LMFDB - Embedded newform 144.2.x.b.133.1

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			133.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	144.133
Dual form			144.2.x.b.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 0.366025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.267949 + 1.00000i) q^{5} +(2.36603 + 0.633975i) q^{6} +(-2.36603 - 1.36603i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.36603 + 0.366025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.267949 + 1.00000i) q^{5} +(2.36603 + 0.633975i) q^{6} +(-2.36603 - 1.36603i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.50000 + 2.59808i) q^{9} -1.46410i q^{10} +(-4.23205 + 1.13397i) q^{11} -3.46410 q^{12} +(-3.36603 - 0.901924i) q^{13} +(3.73205 + 1.00000i) q^{14} +(1.26795 - 1.26795i) q^{15} +(2.00000 - 3.46410i) q^{16} -5.73205 q^{17} +(-3.00000 - 3.00000i) q^{18} +(-2.36603 + 2.36603i) q^{19} +(0.535898 + 2.00000i) q^{20} +(2.36603 + 4.09808i) q^{21} +(5.36603 - 3.09808i) q^{22} +(4.09808 - 2.36603i) q^{23} +(4.73205 - 1.26795i) q^{24} +(3.40192 + 1.96410i) q^{25} +4.92820 q^{26} -5.19615i q^{27} -5.46410 q^{28} +(-0.633975 - 2.36603i) q^{29} +(-1.26795 + 2.19615i) q^{30} +(-0.267949 - 0.464102i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(7.33013 + 1.96410i) q^{33} +(7.83013 - 2.09808i) q^{34} +(2.00000 - 2.00000i) q^{35} +(5.19615 + 3.00000i) q^{36} +(4.73205 + 4.73205i) q^{37} +(2.36603 - 4.09808i) q^{38} +(4.26795 + 4.26795i) q^{39} +(-1.46410 - 2.53590i) q^{40} +(2.59808 - 1.50000i) q^{41} +(-4.73205 - 4.73205i) q^{42} +(-8.33013 + 2.23205i) q^{43} +(-6.19615 + 6.19615i) q^{44} +(-3.00000 + 0.803848i) q^{45} +(-4.73205 + 4.73205i) q^{46} +(3.83013 - 6.63397i) q^{47} +(-6.00000 + 3.46410i) q^{48} +(0.232051 + 0.401924i) q^{49} +(-5.36603 - 1.43782i) q^{50} +(8.59808 + 4.96410i) q^{51} +(-6.73205 + 1.80385i) q^{52} +(-7.46410 - 7.46410i) q^{53} +(1.90192 + 7.09808i) q^{54} -4.53590i q^{55} +(7.46410 - 2.00000i) q^{56} +(5.59808 - 1.50000i) q^{57} +(1.73205 + 3.00000i) q^{58} +(-1.96410 + 7.33013i) q^{59} +(0.928203 - 3.46410i) q^{60} +(-3.00000 - 11.1962i) q^{61} +(0.535898 + 0.535898i) q^{62} -8.19615i q^{63} -8.00000i q^{64} +(1.80385 - 3.12436i) q^{65} -10.7321 q^{66} +(6.59808 + 1.76795i) q^{67} +(-9.92820 + 5.73205i) q^{68} -8.19615 q^{69} +(-2.00000 + 3.46410i) q^{70} -2.92820i q^{71} +(-8.19615 - 2.19615i) q^{72} +6.26795i q^{73} +(-8.19615 - 4.73205i) q^{74} +(-3.40192 - 5.89230i) q^{75} +(-1.73205 + 6.46410i) q^{76} +(11.5622 + 3.09808i) q^{77} +(-7.39230 - 4.26795i) q^{78} +(-6.00000 + 10.3923i) q^{79} +(2.92820 + 2.92820i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.00000 + 3.00000i) q^{82} +(0.366025 + 1.36603i) q^{83} +(8.19615 + 4.73205i) q^{84} +(1.53590 - 5.73205i) q^{85} +(10.5622 - 6.09808i) q^{86} +(-1.09808 + 4.09808i) q^{87} +(6.19615 - 10.7321i) q^{88} +2.00000i q^{89} +(3.80385 - 2.19615i) q^{90} +(6.73205 + 6.73205i) q^{91} +(4.73205 - 8.19615i) q^{92} +0.928203i q^{93} +(-2.80385 + 10.4641i) q^{94} +(-1.73205 - 3.00000i) q^{95} +(6.92820 - 6.92820i) q^{96} +(-5.86603 + 10.1603i) q^{97} +(-0.464102 - 0.464102i) q^{98} +(-9.29423 - 9.29423i) 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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$3$	−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
$5$	−0.267949	+	1.00000i	−0.119831	+	0.447214i	−0.999603	−	0.0281817i	$-0.991028\pi$
