727014	+	0.419742i
$292$	9.73205	−	16.8564i	0.569525	−	0.986447i
$293$	13.5622	−	3.63397i	0.792311	−	0.212299i	0.160106	−	0.987100i	$-0.448817\pi$
$293$	13.5622	−	3.63397i	0.792311	−	0.212299i	0.632205	+	0.774801i	$0.282150\pi$
$294$	−15.2942	−	4.09808i	−0.891978	−	0.239005i
$295$	−17.1962	+	9.92820i	−1.00120	+	0.578042i
$296$	−5.07180			−0.294792
$297$	−14.8923	−	3.99038i	−0.864139	−	0.231545i
$298$		−	4.53590i		−	0.262758i
$299$	−2.07180	+	7.73205i	−0.119815	+	0.447156i
$300$	29.7846	−	17.1962i	1.71962	−	0.992820i
$301$	0.241670	+	0.901924i	0.0139296	+	0.0519860i
$302$	1.00000	+	3.73205i	0.0575435	+	0.214755i
$303$	−3.46410	−	12.9282i	−0.199007	−	0.742706i
$304$	−3.46410	−	0.928203i	−0.198680	−	0.0532361i
$305$	12.0000			0.687118
$306$	6.80385	+	6.80385i	0.388950	+	0.388950i
$307$	−16.0263	+	16.0263i	−0.914668	+	0.914668i	−0.996635	−	0.0819670i	$-0.973880\pi$
$307$	−16.0263	+	16.0263i	−0.914668	+	0.914668i	0.0819670	+	0.996635i	$0.473880\pi$
$308$	−1.12436	+	4.19615i	−0.0640661	+	0.239098i
$309$	15.8038			0.899049
$310$	−35.3205	−	20.3923i	−2.00607	−	1.15821i
$311$	13.9019	+	8.02628i	0.788306	+	0.455129i	0.839366	−	0.543567i	$-0.182927\pi$
$311$	13.9019	+	8.02628i	0.788306	+	0.455129i	−0.0510600	+	0.998696i	$0.516260\pi$
$312$	−30.9282			−1.75096
$313$	24.6506	−	14.2321i	1.39334	−	0.804443i	0.399653	−	0.916666i	$-0.369131\pi$
$313$	24.6506	−	14.2321i	1.39334	−	0.804443i	0.993683	+	0.112223i	$0.0357972\pi$
$314$	−6.92820			−0.390981
$315$	−2.19615	−	8.19615i	−0.123739	−	0.461801i
$316$			24.0000i			1.35011i
$317$	31.4904	+	8.43782i	1.76868	+	0.473915i	0.988445	−	0.151577i	$-0.0484351\pi$
$317$	31.4904	+	8.43782i	1.76868	+	0.473915i	0.780231	+	0.625492i	$0.215102\pi$
$318$	0.928203	−	1.60770i	0.0520511	−	0.0901551i
$319$	3.63397	−	6.29423i	0.203464	−	0.352409i
$320$	8.00000	+	29.8564i	0.447214	+	1.66902i
$321$	31.9186	+	8.55256i	1.78152	+	0.477357i
$322$	0.339746	−	1.26795i	0.0189333	−	0.0706600i
$323$	1.43782	−	1.43782i	0.0800026	−	0.0800026i
$324$			18.0000i			1.00000i
$325$	−44.3205	−	44.3205i	−2.45846	−	2.45846i
$326$	7.00000	+	12.1244i	0.387694	+	0.671506i
$327$	−4.60770	+	17.1962i	−0.254806	+	0.950949i
$328$	8.19615	−	2.19615i	0.452557	−	0.121262i
$329$	6.12436	+	3.53590i	0.337647	+	0.194940i
$330$	27.1244	−	7.26795i	1.49315	−	0.400087i
$331$	5.09808	−	19.0263i	0.280216	−	1.04578i	−0.672049	−	0.740506i	$-0.734586\pi$
$331$	5.09808	−	19.0263i	0.280216	−	1.04578i	0.952265	−	0.305273i	$-0.0987476\pi$
$332$	2.00000	+	2.00000i	0.109764	+	0.109764i
$333$	5.19615	−	1.39230i	0.284747	−	0.0762978i
$334$	0.535898	−	0.535898i	0.0293231	−	0.0293231i
$335$	−10.4641	−	18.1244i	−0.571715	−	0.990239i
$336$	5.07180			0.276689
$337$	−11.8923	+	20.5981i	−0.647815	+	1.12205i	0.335829	+	0.941923i	$0.390984\pi$
$337$	−11.8923	+	20.5981i	−0.647815	+	1.12205i	−0.983644	+	0.180126i	$0.942350\pi$
$338$	9.83013	+	36.6865i	0.534688	+	1.99548i
$339$			24.0000i			1.30350i
$340$	−16.9282	−	4.53590i	−0.918061	−	0.245994i
$341$	−15.6603	−	15.6603i	−0.848050	−	0.848050i
$342$	3.80385			0.205689
$343$		−	9.85641i		−	0.532196i
$344$	1.80385	+	3.12436i	0.0972569	+	0.168454i
$345$	−8.19615	+	2.19615i	−0.441266	+	0.118237i
$346$	−9.19615	+	15.9282i	−0.494388	+	0.856306i
$347$	−24.7224	+	6.62436i	−1.32717	+	0.355614i	−0.851659	−	0.524096i	$-0.824403\pi$
$347$	−24.7224	+	6.62436i	−1.32717	+	0.355614i	−0.475510	+	0.879710i	$0.657737\pi$
$348$	−8.19615	−	2.19615i	−0.439360	−	0.117726i
$349$	−7.73205	−	2.07180i	−0.413887	−	0.110901i	0.0458657	−	0.998948i	$-0.485395\pi$
$349$	−7.73205	−	2.07180i	−0.413887	−	0.110901i	−0.459753	+	0.888047i	$0.652062\pi$
$350$	7.26795	+	7.26795i	0.388488	+	0.388488i
$351$	31.6865	−	8.49038i	1.69130	−	0.453183i
$352$			16.7846i			0.894623i
$353$	−10.1603	−	17.5981i	−0.540776	−	0.936651i	−0.998860	−	0.0477421i	$-0.984797\pi$
$353$	−10.1603	−	17.5981i	−0.540776	−	0.936651i	0.458084	−	0.888909i	$-0.348536\pi$
$354$	6.29423	+	10.9019i	0.334534	+	0.579431i
$355$	−10.9282	−	40.7846i	−0.580009	−	2.16462i
$356$	2.00000	−	3.46410i	0.106000	−	0.183597i
$357$	−1.43782	+	2.49038i	−0.0760976	+	0.131805i
$358$	−11.9282	−	20.6603i	−0.630425	−	1.09193i
$359$		−	14.7321i		−	0.777528i	−0.921337	−	0.388764i	$-0.872902\pi$
$359$		−	14.7321i		−	0.777528i	0.921337	−	0.388764i	$-0.127098\pi$
$360$	−16.3923	−	28.3923i	−0.863950	−	1.49641i