$5$	−0.267949	+	1.00000i	−0.119831	+	0.447214i	0.879772	+	0.475395i	$0.157695\pi$
$6$	2.36603	+	0.633975i	0.965926	+	0.258819i
$7$	−2.36603	−	1.36603i	−0.894274	−	0.516309i	−0.0189356	−	0.999821i	$-0.506028\pi$
$7$	−2.36603	−	1.36603i	−0.894274	−	0.516309i	−0.875338	+	0.483512i	$0.839361\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		−	1.46410i		−	0.462990i
$11$	−4.23205	+	1.13397i	−1.27601	+	0.341906i	−0.832331	−	0.554279i	$-0.812994\pi$
$11$	−4.23205	+	1.13397i	−1.27601	+	0.341906i	−0.443680	+	0.896185i	$0.646327\pi$
$12$	−3.46410			−1.00000
$13$	−3.36603	−	0.901924i	−0.933567	−	0.250149i	−0.240192	−	0.970725i	$-0.577210\pi$
$13$	−3.36603	−	0.901924i	−0.933567	−	0.250149i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	3.73205	+	1.00000i	0.997433	+	0.267261i
$15$	1.26795	−	1.26795i	0.327383	−	0.327383i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−5.73205			−1.39023			−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−5.73205			−1.39023			−0.695113	+	0.718900i	$0.744646\pi$
$18$	−3.00000	−	3.00000i	−0.707107	−	0.707107i
$19$	−2.36603	+	2.36603i	−0.542803	+	0.542803i	−0.924350	−	0.381546i	$-0.875392\pi$
$19$	−2.36603	+	2.36603i	−0.542803	+	0.542803i	0.381546	+	0.924350i	$0.375392\pi$
$20$	0.535898	+	2.00000i	0.119831	+	0.447214i
$21$	2.36603	+	4.09808i	0.516309	+	0.894274i
$22$	5.36603	−	3.09808i	1.14404	−	0.660512i
$23$	4.09808	−	2.36603i	0.854508	−	0.493350i	−0.00766135	−	0.999971i	$-0.502439\pi$
$23$	4.09808	−	2.36603i	0.854508	−	0.493350i	0.862169	+	0.506620i	$0.169105\pi$
$24$	4.73205	−	1.26795i	0.965926	−	0.258819i
$25$	3.40192	+	1.96410i	0.680385	+	0.392820i
$26$	4.92820			0.966500
$27$		−	5.19615i		−	1.00000i
$28$	−5.46410			−1.03262
$29$	−0.633975	−	2.36603i	−0.117726	−	0.439360i	0.881750	−	0.471717i	$-0.156365\pi$
$29$	−0.633975	−	2.36603i	−0.117726	−	0.439360i	−0.999476	+	0.0323566i	$0.989699\pi$
$30$	−1.26795	+	2.19615i	−0.231495	+	0.400961i
$31$	−0.267949	−	0.464102i	−0.0481251	−	0.0833551i	0.840959	−	0.541098i	$-0.181991\pi$
$31$	−0.267949	−	0.464102i	−0.0481251	−	0.0833551i	−0.889085	+	0.457743i	$0.848658\pi$
$32$	−1.46410	+	5.46410i	−0.258819	+	0.965926i
$33$	7.33013	+	1.96410i	1.27601	+	0.341906i
$34$	7.83013	−	2.09808i	1.34286	−	0.359817i
$35$	2.00000	−	2.00000i	0.338062	−	0.338062i
$36$	5.19615	+	3.00000i	0.866025	+	0.500000i
$37$	4.73205	+	4.73205i	0.777944	+	0.777944i	0.979481	−	0.201537i	$-0.0645935\pi$
$37$	4.73205	+	4.73205i	0.777944	+	0.777944i	−0.201537	+	0.979481i	$0.564594\pi$
$38$	2.36603	−	4.09808i	0.383820	−	0.664796i
$39$	4.26795	+	4.26795i	0.683419	+	0.683419i
$40$	−1.46410	−	2.53590i	−0.231495	−	0.400961i
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	−0.283211	−	0.959058i	$-0.591400\pi$
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	0.688963	+	0.724797i	$0.258066\pi$
$42$	−4.73205	−	4.73205i	−0.730171	−	0.730171i
$43$	−8.33013	+	2.23205i	−1.27033	+	0.340385i	−0.830158	−	0.557528i	$-0.811750\pi$
$43$	−8.33013	+	2.23205i	−1.27033	+	0.340385i	−0.440174	+	0.897912i	$0.645083\pi$
$44$	−6.19615	+	6.19615i	−0.934105	+	0.934105i
$45$	−3.00000	+	0.803848i	−0.447214	+	0.119831i
$46$	−4.73205	+	4.73205i	−0.697703	+	0.697703i
$47$	3.83013	−	6.63397i	0.558681	−	0.967665i	−0.438925	−	0.898523i	$-0.644641\pi$
$47$	3.83013	−	6.63397i	0.558681	−	0.967665i	0.997607	−	0.0691412i	$-0.0220259\pi$
$48$	−6.00000	+	3.46410i	−0.866025	+	0.500000i
$49$	0.232051	+	0.401924i	0.0331501	+	0.0574177i
$50$	−5.36603	−	1.43782i	−0.758871	−	0.203339i
$51$	8.59808	+	4.96410i	1.20397	+	0.695113i
$52$	−6.73205	+	1.80385i	−0.933567	+	0.250149i
$53$	−7.46410	−	7.46410i	−1.02527	−	1.02527i	−0.999672	−	0.0256010i	$-0.991850\pi$
$53$	−7.46410	−	7.46410i	−1.02527	−	1.02527i	−0.0256010	−	0.999672i	$-0.508150\pi$
$54$	1.90192	+	7.09808i	0.258819	+	0.965926i
$55$		−	4.53590i		−	0.611620i
$56$	7.46410	−	2.00000i	0.997433	−	0.267261i
$57$	5.59808	−	1.50000i	0.741483	−	0.198680i
$58$	1.73205	+	3.00000i	0.227429	+	0.393919i
$59$	−1.96410	+	7.33013i	−0.255704	+	0.954301i	0.711993	+	0.702186i	$0.247793\pi$
$59$	−1.96410	+	7.33013i	−0.255704	+	0.954301i	−0.967697	+	0.252115i	$0.918874\pi$
$60$	0.928203	−	3.46410i	0.119831	−	0.447214i
$61$	−3.00000	−	11.1962i	−0.384111	−	1.43352i	−0.839564	−	0.543261i	$-0.817189\pi$
$61$	−3.00000	−	11.1962i	−0.384111	−	1.43352i	0.455453	−	0.890260i	$-0.349477\pi$
$62$	0.535898	+	0.535898i	0.0680592	+	0.0680592i
$63$		−	8.19615i		−	1.03262i
$64$		−	8.00000i		−	1.00000i
$65$	1.80385	−	3.12436i	0.223740	−	0.387529i
$66$	−10.7321			−1.32102
$67$	6.59808	+	1.76795i	0.806083	+	0.215989i	0.638253	−	0.769827i	$-0.279657\pi$
$67$	6.59808	+	1.76795i	0.806083	+	0.215989i	0.167830	+	0.985816i	$0.446324\pi$
$68$	−9.92820	+	5.73205i	−1.20397	+	0.695113i
$69$	−8.19615			−0.986701
$70$	−2.00000	+	3.46410i	−0.239046	+	0.414039i
$71$		−	2.92820i		−	0.347514i	−0.984789	−	0.173757i	$-0.944409\pi$
$71$		−	2.92820i		−	0.347514i	0.984789	−	0.173757i	$-0.0555907\pi$
$72$	−8.19615	−	2.19615i	−0.965926	−	0.258819i
$73$			6.26795i			0.733608i	0.930298	+	0.366804i	$0.119548\pi$
$73$			6.26795i			0.733608i	−0.930298	+	0.366804i	$0.880452\pi$
$74$	−8.19615	−	4.73205i	−0.952783	−	0.550090i
$75$	−3.40192	−	5.89230i	−0.392820	−	0.680385i
$76$	−1.73205	+	6.46410i	−0.198680	+	0.741483i
$77$	11.5622	+	3.09808i	1.31763	+	0.353059i
$78$	−7.39230	−	4.26795i	−0.837014	−	0.483250i
$79$	−6.00000	+	10.3923i	−0.675053	+	1.16923i	0.301401	+	0.953498i	$0.402546\pi$
$79$	−6.00000	+	10.3923i	−0.675053	+	1.16923i	−0.976453	+	0.215728i	$0.930788\pi$
$80$	2.92820	+	2.92820i	0.327383	+	0.327383i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−3.00000	+	3.00000i	−0.331295	+	0.331295i
$83$	0.366025	+	1.36603i	0.0401765	+	0.149941i	0.983100	−	0.183068i	$-0.0586028\pi$
$83$	0.366025	+	1.36603i	0.0401765	+	0.149941i	−0.942924	+	0.333009i	$0.891936\pi$
$84$	8.19615	+	4.73205i	0.894274	+	0.516309i
$85$	1.53590	−	5.73205i	0.166592	−	0.621728i
$86$	10.5622	−	6.09808i	1.13895	−	0.657572i
$87$	−1.09808	+	4.09808i	−0.117726	+	0.439360i
$88$	6.19615	−	10.7321i	0.660512	−	1.14404i
$89$			2.00000i			0.212000i	0.994366	+	0.106000i	$0.0338043\pi$
$89$			2.00000i			0.212000i	−0.994366	+	0.106000i	$0.966196\pi$
$90$	3.80385	−	2.19615i	0.400961	−	0.231495i
$91$	6.73205	+	6.73205i	0.705711	+	0.705711i
$92$	4.73205	−	8.19615i	0.493350	−	0.854508i
$93$			0.928203i			0.0962502i
$94$	−2.80385	+	10.4641i	−0.289195	+	1.07929i
$95$	−1.73205	−	3.00000i	−0.177705	−	0.307794i
$96$	6.92820	−	6.92820i	0.707107	−	0.707107i
$97$	−5.86603	+	10.1603i	−0.595605	+	1.03162i	0.397857	+	0.917448i	$0.369754\pi$
$97$	−5.86603	+	10.1603i	−0.595605	+	1.03162i	−0.993461	+	0.114170i	$0.963579\pi$
$98$	−0.464102	−	0.464102i	−0.0468813	−	0.0468813i
$99$	−9.29423	−	9.29423i	−0.934105	−	0.934105i
$100$	7.85641			0.785641
$101$	−2.00000	+	0.535898i	−0.199007	+	0.0533239i	−0.356946	−	0.934125i	$-0.616182\pi$