$361$			18.1962i			0.957692i
$362$	23.1962	−	13.3923i	1.21916	−	0.703884i
$363$	−3.80385			−0.199650
$364$	−2.39230	−	8.92820i	−0.125391	−	0.467965i
$365$	−9.73205	−	36.3205i	−0.509399	−	1.90110i
$366$		−	7.60770i		−	0.397661i
$367$	−10.1244	−	17.5359i	−0.528487	−	0.915366i	−0.999448	−	0.0332125i	$-0.989426\pi$
$367$	−10.1244	−	17.5359i	−0.528487	−	0.915366i	0.470961	−	0.882154i	$-0.343907\pi$
$368$		−	5.07180i		−	0.264386i
$369$	−7.79423	+	4.50000i	−0.405751	+	0.234261i
$370$	−6.92820	+	6.92820i	−0.360180	+	0.360180i
$371$	0.535898	+	0.143594i	0.0278225	+	0.00745501i
$372$	−12.9282	+	22.3923i	−0.670296	+	1.16099i
$373$	−5.63397	+	1.50962i	−0.291716	+	0.0781651i	−0.401709	−	0.915767i	$-0.631584\pi$
$373$	−5.63397	+	1.50962i	−0.291716	+	0.0781651i	0.109993	+	0.993932i	$0.464917\pi$
$374$	−8.24167	−	4.75833i	−0.426167	−	0.246047i
$375$	8.53590	−	31.8564i	0.440792	−	1.64506i
$376$	26.3923	+	7.07180i	1.36108	+	0.364700i
$377$			15.4641i			0.796442i
$378$	−5.19615	+	1.39230i	−0.267261	+	0.0716124i
$379$	−18.7583	−	18.7583i	−0.963551	−	0.963551i	0.0358080	−	0.999359i	$-0.488600\pi$
$379$	−18.7583	−	18.7583i	−0.963551	−	0.963551i	−0.999359	+	0.0358080i	$0.988600\pi$
$380$	−6.00000	+	3.46410i	−0.307794	+	0.177705i
$381$	9.29423	−	5.36603i	0.476158	−	0.274910i
$382$	19.1962	−	5.14359i	0.982161	−	0.263169i
$383$	−3.26795	+	5.66025i	−0.166984	+	0.289225i	−0.937358	−	0.348367i	$-0.886736\pi$
$383$	−3.26795	+	5.66025i	−0.166984	+	0.289225i	0.770374	+	0.637593i	$0.220070\pi$
$384$	18.9282	−	5.07180i	0.965926	−	0.258819i
$385$	4.19615	+	7.26795i	0.213856	+	0.370409i
$386$	18.2679	+	18.2679i	0.929814	+	0.929814i
$387$	−2.70577	−	2.70577i	−0.137542	−	0.137542i
$388$			16.5359i			0.839483i
$389$	−2.75833	+	10.2942i	−0.139853	+	0.521938i	0.860078	+	0.510163i	$0.170415\pi$
$389$	−2.75833	+	10.2942i	−0.139853	+	0.521938i	−0.999931	+	0.0117752i	$0.996252\pi$
$390$	−42.2487	+	42.2487i	−2.13935	+	2.13935i
$391$	2.49038	+	1.43782i	0.125944	+	0.0727138i
$392$	−4.73205	−	17.6603i	−0.239005	−	0.891978i
$393$	−3.92820	−	3.92820i	−0.198152	−	0.198152i
$394$	−6.33975	+	3.66025i	−0.319392	+	0.184401i
$395$	32.7846	+	32.7846i	1.64957	+	1.64957i
$396$	−4.60770	−	17.1962i	−0.231545	−	0.864139i
$397$	−12.7321	+	12.7321i	−0.639003	+	0.639003i	−0.950310	−	0.311306i	$-0.899233\pi$
$397$	−12.7321	+	12.7321i	−0.639003	+	0.639003i	0.311306	+	0.950310i	$0.399233\pi$
$398$	−1.19615	−	0.320508i	−0.0599577	−	0.0160656i
$399$	0.294229	+	1.09808i	0.0147299	+	0.0549726i
$400$	34.3923	+	19.8564i	1.71962	+	0.992820i
$401$	13.7942	−	23.8923i	0.688851	−	1.19312i	−0.283359	−	0.959014i	$-0.591449\pi$
$401$	13.7942	−	23.8923i	0.688851	−	1.19312i	0.972210	−	0.234111i	$-0.0752179\pi$
$402$	−11.4904	+	6.63397i	−0.573088	+	0.330873i
$403$	45.5167	+	12.1962i	2.26735	+	0.607534i
$404$	10.9282	−	10.9282i	0.543698	−	0.543698i
$405$	24.5885	+	24.5885i	1.22181	+	1.22181i
$406$		−	2.53590i		−	0.125855i
$407$	−4.60770	+	2.66025i	−0.228395	+	0.131864i
$408$	−2.87564	+	10.7321i	−0.142366	+	0.531316i
$409$	−26.1340	−	15.0885i	−1.29224	−	0.746076i	−0.313191	−	0.949690i	$-0.601398\pi$
$409$	−26.1340	−	15.0885i	−1.29224	−	0.746076i	−0.979051	+	0.203614i	$0.934731\pi$
$410$	8.19615	−	14.1962i	0.404779	−	0.701098i
$411$	−14.2583	+	24.6962i	−0.703312	+	1.21817i
$412$	9.12436	+	15.8038i	0.449525	+	0.778600i
$413$	−2.66025	+	2.66025i	−0.130903	+	0.130903i
$414$	1.39230	+	5.19615i	0.0684280	+	0.255377i
$415$	5.46410			0.268222
$416$	−17.8564	−	30.9282i	−0.875482	−	1.51638i
$417$	11.4904	−	11.4904i	0.562686	−	0.562686i
$418$	−3.63397	+	0.973721i	−0.177744	+	0.0476262i
$419$	−8.36603	−	31.2224i	−0.408707	−	1.52532i	−0.797115	−	0.603828i	$-0.793641\pi$
$419$	−8.36603	−	31.2224i	−0.408707	−	1.52532i	0.388408	−	0.921488i	$-0.373025\pi$
$420$	6.92820	−	6.92820i	0.338062	−	0.338062i
$421$	0.588457	−	2.19615i	0.0286797	−	0.107034i	−0.950102	−	0.311938i	$-0.899022\pi$
$421$	0.588457	−	2.19615i	0.0286797	−	0.107034i	0.978782	+	0.204905i	$0.0656884\pi$
$422$	−6.00000			−0.292075
$423$	−28.9808			−1.40909
$424$	2.14359			0.104102
$425$	−19.5000	+	11.2583i	−0.945889	+	0.546109i
$426$	−25.8564	+	6.92820i	−1.25275	+	0.335673i
$427$	2.19615	−	0.588457i	0.106279	−	0.0284774i
$428$	9.87564	+	36.8564i	0.477357	+	1.78152i
$429$	−28.0981	+	16.2224i	−1.35659	+	0.783226i
$430$	6.73205	+	1.80385i	0.324648	+	0.0869893i
$431$	−5.80385			−0.279562			−0.139781	−	0.990182i	$-0.544640\pi$
$431$	−5.80385			−0.279562			−0.139781	+	0.990182i	$0.544640\pi$
$432$	−18.0000	+	10.3923i	−0.866025	+	0.500000i
$433$	−2.26795			−0.108991			−0.0544953	−	0.998514i	$-0.517355\pi$
$433$	−2.26795			−0.108991			−0.0544953	+	0.998514i	$0.517355\pi$
$434$	−7.46410	−	2.00000i	−0.358288	−	0.0960031i
$435$	−14.1962	+	8.19615i	−0.680653	+	0.392975i
$436$	−19.8564	+	5.32051i	−0.950949	+	0.254806i
$437$	1.09808	−	0.294229i	0.0525281	−	0.0140749i
$438$	−23.0263	+	6.16987i	−1.10024	+	0.294808i
$439$	−4.85641	+	2.80385i	−0.231784	+	0.133820i	−0.611395	−	0.791326i	$-0.709391\pi$
$439$	−4.85641	+	2.80385i	−0.231784	+	0.133820i	0.379611	+	0.925146i	$0.376058\pi$
$440$	22.9282	+	22.9282i	1.09306	+	1.09306i
$441$	9.69615	+	16.7942i	0.461722	+	0.799725i
$442$	20.2487			0.963133
$443$	−5.25833	+	19.6244i	−0.249831	+	0.932381i	0.721063	+	0.692870i	$0.243654\pi$
$443$	−5.25833	+	19.6244i	−0.249831	+	0.932381i	−0.970894	+	0.239511i	$0.923013\pi$
$444$	4.39230	+	4.39230i	0.208450	+	0.208450i
$445$	−2.00000	−	7.46410i	−0.0948091	−	0.353832i
$446$	30.1244	−	8.07180i	1.42643	−	0.382211i
$447$	−3.92820	+	3.92820i	−0.185798	+	0.185798i
$448$	2.92820	+	5.07180i	0.138345	+	0.239620i
$449$	−20.6603			−0.975018			−0.487509	−	0.873118i	$-0.662094\pi$
$449$	−20.6603			−0.975018			−0.487509	+	0.873118i	$0.662094\pi$
$450$	−40.6865	−	10.9019i	−1.91798	−	0.513922i
$451$	6.29423	−	6.29423i	0.296384	−	0.296384i
$452$	−24.0000	+	13.8564i	−1.12887	+	0.651751i
$453$	2.36603	−	4.09808i	0.111166	−	0.192544i
$454$	−10.5622	+	18.2942i	−0.495708	+	0.858591i
$455$	−15.4641	−	8.92820i	−0.724968	−	0.418561i
$456$	2.19615	+	3.80385i	0.102844	+	0.178131i
$457$	20.2583	−	11.6962i	0.947645	−	0.547123i	0.0552962	−	0.998470i	$-0.482390\pi$
$457$	20.2583	−	11.6962i	0.947645	−	0.547123i	0.892348	+	0.451347i	$0.149056\pi$
$458$		−	10.0000i		−	0.467269i
$459$		−	11.7846i		−	0.550058i
$460$	−6.92820	−	6.92820i	−0.323029	−	0.323029i
$461$	2.56218	+	0.686533i	0.119333	+	0.0319751i	0.317991	−	0.948094i	$-0.396992\pi$
$461$	2.56218	+	0.686533i	0.119333	+	0.0319751i	−0.198659	+	0.980069i	$0.563658\pi$
$462$	4.60770	−	2.66025i	0.214369	−	0.123766i
$463$	−9.19615	+	15.9282i	−0.427381	+	0.740246i	−0.996640	−	0.0819125i	$-0.973897\pi$
$463$	−9.19615	+	15.9282i	−0.427381	+	0.740246i	0.569258	+	0.822159i	$0.307231\pi$
$464$	−2.53590	−	9.46410i	−0.117726	−	0.439360i
$465$	12.9282	+	48.2487i	0.599531	+	2.23748i
$466$	−9.83013	−	2.63397i	−0.455372	−	0.122017i
$467$	4.36603	−	4.36603i	0.202036	−	0.202036i	−0.598836	−	0.800872i	$-0.704370\pi$
$467$	4.36603	−	4.36603i	0.202036	−	0.202036i	0.800872	+	0.598836i	$0.204370\pi$
$468$	26.7846	+	26.7846i	1.23812	+	1.23812i
$469$	−2.80385	−	2.80385i	−0.129470	−	0.129470i
$470$	45.7128	−	26.3923i	2.10857	−	1.21739i
$471$	6.00000	+	6.00000i	0.276465	+	0.276465i
$472$	−7.26795	+	12.5885i	−0.334534	+	0.579431i
$473$	3.27757	+	1.89230i	0.150703	+	0.0870083i
$474$	20.7846	−	20.7846i	0.954669	−	0.954669i
$475$	−2.30385	+	8.59808i	−0.105708	+	0.394507i
$476$	−3.32051			−0.152195
$477$	−2.19615	+	0.588457i	−0.100555	+	0.0269436i
$478$	26.1962	+	26.1962i	1.19818	+	1.19818i
$479$	12.8301	+	22.2224i	0.586223	+	1.01537i	0.994722	+	0.102610i	$0.0327193\pi$
$479$	12.8301	+	22.2224i	0.586223	+	1.01537i	−0.408498	+	0.912759i	$0.633947\pi$
$480$	18.9282	−	32.7846i	0.863950	−	1.49641i
$481$	5.66025	−	9.80385i	0.258085	−	0.447017i
$482$	−17.4904	+	4.68653i	−0.796665	+	0.213466i
$483$	−1.39230	+	0.803848i	−0.0633521	+	0.0365763i
$484$	−2.19615	−	3.80385i	−0.0998251	−	0.172902i
$485$	22.5885	+	22.5885i	1.02569	+	1.02569i
$486$	15.5885	−	15.5885i	0.707107	−	0.707107i
$487$		−	16.1962i		−	0.733918i	−0.930237	−	0.366959i	$-0.880399\pi$
$487$		−	16.1962i		−	0.733918i	0.930237	−	0.366959i	$-0.119601\pi$
$488$	7.60770	−	4.39230i	0.344384	−	0.198830i
$489$	4.43782	−	16.5622i	0.200685	−	0.748968i
$490$	−30.5885	−	17.6603i	−1.38185	−	0.797809i
$491$	−25.7224	+	6.89230i	−1.16084	+	0.311045i	−0.787300	−	0.616570i	$-0.788522\pi$
$491$	−25.7224	+	6.89230i	−1.16084	+	0.311045i	−0.373537	+	0.927615i	$0.621855\pi$
$492$	−9.00000	−	5.19615i	−0.405751	−	0.234261i
$493$	5.36603	+	1.43782i	0.241674	+	0.0647563i
$494$	5.66025	−	5.66025i	0.254667	−	0.254667i
$495$	−29.7846	−	17.1962i	−1.33872	−	0.772910i
$496$	−29.8564			−1.34059