$101$	−2.00000	+	0.535898i	−0.199007	+	0.0533239i	0.157938	+	0.987449i	$0.449515\pi$
$102$	−13.5622	−	3.63397i	−1.34286	−	0.359817i
$103$	−13.0981	+	7.56218i	−1.29059	+	0.745124i	−0.978759	−	0.205014i	$-0.934276\pi$
$103$	−13.0981	+	7.56218i	−1.29059	+	0.745124i	−0.311833	+	0.950137i	$0.600943\pi$
$104$	8.53590	−	4.92820i	0.837014	−	0.483250i
$105$	−4.73205	+	1.26795i	−0.461801	+	0.123739i
$106$	12.9282	+	7.46410i	1.25570	+	0.724978i
$107$	12.4904	+	12.4904i	1.20749	+	1.20749i	0.971837	+	0.235654i	$0.0757231\pi$
$107$	12.4904	+	12.4904i	1.20749	+	1.20749i	0.235654	+	0.971837i	$0.424277\pi$
$108$	−5.19615	−	9.00000i	−0.500000	−	0.866025i
$109$	10.7321	−	10.7321i	1.02794	−	1.02794i	0.0283459	−	0.999598i	$-0.490976\pi$
$109$	10.7321	−	10.7321i	1.02794	−	1.02794i	0.999598	−	0.0283459i	$-0.00902398\pi$
$110$	1.66025	+	6.19615i	0.158299	+	0.590780i
$111$	−3.00000	−	11.1962i	−0.284747	−	1.06269i
$112$	−9.46410	+	5.46410i	−0.894274	+	0.516309i
$113$	−6.92820	−	12.0000i	−0.651751	−	1.12887i	−0.982698	−	0.185216i	$-0.940702\pi$
$113$	−6.92820	−	12.0000i	−0.651751	−	1.12887i	0.330947	−	0.943649i	$-0.392632\pi$
$114$	−7.09808	+	4.09808i	−0.664796	+	0.383820i
$115$	1.26795	+	4.73205i	0.118237	+	0.441266i
$116$	−3.46410	−	3.46410i	−0.321634	−	0.321634i
$117$	−2.70577	−	10.0981i	−0.250149	−	0.933567i
$118$		−	10.7321i		−	0.987965i
$119$	13.5622	+	7.83013i	1.24324	+	0.717787i
$120$			5.07180i			0.462990i
$121$	7.09808	−	4.09808i	0.645280	−	0.372552i
$122$	8.19615	+	14.1962i	0.742045	+	1.28526i
$123$	−5.19615			−0.468521
$124$	−0.928203	−	0.535898i	−0.0833551	−	0.0481251i
$125$	−6.53590	+	6.53590i	−0.584589	+	0.584589i
$126$	3.00000	+	11.1962i	0.267261	+	0.997433i
$127$	4.19615			0.372348			0.186174	−	0.982517i	$-0.440391\pi$
$127$	4.19615			0.372348			0.186174	+	0.982517i	$0.440391\pi$
$128$	2.92820	+	10.9282i	0.258819	+	0.965926i
$129$	14.4282	+	3.86603i	1.27033	+	0.340385i
$130$	−1.32051	+	4.92820i	−0.115816	+	0.432232i
$131$	−7.83013	−	2.09808i	−0.684121	−	0.183310i	−0.100014	−	0.994986i	$-0.531889\pi$
$131$	−7.83013	−	2.09808i	−0.684121	−	0.183310i	−0.584108	+	0.811676i	$0.698555\pi$
$132$	14.6603	−	3.92820i	1.27601	−	0.341906i
$133$	8.83013	−	2.36603i	0.765669	−	0.205160i
$134$	−9.66025			−0.834519
$135$	5.19615	+	1.39230i	0.447214	+	0.119831i
$136$	11.4641	−	11.4641i	0.983039	−	0.983039i
$137$	−8.25833	−	4.76795i	−0.705557	−	0.407353i	0.103857	−	0.994592i	$-0.466882\pi$
$137$	−8.25833	−	4.76795i	−0.705557	−	0.407353i	−0.809414	+	0.587239i	$0.800215\pi$
$138$	11.1962	−	3.00000i	0.953080	−	0.255377i
$139$	3.06218	−	11.4282i	0.259731	−	0.969328i	−0.705667	−	0.708544i	$-0.749352\pi$
$139$	3.06218	−	11.4282i	0.259731	−	0.969328i	0.965397	−	0.260784i	$-0.0839809\pi$
$140$	1.46410	−	5.46410i	0.123739	−	0.461801i
$141$	−11.4904	+	6.63397i	−0.967665	+	0.558681i
$142$	1.07180	+	4.00000i	0.0899432	+	0.335673i
$143$	15.2679			1.27677
$144$	12.0000			1.00000
$145$	2.53590			0.210595
$146$	−2.29423	−	8.56218i	−0.189872	−	0.708611i
$147$		−	0.803848i		−	0.0663002i
$148$	12.9282	+	3.46410i	1.06269	+	0.284747i
$149$	−2.09808	+	7.83013i	−0.171881	+	0.641469i	0.825181	+	0.564869i	$0.191073\pi$
$149$	−2.09808	+	7.83013i	−0.171881	+	0.641469i	−0.997062	+	0.0766003i	$0.975593\pi$
$150$	6.80385	+	6.80385i	0.555532	+	0.555532i
$151$	−0.633975	−	0.366025i	−0.0515921	−	0.0297867i	0.473982	−	0.880534i	$-0.342816\pi$
$151$	−0.633975	−	0.366025i	−0.0515921	−	0.0297867i	−0.525574	+	0.850748i	$0.676149\pi$