$497$	−4.00000	−	6.92820i	−0.179425	−	0.310772i
$498$		−	3.46410i		−	0.155230i
$499$	−1.69615	−	6.33013i	−0.0759302	−	0.283375i	0.917512	−	0.397707i	$-0.130194\pi$
$499$	−1.69615	−	6.33013i	−0.0759302	−	0.283375i	−0.993443	+	0.114332i	$0.963527\pi$
$500$	36.7846	−	9.85641i	1.64506	−	0.440792i
$501$	−0.928203			−0.0414691
$502$	4.90192	−	2.83013i	0.218784	−	0.126315i
$503$		−	27.7128i		−	1.23565i	−0.786314	−	0.617827i	$-0.788013\pi$
$503$		−	27.7128i		−	1.23565i	0.786314	−	0.617827i	$-0.211987\pi$
$504$	−4.39230	−	4.39230i	−0.195649	−	0.195649i
$505$		−	29.8564i		−	1.32859i
$506$	−2.66025	−	4.60770i	−0.118263	−	0.204837i
$507$	23.2583	−	40.2846i	1.03294	−	1.78910i
$508$	10.7321	+	6.19615i	0.476158	+	0.274910i
$509$	−4.53590	−	16.9282i	−0.201050	−	0.750329i	−0.990617	−	0.136665i	$-0.956362\pi$
$509$	−4.53590	−	16.9282i	−0.201050	−	0.750329i	0.789567	−	0.613664i	$-0.210305\pi$
$510$	10.7321	+	18.5885i	0.475223	+	0.823111i
$511$	−3.56218	−	6.16987i	−0.157581	−	0.272939i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−3.29423	−	3.29423i	−0.145444	−	0.145444i
$514$	8.85641	+	8.85641i	0.390639	+	0.390639i
$515$	34.0526	+	9.12436i	1.50054	+	0.402067i
$516$	1.14359	−	4.26795i	0.0503439	−	0.187886i
$517$	27.6865	−	7.41858i	1.21765	−	0.326269i
$518$	−0.928203	+	1.60770i	−0.0407829	+	0.0706381i
$519$	21.7583	−	5.83013i	0.955085	−	0.255914i
$520$	−66.6410	−	17.8564i	−2.92240	−	0.783055i
$521$		−	13.0000i		−	0.569540i	−0.958596	−	0.284770i	$-0.908083\pi$
$521$		−	13.0000i		−	0.569540i	0.958596	−	0.284770i	$-0.0919173\pi$
$522$	5.19615	+	9.00000i	0.227429	+	0.393919i
$523$	−14.4641	−	14.4641i	−0.632471	−	0.632471i	0.316216	−	0.948687i	$-0.397588\pi$
$523$	−14.4641	−	14.4641i	−0.632471	−	0.632471i	−0.948687	+	0.316216i	$0.897588\pi$
$524$	1.66025	−	6.19615i	0.0725285	−	0.270680i
$525$		−	12.5885i		−	0.549405i
$526$	9.92820	+	37.0526i	0.432890	+	1.61557i
$527$	8.46410	−	14.6603i	0.368702	−	0.638611i
$528$	14.5359	−	14.5359i	0.632594	−	0.632594i
$529$	−10.6962	−	18.5263i	−0.465050	−	0.805490i
$530$	2.92820	−	2.92820i	0.127193	−	0.127193i
$531$	3.99038	−	14.8923i	0.173168	−	0.646271i
$532$	−0.928203	+	0.928203i	−0.0402427	+	0.0402427i
$533$	−4.90192	+	18.2942i	−0.212326	+	0.792411i
$534$	−4.73205	+	1.26795i	−0.204776	+	0.0548695i
$535$	63.8372	+	36.8564i	2.75992	+	1.59344i
$536$	−13.2679	−	7.66025i	−0.573088	−	0.330873i
$537$	−7.56218	+	28.2224i	−0.326332	+	1.21789i
$538$	−4.73205	−	8.19615i	−0.204013	−	0.353361i
$539$	−13.5622	−	13.5622i	−0.584164	−	0.584164i
$540$	−10.3923	+	38.7846i	−0.447214	+	1.66902i
$541$	−8.19615	+	8.19615i	−0.352380	+	0.352380i	−0.860994	−	0.508614i	$-0.830158\pi$
$541$	−8.19615	+	8.19615i	−0.352380	+	0.352380i	0.508614	+	0.860994i	$0.330158\pi$
$542$	7.46410	−	27.8564i	0.320611	−	1.19654i
$543$	−31.6865	−	8.49038i	−1.35980	−	0.364357i
$544$	−12.3923	+	3.32051i	−0.531316	+	0.142366i
$545$	−19.8564	+	34.3923i	−0.850555	+	1.47320i
$546$	−5.66025	+	9.80385i	−0.242237	+	0.419566i
$547$	−31.2583	−	8.37564i	−1.33651	−	0.358117i	−0.481371	−	0.876517i	$-0.659861\pi$
$547$	−31.2583	−	8.37564i	−1.33651	−	0.358117i	−0.855138	+	0.518400i	$0.826528\pi$
$548$	−32.9282			−1.40662
$549$	−6.58846	+	6.58846i	−0.281189	+	0.281189i
$550$	41.6603			1.77640
$551$	1.90192	−	1.09808i	0.0810247	−	0.0467796i
$552$	−4.39230	+	4.39230i	−0.186949	+	0.186949i
$553$	7.60770	+	4.39230i	0.323512	+	0.186780i
$554$	19.9808	+	11.5359i	0.848901	+	0.490113i
$555$	12.0000			0.509372
$556$	18.1244	+	4.85641i	0.768644	+	0.205958i
$557$	−25.1962	+	25.1962i	−1.06760	+	1.06760i	−0.0700519	+	0.997543i	$0.522316\pi$
$557$	−25.1962	+	25.1962i	−1.06760	+	1.06760i	−0.997543	+	0.0700519i	$0.977684\pi$
$558$	30.5885	−	8.19615i	1.29491	−	0.346971i
$559$	−8.05256			−0.340587
$560$	10.9282	+	2.92820i	0.461801	+	0.123739i
$561$	3.01666	+	11.2583i	0.127364	+	0.475327i
$562$	3.66025	+	13.6603i	0.154398	+	0.576223i
$563$	1.00962	+	3.76795i	0.0425504	+	0.158800i	0.983932	−	0.178543i	$-0.0571384\pi$
$563$	1.00962	+	3.76795i	0.0425504	+	0.158800i	−0.941382	+	0.337343i	$0.890472\pi$
$564$	−16.7321	−	28.9808i	−0.704546	−	1.22031i
$565$	−13.8564	+	51.7128i	−0.582943	+	2.17557i
$566$		−	40.6410i		−	1.70827i
$567$	5.70577	+	3.29423i	0.239620	+	0.138345i
$568$	−21.8564	−	21.8564i	−0.917074	−	0.917074i
$569$	23.5981	−	13.6244i	0.989283	−	0.571163i	0.0842230	−	0.996447i	$-0.473159\pi$