$152$		−	9.46410i		−	0.767640i
$153$	−8.59808	−	14.8923i	−0.695113	−	1.20397i
$154$	−16.9282			−1.36411
$155$	0.535898	−	0.143594i	0.0430444	−	0.0115337i
$156$	11.6603	+	3.12436i	0.933567	+	0.250149i
$157$	−4.73205	−	1.26795i	−0.377659	−	0.101193i	0.0649959	−	0.997886i	$-0.479297\pi$
$157$	−4.73205	−	1.26795i	−0.377659	−	0.101193i	−0.442655	+	0.896692i	$0.645963\pi$
$158$	4.39230	−	16.3923i	0.349433	−	1.30410i
$159$	4.73205	+	17.6603i	0.375276	+	1.40055i
$160$	−5.07180	−	2.92820i	−0.400961	−	0.231495i
$161$	−12.9282			−1.01889
$162$	3.29423	−	12.2942i	0.258819	−	0.965926i
$163$	−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
$165$	−3.92820	+	6.80385i	−0.305810	+	0.529679i
$166$	−1.00000	−	1.73205i	−0.0776151	−	0.134433i
$167$	−6.46410	+	3.73205i	−0.500207	+	0.288795i	−0.728799	−	0.684728i	$-0.759921\pi$
$167$	−6.46410	+	3.73205i	−0.500207	+	0.288795i	0.228592	+	0.973522i	$0.426588\pi$
$168$	−12.9282	−	3.46410i	−0.997433	−	0.267261i
$169$	−0.741670	−	0.428203i	−0.0570515	−	0.0329387i
$170$			8.39230i			0.643660i
$171$	−9.69615	−	2.59808i	−0.741483	−	0.198680i
$172$	−12.1962	+	12.1962i	−0.929948	+	0.929948i
$173$	−0.437822	−	1.63397i	−0.0332870	−	0.124229i	0.947283	−	0.320398i	$-0.103817\pi$
$173$	−0.437822	−	1.63397i	−0.0332870	−	0.124229i	−0.980570	+	0.196169i	$0.937150\pi$
$174$		−	6.00000i		−	0.454859i
$175$	−5.36603	−	9.29423i	−0.405633	−	0.702578i
$176$	−4.53590	+	16.9282i	−0.341906	+	1.27601i
$177$	9.29423	−	9.29423i	0.698597	−	0.698597i
$178$	−0.732051	−	2.73205i	−0.0548695	−	0.204776i
$179$	−1.92820	+	1.92820i	−0.144121	+	0.144121i	−0.775486	−	0.631365i	$-0.782495\pi$
$179$	−1.92820	+	1.92820i	−0.144121	+	0.144121i	0.631365	+	0.775486i	$0.282495\pi$
$180$	−4.39230	+	4.39230i	−0.327383	+	0.327383i
$181$	−7.39230	−	7.39230i	−0.549466	−	0.549466i	0.376821	−	0.926286i	$-0.377017\pi$
$181$	−7.39230	−	7.39230i	−0.549466	−	0.549466i	−0.926286	+	0.376821i	$0.877017\pi$
$182$	−11.6603	−	6.73205i	−0.864316	−	0.499013i
$183$	−5.19615	+	19.3923i	−0.384111	+	1.43352i
$184$	−3.46410	+	12.9282i	−0.255377	+	0.953080i
$185$	−6.00000	+	3.46410i	−0.441129	+	0.254686i
$186$	−0.339746	−	1.26795i	−0.0249114	−	0.0929705i
$187$	24.2583	−	6.50000i	1.77394	−	0.475327i
$188$		−	15.3205i		−	1.11736i
$189$	−7.09808	+	12.2942i	−0.516309	+	0.894274i
$190$	3.46410	+	3.46410i	0.251312	+	0.251312i
$191$	−12.0263	+	20.8301i	−0.870191	+	1.50722i	−0.00839227	+	0.999965i	$0.502671\pi$
$191$	−12.0263	+	20.8301i	−0.870191	+	1.50722i	−0.861799	+	0.507250i	$0.830662\pi$
$192$	−6.92820	+	12.0000i	−0.500000	+	0.866025i
$193$	−10.8660	−	18.8205i	−0.782154	−	1.35473i	−0.930685	−	0.365822i	$-0.880788\pi$
$193$	−10.8660	−	18.8205i	−0.782154	−	1.35473i	0.148531	−	0.988908i	$-0.452545\pi$
$194$	4.29423	−	16.0263i	0.308308	−	1.15062i
$195$	−5.41154	+	3.12436i	−0.387529	+	0.223740i
$196$	0.803848	+	0.464102i	0.0574177	+	0.0331501i
$197$	13.6603	+	13.6603i	0.973253	+	0.973253i	0.999651	−	0.0263987i	$-0.00840394\pi$
$197$	13.6603	+	13.6603i	0.973253	+	0.973253i	−0.0263987	+	0.999651i	$0.508404\pi$
$198$	16.0981	+	9.29423i	1.14404	+	0.660512i
$199$		−	25.1244i		−	1.78102i	−0.454965	−	0.890509i	$-0.650348\pi$
$199$		−	25.1244i		−	1.78102i	0.454965	−	0.890509i	$-0.349652\pi$
$200$	−10.7321	+	2.87564i	−0.758871	+	0.203339i
$201$	−8.36603	−	8.36603i	−0.590094	−	0.590094i
$202$	2.53590	−	1.46410i	0.178425	−	0.103014i
$203$	−1.73205	+	6.46410i	−0.121566	+	0.453691i
$204$	19.8564			1.39023
$205$	0.803848	+	3.00000i	0.0561432	+	0.209529i
$206$	15.1244	−	15.1244i	1.05376	−	1.05376i
$207$	12.2942	+	7.09808i	0.854508	+	0.493350i
$208$	−9.85641	+	9.85641i	−0.683419	+	0.683419i
$209$	7.33013	−	12.6962i	0.507035	−	0.878211i
$210$	6.00000	−	3.46410i	0.414039	−	0.239046i
$211$	4.09808	+	1.09808i	0.282123	+	0.0755947i	0.397106	−	0.917773i	$-0.370015\pi$
$211$	4.09808	+	1.09808i	0.282123	+	0.0755947i	−0.114983	+	0.993367i	$0.536681\pi$
$212$	−20.3923	−	5.46410i	−1.40055	−	0.375276i
$213$	−2.53590	+	4.39230i	−0.173757	+	0.300956i
$214$	−21.6340	−	12.4904i	−1.47887	−	0.853825i
$215$		−	8.92820i		−	0.608898i
$216$	10.3923	+	10.3923i	0.707107	+	0.707107i
$217$			1.46410i			0.0993897i
$218$	−10.7321	+	18.5885i	−0.726866	+	1.25897i
$219$	5.42820	−	9.40192i	0.366804	−	0.635323i
$220$	−4.53590	−	7.85641i	−0.305810	−	0.529679i
$221$	19.2942	+	5.16987i	1.29787	+	0.347763i
$222$	8.19615	+	14.1962i	0.550090	+	0.952783i
$223$	−8.02628	+	13.9019i	−0.537479	+	0.930942i	0.461559	+	0.887109i	$0.347290\pi$
$223$	−8.02628	+	13.9019i	−0.537479	+	0.930942i	−0.999039	+	0.0438324i	$0.986043\pi$
$224$	10.9282	−	10.9282i	0.730171	−	0.730171i
$225$			11.7846i			0.785641i
$226$	13.8564	+	13.8564i	0.921714	+	0.921714i
$227$	−0.571797	−	2.13397i	−0.0379515	−	0.141637i	0.944351	−	0.328941i	$-0.106692\pi$
$227$	−0.571797	−	2.13397i	−0.0379515	−	0.141637i	−0.982302	+	0.187304i	$0.940025\pi$
$228$	8.19615	−	8.19615i	0.542803	−	0.542803i
$229$	−1.83013	+	6.83013i	−0.120938	+	0.451347i	−0.999662	−	0.0259823i	$-0.991729\pi$
$229$	−1.83013	+	6.83013i	−0.120938	+	0.451347i	0.878724	+	0.477330i	$0.158395\pi$
$230$	−3.46410	−	6.00000i	−0.228416	−	0.395628i
$231$	−14.6603	−	14.6603i	−0.964574	−	0.964574i
$232$	6.00000	+	3.46410i	0.393919	+	0.227429i
$233$			3.19615i			0.209387i	0.994505	+	0.104693i	$0.0333861\pi$
$233$			3.19615i			0.209387i	−0.994505	+	0.104693i	$0.966614\pi$
$234$	7.39230	+	12.8038i	0.483250	+	0.837014i
$235$	5.60770	+	5.60770i	0.365806	+	0.365806i
$236$	3.92820	+	14.6603i	0.255704	+	0.954301i
$237$	18.0000	−	10.3923i	1.16923	−	0.675053i
$238$	−21.3923	−	5.73205i	−1.38666	−	0.371554i
$239$	−7.90192	−	13.6865i	−0.511133	−	0.885308i	−0.999917	−	0.0129033i	$-0.995893\pi$
$239$	−7.90192	−	13.6865i	−0.511133	−	0.885308i	0.488784	−	0.872405i	$-0.337441\pi$
$240$	−1.85641	−	6.92820i	−0.119831	−	0.447214i
$241$	−11.5981	+	20.0885i	−0.747098	+	1.29401i	0.202110	+	0.979363i	$0.435220\pi$
$241$	−11.5981	+	20.0885i	−0.747098	+	1.29401i	−0.949208	+	0.314649i	$0.898113\pi$
$242$	−8.19615	+	8.19615i	−0.526869	+	0.526869i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	−16.3923	−	16.3923i	−1.04941	−	1.04941i
$245$	−0.464102	+	0.124356i	−0.0296504	+	0.00794479i
$246$	7.09808	−	1.90192i	0.452557	−	0.121262i
$247$	10.0981	−	5.83013i	0.642525	−	0.370962i
$248$	1.46410	+	0.392305i	0.0929705	+	0.0249114i
$249$	0.633975	−	2.36603i	0.0401765	−	0.149941i
$250$	6.53590	−	11.3205i	0.413367	−	0.715972i
$251$	−5.83013	−	5.83013i	−0.367994	−	0.367994i	0.498751	−	0.866745i	$-0.333792\pi$
$251$	−5.83013	−	5.83013i	−0.367994	−	0.367994i	−0.866745	+	0.498751i	$0.833792\pi$
$252$	−8.19615	−	14.1962i	−0.516309	−	0.894274i
$253$	−14.6603	+	14.6603i	−0.921682	+	0.921682i
$254$	−5.73205	+	1.53590i	−0.359661	+	0.0963708i
$255$	−7.26795	+	7.26795i	−0.455137	+	0.455137i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	9.42820	+	16.3301i	0.588115	+	1.01865i	0.994479	+	0.104934i	$0.0334632\pi$