$569$	23.5981	−	13.6244i	0.989283	−	0.571163i	0.905060	+	0.425284i	$0.139826\pi$
$570$	8.19615	+	2.19615i	0.343299	+	0.0919867i
$571$	−19.8923	+	5.33013i	−0.832467	+	0.223059i	−0.649790	−	0.760114i	$-0.725143\pi$
$571$	−19.8923	+	5.33013i	−0.832467	+	0.223059i	−0.182677	+	0.983173i	$0.558476\pi$
$572$	−32.4449	−	18.7321i	−1.35659	−	0.783226i
$573$	−21.0788	−	12.1699i	−0.880581	−	0.508404i
$574$	0.803848	−	3.00000i	0.0335519	−	0.125218i
$575$	−12.5885			−0.524975
$576$	−20.7846	−	12.0000i	−0.866025	−	0.500000i
$577$	35.7846			1.48973			0.744866	−	0.667214i	$-0.232513\pi$
$577$	35.7846			1.48973			0.744866	+	0.667214i	$0.232513\pi$
$578$	−4.33975	+	16.1962i	−0.180510	+	0.673671i
$579$		−	31.6410i		−	1.31496i
$580$	−16.3923	−	9.46410i	−0.680653	−	0.392975i
$581$	1.00000	−	0.267949i	0.0414870	−	0.0111164i
$582$	14.3205	−	14.3205i	0.593604	−	0.593604i
$583$	1.94744	−	1.12436i	0.0806548	−	0.0465661i
$584$	−19.4641	−	19.4641i	−0.805430	−	0.805430i
$585$	73.1769			3.02549
$586$		−	19.8564i		−	0.820261i
$587$	−1.00962	+	3.76795i	−0.0416714	+	0.155520i	−0.983626	−	0.180219i	$-0.942319\pi$
$587$	−1.00962	+	3.76795i	−0.0416714	+	0.155520i	0.941955	+	0.335739i	$0.108986\pi$
$588$	−11.1962	+	19.3923i	−0.461722	+	0.799725i
$589$	−1.73205	−	6.46410i	−0.0713679	−	0.266349i
$590$	7.26795	+	27.1244i	0.299217	+	1.11669i
$591$	8.66025	+	2.32051i	0.356235	+	0.0954529i
$592$	−1.85641	+	6.92820i	−0.0762978	+	0.284747i
$593$	10.5359			0.432657			0.216329	−	0.976321i	$-0.430592\pi$
$593$	10.5359			0.432657			0.216329	+	0.976321i	$0.430592\pi$
$594$	−10.9019	+	18.8827i	−0.447311	+	0.774766i
$595$	−4.53590	+	4.53590i	−0.185954	+	0.185954i
$596$	−6.19615	−	1.66025i	−0.253804	−	0.0680067i
$597$	0.758330	+	1.31347i	0.0310364	+	0.0537566i
$598$	9.80385	+	5.66025i	0.400909	+	0.231465i
$599$	23.3205	+	13.4641i	0.952850	+	0.550128i	0.893965	−	0.448136i	$-0.147912\pi$
$599$	23.3205	+	13.4641i	0.952850	+	0.550128i	0.0588850	+	0.998265i	$0.481245\pi$
$600$	−12.5885	−	46.9808i	−0.513922	−	1.91798i
$601$	−17.5526	+	10.1340i	−0.715984	+	0.413373i	−0.813273	−	0.581883i	$-0.802316\pi$
$601$	−17.5526	+	10.1340i	−0.715984	+	0.413373i	0.0972889	+	0.995256i	$0.468983\pi$
$602$	1.32051			0.0538199
$603$	15.6962	+	4.20577i	0.639197	+	0.171272i
$604$	5.46410			0.222331
$605$	−8.19615	−	2.19615i	−0.333221	−	0.0892863i
$606$	−18.9282			−0.768906
$607$	22.5885	−	39.1244i	0.916837	−	1.58801i	0.112648	−	0.993635i	$-0.464067\pi$
$607$	22.5885	−	39.1244i	0.916837	−	1.58801i	0.804189	−	0.594374i	$-0.202600\pi$
$608$	−2.53590	+	4.39230i	−0.102844	+	0.178131i
$609$	−2.19615	+	2.19615i	−0.0889926	+	0.0889926i
$610$	4.39230	−	16.3923i	0.177839	−	0.663705i
$611$	−43.1244	+	43.1244i	−1.74462	+	1.74462i
$612$	11.7846	−	6.80385i	0.476365	−	0.275029i
$613$	1.66025	+	1.66025i	0.0670570	+	0.0670570i	0.739840	−	0.672783i	$-0.234901\pi$
$613$	1.66025	+	1.66025i	0.0670570	+	0.0670570i	−0.672783	+	0.739840i	$0.734901\pi$
$614$	16.0263	+	27.7583i	0.646768	+	1.12024i
$615$	−19.3923	+	5.19615i	−0.781973	+	0.209529i
$616$	5.32051	+	3.07180i	0.214369	+	0.123766i
$617$	3.91154	+	2.25833i	0.157473	+	0.0909170i	0.576666	−	0.816980i	$-0.304354\pi$
$617$	3.91154	+	2.25833i	0.157473	+	0.0909170i	−0.419193	+	0.907897i	$0.637687\pi$
$618$	5.78461	−	21.5885i	0.232691	−	0.868415i
$619$	−10.4019	+	38.8205i	−0.418089	+	1.56033i	0.360479	+	0.932767i	$0.382613\pi$
$619$	−10.4019	+	38.8205i	−0.418089	+	1.56033i	−0.778568	+	0.627561i	$0.784053\pi$
$620$	−40.7846	+	40.7846i	−1.63795	+	1.63795i
$621$	3.29423	−	5.70577i	0.132193	−	0.228965i
$622$	16.0526	−	16.0526i	0.643649	−	0.643649i
$623$	−0.732051	−	1.26795i	−0.0293290	−	0.0507993i
$624$	−11.3205	+	42.2487i	−0.453183	+	1.69130i
$625$	11.9641	−	20.7224i	0.478564	−	0.828897i
$626$	−10.4186	−	38.8827i	−0.416410	−	1.55406i
$627$	3.99038	+	2.30385i	0.159360	+	0.0920068i
$628$	−2.53590	+	9.46410i	−0.101193	+	0.377659i
$629$	−2.87564	−	2.87564i	−0.114659	−	0.114659i
$630$	−12.0000			−0.478091
$631$		−	38.3923i		−	1.52837i	−0.644995	−	0.764187i	$-0.723141\pi$
$631$		−	38.3923i		−	1.52837i	0.644995	−	0.764187i	$-0.276859\pi$
$632$	32.7846	+	8.78461i	1.30410	+	0.349433i
$633$	5.19615	+	5.19615i	0.206529	+	0.206529i
$634$	23.0526	−	39.9282i	0.915534	−	1.58575i
$635$	23.1244	−	6.19615i	0.917662	−	0.245887i
$636$	−1.85641	−	1.85641i	−0.0736113	−	0.0736113i