$257$	9.42820	+	16.3301i	0.588115	+	1.01865i	−0.406364	+	0.913711i	$0.633204\pi$
$258$	−21.1244			−1.31514
$259$	−4.73205	−	17.6603i	−0.294035	−	1.09735i
$260$		−	7.21539i		−	0.447480i
$261$	5.19615	−	5.19615i	0.321634	−	0.321634i
$262$	11.4641			0.708255
$263$	2.49038	+	1.43782i	0.153563	+	0.0886599i	0.574813	−	0.818285i	$-0.305075\pi$
$263$	2.49038	+	1.43782i	0.153563	+	0.0886599i	−0.421249	+	0.906945i	$0.638408\pi$
$264$	−18.5885	+	10.7321i	−1.14404	+	0.660512i
$265$	9.46410	−	5.46410i	0.581375	−	0.335657i
$266$	−11.1962	+	6.46410i	−0.686480	+	0.396339i
$267$	1.73205	−	3.00000i	0.106000	−	0.183597i
$268$	13.1962	−	3.53590i	0.806083	−	0.215989i
$269$	1.26795	−	1.26795i	0.0773082	−	0.0773082i	−0.667395	−	0.744704i	$-0.732591\pi$
$269$	1.26795	−	1.26795i	0.0773082	−	0.0773082i	0.744704	+	0.667395i	$0.232591\pi$
$270$	−7.60770			−0.462990
$271$	−0.392305			−0.0238308			−0.0119154	−	0.999929i	$-0.503793\pi$
$271$	−0.392305			−0.0238308			−0.0119154	+	0.999929i	$0.503793\pi$
$272$	−11.4641	+	19.8564i	−0.695113	+	1.20397i
$273$	−4.26795	−	15.9282i	−0.258308	−	0.964019i
$274$	13.0263	+	3.49038i	0.786946	+	0.210862i
$275$	−16.6244	−	4.45448i	−1.00249	−	0.268615i
$276$	−14.1962	+	8.19615i	−0.854508	+	0.493350i
$277$	25.2224	−	6.75833i	1.51547	−	0.406069i	0.597222	−	0.802076i	$-0.296271\pi$
$277$	25.2224	−	6.75833i	1.51547	−	0.406069i	0.918247	+	0.396007i	$0.129605\pi$
$278$			16.7321i			1.00352i
$279$	0.803848	−	1.39230i	0.0481251	−	0.0833551i
$280$			8.00000i			0.478091i
$281$	8.66025	+	5.00000i	0.516627	+	0.298275i	0.735554	−	0.677466i	$-0.236922\pi$
$281$	8.66025	+	5.00000i	0.516627	+	0.298275i	−0.218926	+	0.975741i	$0.570255\pi$
$282$	13.2679	−	13.2679i	0.790095	−	0.790095i
$283$	5.24167	−	19.5622i	0.311585	−	1.16285i	−0.615542	−	0.788104i	$-0.711063\pi$
$283$	5.24167	−	19.5622i	0.311585	−	1.16285i	0.927127	−	0.374747i	$-0.122270\pi$
$284$	−2.92820	−	5.07180i	−0.173757	−	0.300956i
$285$			6.00000i			0.355409i
$286$	−20.8564	+	5.58846i	−1.23327	+	0.330452i
$287$	−8.19615			−0.483804
$288$	−16.3923	+	4.39230i	−0.965926	+	0.258819i
$289$	15.8564			0.932730
$290$	−3.46410	+	0.928203i	−0.203419	+	0.0545060i
$291$	17.5981	−	10.1603i	1.03162	−	0.595605i
$292$	6.26795	+	10.8564i	0.366804	+	0.635323i
$293$	1.43782	−	5.36603i	0.0839985	−	0.313487i	−0.911124	−	0.412132i	$-0.864784\pi$
$293$	1.43782	−	5.36603i	0.0839985	−	0.313487i	0.995123	+	0.0986454i	$0.0314509\pi$
$294$	0.294229	+	1.09808i	0.0171598	+	0.0640411i
$295$	−6.80385	−	3.92820i	−0.396135	−	0.228709i
$296$	−18.9282			−1.10018
$297$	5.89230	+	21.9904i	0.341906	+	1.27601i
$298$		−	11.4641i		−	0.664098i
$299$	−15.9282	+	4.26795i	−0.921152	+	0.246822i
$300$	−11.7846	−	6.80385i	−0.680385	−	0.392820i
$301$	22.7583	+	6.09808i	1.31177	+	0.351487i
$302$	1.00000	+	0.267949i	0.0575435	+	0.0154187i
$303$	3.46410	+	0.928203i	0.199007	+	0.0533239i
$304$	3.46410	+	12.9282i	0.198680	+	0.741483i
$305$	12.0000			0.687118
$306$	17.1962	+	17.1962i	0.983039	+	0.983039i
$307$	3.02628	−	3.02628i	0.172719	−	0.172719i	−0.615454	−	0.788173i	$-0.711027\pi$
$307$	3.02628	−	3.02628i	0.172719	−	0.172719i	0.788173	+	0.615454i	$0.211027\pi$
$308$	23.1244	−	6.19615i	1.31763	−	0.353059i
$309$	26.1962			1.49025
$310$	−0.679492	+	0.392305i	−0.0385925	+	0.0222814i
$311$	19.0981	−	11.0263i	1.08295	−	0.625243i	0.151261	−	0.988494i	$-0.451667\pi$