$637$	39.4186	+	10.5622i	1.56182	+	0.418489i
$638$	−7.26795	−	7.26795i	−0.287741	−	0.287741i
$639$	28.3923	+	16.3923i	1.12318	+	0.648470i
$640$	43.7128			1.72790
$641$	−4.20577	−	7.28461i	−0.166118	−	0.287725i	0.770934	−	0.636915i	$-0.219790\pi$
$641$	−4.20577	−	7.28461i	−0.166118	−	0.287725i	−0.937052	+	0.349191i	$0.886457\pi$
$642$	23.3660	−	40.4711i	0.922183	−	1.59727i
$643$	12.2321	+	45.6506i	0.482385	+	1.80029i	0.591558	+	0.806263i	$0.298513\pi$
$643$	12.2321	+	45.6506i	0.482385	+	1.80029i	−0.109173	+	0.994023i	$0.534820\pi$
$644$	−1.60770	−	0.928203i	−0.0633521	−	0.0365763i
$645$	−4.26795	−	7.39230i	−0.168050	−	0.291072i
$646$	−1.43782	−	2.49038i	−0.0565704	−	0.0979827i
$647$		−	13.2679i		−	0.521617i	−0.965391	−	0.260808i	$-0.916011\pi$
$647$		−	13.2679i		−	0.521617i	0.965391	−	0.260808i	$-0.0839891\pi$
$648$	24.5885	+	6.58846i	0.965926	+	0.258819i
$649$			15.2487i			0.598564i
$650$	−76.7654	+	44.3205i	−3.01099	+	1.73839i
$651$	4.73205	+	8.19615i	0.185464	+	0.321233i
$652$	19.1244	−	5.12436i	0.748968	−	0.200685i
$653$	−1.50962	−	5.63397i	−0.0590760	−	0.220474i	0.930077	−	0.367365i	$-0.119740\pi$
$653$	−1.50962	−	5.63397i	−0.0590760	−	0.220474i	−0.989153	+	0.146891i	$0.953073\pi$
$654$	21.8038	+	12.5885i	0.852598	+	0.492248i
$655$	−6.19615	−	10.7321i	−0.242104	−	0.419336i
$656$		−	12.0000i		−	0.468521i
$657$	25.2846	+	14.5981i	0.986447	+	0.569525i
$658$	7.07180	−	7.07180i	0.275687	−	0.275687i
$659$	−15.0263	−	4.02628i	−0.585341	−	0.156842i	−0.0460178	−	0.998941i	$-0.514653\pi$
$659$	−15.0263	−	4.02628i	−0.585341	−	0.156842i	−0.539323	+	0.842099i	$0.681320\pi$
$660$		−	39.7128i		−	1.54582i
$661$	−8.19615	+	2.19615i	−0.318793	+	0.0854204i	−0.414667	−	0.909973i	$-0.636102\pi$
$661$	−8.19615	+	2.19615i	−0.318793	+	0.0854204i	0.0958740	+	0.995393i	$0.469435\pi$
$662$	−24.1244	−	13.9282i	−0.937620	−	0.541335i
$663$	−17.5359	−	17.5359i	−0.681038	−	0.681038i
$664$	3.46410	−	2.00000i	0.134433	−	0.0776151i
$665$			2.53590i			0.0983379i
$666$		−	7.60770i		−	0.294792i
$667$	2.19615	+	2.19615i	0.0850354	+	0.0850354i
$668$	−0.535898	−	0.928203i	−0.0207345	−	0.0359133i
$669$	−33.0788	−	19.0981i	−1.27890	−	0.738374i
$670$	−28.5885	+	7.66025i	−1.10447	+	0.295941i
$671$	4.60770	−	7.98076i	0.177878	−	0.308094i
$672$	1.85641	−	6.92820i	0.0716124	−	0.267261i
$673$	8.80385	+	15.2487i	0.339363	+	0.587795i	0.984313	−	0.176430i	$-0.0564550\pi$
$673$	8.80385	+	15.2487i	0.339363	+	0.587795i	−0.644950	+	0.764225i	$0.723122\pi$
$674$	23.7846	+	23.7846i	0.916149	+	0.916149i
$675$	25.7942	+	44.6769i	0.992820	+	1.71962i
$676$	53.7128			2.06588
$677$	−1.26795	+	4.73205i	−0.0487312	+	0.181867i	−0.986002	−	0.166736i	$-0.946677\pi$
$677$	−1.26795	+	4.73205i	−0.0487312	+	0.181867i	0.937270	+	0.348603i	$0.113344\pi$
$678$	32.7846	+	8.78461i	1.25909	+	0.337371i
$679$	5.24167	+	3.02628i	0.201157	+	0.116138i
$680$	−12.3923	+	21.4641i	−0.475223	+	0.823111i
$681$	24.9904	−	6.69615i	0.957633	−	0.256597i
$682$	−27.1244	+	15.6603i	−1.03865	+	0.599662i
$683$	−4.70577	−	4.70577i	−0.180061	−	0.180061i	0.611321	−	0.791383i	$-0.290638\pi$
$683$	−4.70577	−	4.70577i	−0.180061	−	0.180061i	−0.791383	+	0.611321i	$0.790638\pi$
$684$	1.39230	−	5.19615i	0.0532361	−	0.198680i
$685$	−44.9808	+	44.9808i	−1.71863	+	1.71863i
$686$	−13.4641	−	3.60770i	−0.514062	−	0.137742i
$687$	−8.66025	+	8.66025i	−0.330409	+	0.330409i
$688$	4.92820	−	1.32051i	0.187886	−	0.0503439i
$689$	−2.39230	+	4.14359i	−0.0911396	+	0.157858i
$690$			12.0000i			0.456832i
$691$	23.4904	+	6.29423i	0.893616	+	0.239444i	0.676273	−	0.736651i	$-0.263594\pi$
$691$	23.4904	+	6.29423i	0.893616	+	0.239444i	0.217344	+	0.976095i	$0.430261\pi$
$692$	18.3923	+	18.3923i	0.699171	+	0.699171i
$693$	−6.29423	−	1.68653i	−0.239098	−	0.0640661i
$694$			36.1962i			1.37399i
$695$	31.3923	−	18.1244i	1.19078	−	0.687496i
$696$	−6.00000	+	10.3923i	−0.227429	+	0.393919i
$697$	5.89230	+	3.40192i	0.223187	+	0.128857i
$698$	−5.66025	+	9.80385i	−0.214244	+	0.371081i
$699$	6.23205	+	10.7942i	0.235718	+	0.408275i
$700$	12.5885	−	7.26795i	0.475799	−	0.274703i
$701$	10.6603	−	10.6603i	0.402632	−	0.402632i	−0.476527	−	0.879160i	$-0.658105\pi$
$701$	10.6603	−	10.6603i	0.402632	−	0.402632i	0.879160	+	0.476527i	$0.158105\pi$
$702$		−	46.3923i		−	1.75096i
$703$	−1.60770			−0.0606354
$704$	22.9282	+	6.14359i	0.864139	+	0.231545i
$705$	−62.4449	−	16.7321i	−2.35181	−	0.630165i
$706$	−27.7583	+	7.43782i	−1.04470	+	0.279926i
$707$	−1.46410	−	5.46410i	−0.0550632	−	0.205499i
$708$	17.1962	−	4.60770i	0.646271	−	0.173168i
$709$	5.41154	−	20.1962i	0.203235	−	0.758482i	−0.786746	−	0.617277i	$-0.788236\pi$
$709$	5.41154	−	20.1962i	0.203235	−	0.758482i	0.989980	−	0.141205i	$-0.0450977\pi$
$710$	−59.7128			−2.24098
$711$	−36.0000			−1.35011
$712$	−4.00000	−	4.00000i	−0.149906	−	0.149906i
$713$	8.19615	−	4.73205i	0.306948	−	0.177217i
$714$	2.87564	+	2.87564i	0.107618	+	0.107618i
$715$	−69.9090	+	18.7321i	−2.61445	+	0.700539i
$716$	−32.5885	+	8.73205i	−1.21789	+	0.326332i
$717$		−	45.3731i		−	1.69449i
$718$	−20.1244	−	5.39230i	−0.751034	−	0.201239i
$719$	−16.3923			−0.611330			−0.305665	−	0.952139i	$-0.598879\pi$
$719$	−16.3923			−0.611330			−0.305665	+	0.952139i	$0.598879\pi$
$720$	−44.7846	+	12.0000i	−1.66902	+	0.447214i
$721$	6.67949			0.248757
$722$	24.8564	+	6.66025i	0.925060	+	0.247869i
$723$	19.2058	+	11.0885i	0.714270	+	0.412384i
$724$	−9.80385	−	36.5885i	−0.364357	−	1.35980i
$725$	−23.4904	+	6.29423i	−0.872411	+	0.233762i
$726$	−1.39230	+	5.19615i	−0.0516733	+	0.192847i
$727$	−31.8109	+	18.3660i	−1.17980	+	0.681158i	−0.955968	−	0.293470i	$-0.905190\pi$
$727$	−31.8109	+	18.3660i	−1.17980	+	0.681158i	−0.223832	+	0.974628i	$0.571857\pi$
$728$	−13.0718			−0.484473
$729$	−27.0000			−1.00000
$730$	−53.1769			−1.96817
$731$	−0.748711	+	2.79423i	−0.0276921	+	0.103348i
$732$	−10.3923	−	2.78461i	−0.384111	−	0.102922i
$733$	8.02628	+	29.9545i	0.296457	+	1.10639i	0.940053	+	0.341028i	$0.110775\pi$
$733$	8.02628	+	29.9545i	0.296457	+	1.10639i	−0.643596	+	0.765366i	$0.722558\pi$
$734$	−27.6603	+	7.41154i	−1.02096	+	0.273565i
$735$	11.1962	+	41.7846i	0.412976	+	1.54125i
$736$	−6.92820	−	1.85641i	−0.255377	−	0.0684280i
$737$	−16.0718			−0.592012
$738$	3.29423	+	12.2942i	0.121262	+	0.452557i
$739$	21.2224	−	21.2224i	0.780680	−	0.780680i	−0.199266	−	0.979945i	$-0.563856\pi$
$739$	21.2224	−	21.2224i	0.780680	−	0.780680i	0.979945	+	0.199266i	$0.0638557\pi$
$740$	6.92820	+	12.0000i	0.254686	+	0.441129i
$741$	−9.80385			−0.360153
$742$	0.392305	−	0.679492i	0.0144020	−	0.0249449i
$743$	−2.24167	−	1.29423i	−0.0822389	−	0.0474806i	0.458317	−	0.888789i	$-0.348453\pi$
$743$	−2.24167	−	1.29423i	−0.0822389	−	0.0474806i	−0.540556	+	0.841308i	$0.681786\pi$
$744$	25.8564	+	25.8564i	0.947942	+	0.947942i
$745$	−10.7321	+	6.19615i	−0.393192	+	0.227009i
$746$			8.24871i			0.302007i
$747$	−3.00000	+	3.00000i	−0.109764	+	0.109764i
$748$	−9.51666	+	9.51666i	−0.347964	+	0.347964i
$749$	13.4904	+	3.61474i	0.492928	+	0.132080i
$750$	−40.3923	−	23.3205i	−1.47492	−	0.851545i
$751$	18.8564	−	32.6603i	0.688080	−	1.19179i	−0.284378	−	0.958712i	$-0.591787\pi$
$751$	18.8564	−	32.6603i	0.688080	−	1.19179i	0.972458	−	0.233077i	$-0.0748796\pi$
$752$	19.3205	−	33.4641i	0.704546	−	1.22031i
$753$	−6.69615	−	1.79423i	−0.244021	−	0.0653853i
$754$	21.1244	+	5.66025i	0.769304	+	0.206134i
$755$	7.46410	−	7.46410i	0.271646	−	0.271646i
$756$			7.60770i			0.276689i
$757$	−6.07180	−	6.07180i	−0.220683	−	0.220683i	0.588103	−	0.808786i	$-0.299875\pi$
$757$	−6.07180	−	6.07180i	−0.220683	−	0.220683i	−0.808786	+	0.588103i	$0.799875\pi$
$758$	−32.4904	+	18.7583i	−1.18010	+	0.681333i
$759$	−1.68653	+	6.29423i	−0.0612173	+	0.228466i
$760$	2.53590	+	9.46410i	0.0919867	+	0.343299i
$761$	27.3731	+	15.8038i	0.992273	+	0.572889i	0.905953	−	0.423378i	$-0.139156\pi$
$761$	27.3731	+	15.8038i	0.992273	+	0.572889i	0.0863200	+	0.996267i	$0.472489\pi$
$762$	−3.92820	−	14.6603i	−0.142304	−	0.531085i
$763$	−1.94744	+	7.26795i	−0.0705021	+	0.263117i
$764$		−	28.1051i

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-3.73205 + 1.00000i) q^{5} +(0.633975 + 2.36603i) q^{6} +(-0.633975 + 0.366025i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-3.73205 + 1.00000i) q^{5} +(0.633975 + 2.36603i) q^{6} +(-0.633975 + 0.366025i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +5.46410i q^{10} +(-0.767949 + 2.86603i) q^{11} +3.46410 q^{12} +(-1.63397 - 6.09808i) q^{13} +(0.267949 + 1.00000i) q^{14} +(4.73205 - 4.73205i) q^{15} +(2.00000 + 3.46410i) q^{16} -2.26795 q^{17} +(-3.00000 - 3.00000i) q^{18} +(-0.633975 + 0.633975i) q^{19} +(7.46410 + 2.00000i) q^{20} +(0.633975 - 1.09808i) q^{21} +(3.63397 + 2.09808i) q^{22} +(-1.09808 - 0.633975i) q^{23} +(1.26795 - 4.73205i) q^{24} +(8.59808 - 4.96410i) q^{25} -8.92820 q^{26} +5.19615i q^{27} +1.46410 q^{28} +(-2.36603 - 0.633975i) q^{29} +(-4.73205 - 8.19615i) q^{30} +(-3.73205 + 6.46410i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-1.33013 - 4.96410i) q^{33} +(-0.830127 + 3.09808i) q^{34} +(2.00000 - 2.00000i) q^{35} +(-5.19615 + 3.00000i) q^{36} +(1.26795 + 1.26795i) q^{37} +(0.633975 + 1.09808i) q^{38} +(7.73205 + 7.73205i) q^{39} +(5.46410 - 9.46410i) q^{40} +(-2.59808 - 1.50000i) q^{41} +(-1.26795 - 1.26795i) q^{42} +(0.330127 - 1.23205i) q^{43} +(4.19615 - 4.19615i) q^{44} +(-3.00000 + 11.1962i) q^{45} +(-1.26795 + 1.26795i) q^{46} +(-4.83013 - 8.36603i) q^{47} +(-6.00000 - 3.46410i) q^{48} +(-3.23205 + 5.59808i) q^{49} +(-3.63397 - 13.5622i) q^{50} +(3.40192 - 1.96410i) q^{51} +(-3.26795 + 12.1962i) q^{52} +(-0.535898 - 0.535898i) q^{53} +(7.09808 + 1.90192i) q^{54} -11.4641i q^{55} +(0.535898 - 2.00000i) q^{56} +(0.401924 - 1.50000i) q^{57} +(-1.73205 + 3.00000i) q^{58} +(4.96410 - 1.33013i) q^{59} +(-12.9282 + 3.46410i) q^{60} +(-3.00000 - 0.803848i) q^{61} +(7.46410 + 7.46410i) q^{62} +2.19615i q^{63} -8.00000i q^{64} +(12.1962 + 21.1244i) q^{65} -7.26795 q^{66} +(1.40192 + 5.23205i) q^{67} +(3.92820 + 2.26795i) q^{68} +2.19615 q^{69} +(-2.00000 - 3.46410i) q^{70} +10.9282i q^{71} +(2.19615 + 8.19615i) q^{72} +9.73205i q^{73} +(2.19615 - 1.26795i) q^{74} +(-8.59808 + 14.8923i) q^{75} +(1.73205 - 0.464102i) q^{76} +(-0.562178 - 2.09808i) q^{77} +(13.3923 - 7.73205i) q^{78} +(-6.00000 - 10.3923i) q^{79} +(-10.9282 - 10.9282i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-3.00000 + 3.00000i) q^{82} +(-1.36603 - 0.366025i) q^{83} +(-2.19615 + 1.26795i) q^{84} +(8.46410 - 2.26795i) q^{85} +(-1.56218 - 0.901924i) q^{86} +(4.09808 - 1.09808i) q^{87} +(-4.19615 - 7.26795i) q^{88} +2.00000i q^{89} +(14.1962 + 8.19615i) q^{90} +(3.26795 + 3.26795i) q^{91} +(1.26795 + 2.19615i) q^{92} -12.9282i q^{93} +(-13.1962 + 3.53590i) q^{94} +(1.73205 - 3.00000i) q^{95} +(-6.92820 + 6.92820i) q^{96} +(-4.13397 - 7.16025i) q^{97} +(6.46410 + 6.46410i) q^{98} +(6.29423 + 6.29423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{3} - 8 q^{5} + 6 q^{6} - 6 q^{7} - 8 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^3 - 8 * q^5 + 6 * q^6 - 6 * q^7 - 8 * q^8 + 6 * q^9	\( 4 q - 2 q^{2} - 6 q^{3} - 8 q^{5} + 6 q^{6} - 6 q^{7} - 8 q^{8} + 6 q^{9} - 10 q^{11} - 10 q^{13} + 8 q^{14} + 12 q^{15} + 8 q^{16} - 16 q^{17} - 12 q^{18} - 6 q^{19} + 16 q^{20} + 6 q^{21} + 18 q^{22} + 6 q^{23} + 12 q^{24} + 24 q^{25} - 8 q^{26} - 8 q^{28} - 6 q^{29} - 12 q^{30} - 8 q^{31} + 8 q^{32} + 12 q^{33} + 14 q^{34} + 8 q^{35} + 12 q^{37} + 6 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{42} - 16 q^{43} - 4 q^{44} - 12 q^{45} - 12 q^{46} - 2 q^{47} - 24 q^{48} - 6 q^{49} - 18 q^{50} + 24 q^{51} - 20 q^{52} - 16 q^{53} + 18 q^{54} + 16 q^{56} + 12 q^{57} + 6 q^{59} - 24 q^{60} - 12 q^{61} + 16 q^{62} + 28 q^{65} - 36 q^{66} + 16 q^{67} - 12 q^{68} - 12 q^{69} - 8 q^{70} - 12 q^{72} - 12 q^{74} - 24 q^{75} + 22 q^{77} + 12 q^{78} - 24 q^{79} - 16 q^{80} - 18 q^{81} - 12 q^{82} - 2 q^{83} + 12 q^{84} + 20 q^{85} + 18 q^{86} + 6 q^{87} + 4 q^{88} + 36 q^{90} + 20 q^{91} + 12 q^{92} - 32 q^{94} - 20 q^{97} + 12 q^{98} - 6 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^3 - 8 * q^5 + 6 * q^6 - 6 * q^7 - 8 * q^8 + 6 * q^9 - 10 * q^11 - 10 * q^13 + 8 * q^14 + 12 * q^15 + 8 * q^16 - 16 * q^17 - 12 * q^18 - 6 * q^19 + 16 * q^20 + 6 * q^21 + 18 * q^22 + 6 * q^23 + 12 * q^24 + 24 * q^25 - 8 * q^26 - 8 * q^28 - 6 * q^29 - 12 * q^30 - 8 * q^31 + 8 * q^32 + 12 * q^33 + 14 * q^34 + 8 * q^35 + 12 * q^37 + 6 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^42 - 16 * q^43 - 4 * q^44 - 12 * q^45 - 12 * q^46 - 2 * q^47 - 24 * q^48 - 6 * q^49 - 18 * q^50 + 24 * q^51 - 20 * q^52 - 16 * q^53 + 18 * q^54 + 16 * q^56 + 12 * q^57 + 6 * q^59 - 24 * q^60 - 12 * q^61 + 16 * q^62 + 28 * q^65 - 36 * q^66 + 16 * q^67 - 12 * q^68 - 12 * q^69 - 8 * q^70 - 12 * q^72 - 12 * q^74 - 24 * q^75 + 22 * q^77 + 12 * q^78 - 24 * q^79 - 16 * q^80 - 18 * q^81 - 12 * q^82 - 2 * q^83 + 12 * q^84 + 20 * q^85 + 18 * q^86 + 6 * q^87 + 4 * q^88 + 36 * q^90 + 20 * q^91 + 12 * q^92 - 32 * q^94 - 20 * q^97 + 12 * q^98 - 6 * q^99

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