$311$	19.0981	−	11.0263i	1.08295	−	0.625243i	0.931691	+	0.363251i	$0.118333\pi$
$312$	−17.0718			−0.966500
$313$	−18.6506	−	10.7679i	−1.05420	−	0.608640i	−0.130375	−	0.991465i	$-0.541618\pi$
$313$	−18.6506	−	10.7679i	−1.05420	−	0.608640i	−0.923821	+	0.382824i	$0.874951\pi$
$314$	6.92820			0.390981
$315$	8.19615	+	2.19615i	0.461801	+	0.123739i
$316$			24.0000i			1.35011i
$317$	5.50962	+	20.5622i	0.309451	+	1.15489i	0.929046	+	0.369965i	$0.120630\pi$
$317$	5.50962	+	20.5622i	0.309451	+	1.15489i	−0.619595	+	0.784922i	$0.712703\pi$
$318$	−12.9282	−	22.3923i	−0.724978	−	1.25570i
$319$	5.36603	+	9.29423i	0.300440	+	0.520377i
$320$	8.00000	+	2.14359i	0.447214	+	0.119831i
$321$	−7.91858	−	29.5526i	−0.441972	−	1.64946i
$322$	17.6603	−	4.73205i	0.984167	−	0.263707i
$323$	13.5622	−	13.5622i	0.754620	−	0.754620i
$324$			18.0000i			1.00000i
$325$	−9.67949	−	9.67949i	−0.536922	−	0.536922i
$326$	7.00000	−	12.1244i	0.387694	−	0.671506i
$327$	−25.3923	+	6.80385i	−1.40420	+	0.376254i
$328$	−2.19615	+	8.19615i	−0.121262	+	0.452557i
$329$	−18.1244	+	10.4641i	−0.999228	+	0.576905i
$330$	2.87564	−	10.7321i	0.158299	−	0.590780i
$331$	−0.0980762	+	0.0262794i	−0.00539076	+	0.00144445i	−0.261513	−	0.965200i	$-0.584222\pi$
$331$	−0.0980762	+	0.0262794i	−0.00539076	+	0.00144445i	0.256123	+	0.966644i	$0.417555\pi$
$332$	2.00000	+	2.00000i	0.109764	+	0.109764i
$333$	−5.19615	+	19.3923i	−0.284747	+	1.06269i
$334$	7.46410	−	7.46410i	0.408417	−	0.408417i
$335$	−3.53590	+	6.12436i	−0.193187	+	0.334609i
$336$	18.9282			1.03262
$337$	8.89230	+	15.4019i	0.484395	+	0.838996i	0.999839	−	0.0179267i	$-0.00570654\pi$
$337$	8.89230	+	15.4019i	0.484395	+	0.838996i	−0.515445	+	0.856923i	$0.672373\pi$
$338$	1.16987	+	0.313467i	0.0636327	+	0.0170503i
$339$			24.0000i			1.30350i
$340$	−3.07180	−	11.4641i	−0.166592	−	0.621728i
$341$	1.66025	+	1.66025i	0.0899078	+	0.0899078i
$342$	14.1962			0.767640
$343$			17.8564i			0.964155i
$344$	12.1962	−	21.1244i	0.657572	−	1.13895i
$345$	2.19615	−	8.19615i	0.118237	−	0.441266i
$346$	1.19615	+	2.07180i	0.0643056	+	0.111380i
$347$	4.72243	−	17.6244i	0.253513	−	0.946125i	−0.715398	−	0.698717i	$-0.753755\pi$
$347$	4.72243	−	17.6244i	0.253513	−	0.946125i	0.968911	−	0.247408i	$-0.0795787\pi$
$348$	2.19615	+	8.19615i	0.117726	+	0.439360i
$349$	−4.26795	−	15.9282i	−0.228458	−	0.852617i	−0.980989	−	0.194061i	$-0.937834\pi$
$349$	−4.26795	−	15.9282i	−0.228458	−	0.852617i	0.752531	−	0.658556i	$-0.228833\pi$
$350$	10.7321	+	10.7321i	0.573652	+	0.573652i
$351$	−4.68653	+	17.4904i	−0.250149	+	0.933567i
$352$		−	24.7846i		−	1.32102i
$353$	7.16025	−	12.4019i	0.381102	−	0.660088i	−0.610118	−	0.792310i	$-0.708878\pi$
$353$	7.16025	−	12.4019i	0.381102	−	0.660088i	0.991220	+	0.132223i	$0.0422114\pi$
$354$	−9.29423	+	16.0981i	−0.493983	+	0.855603i
$355$	2.92820	+	0.784610i	0.155413	+	0.0416428i
$356$	2.00000	+	3.46410i	0.106000	+	0.183597i
$357$	−13.5622	−	23.4904i	−0.717787	−	1.24324i
$358$	1.92820	−	3.33975i	0.101909	−	0.176511i
$359$		−	11.2679i		−	0.594700i	−0.954769	−	0.297350i	$-0.903897\pi$
$359$		−	11.2679i		−	0.594700i	0.954769	−	0.297350i	$-0.0961028\pi$
$360$	4.39230	−	7.60770i	0.231495	−	0.400961i
$361$			7.80385i			0.410729i
$362$	12.8038	+	7.39230i	0.672955	+	0.388531i
$363$	−14.1962			−0.745105
$364$	18.3923	+	4.92820i	0.964019	+	0.258308i
$365$	−6.26795	−	1.67949i	−0.328079	−	0.0879086i
$366$		−	28.3923i		−	1.48409i
$367$	14.1244	−	24.4641i	0.737285	−	1.27702i	−0.216428	−	0.976299i	$-0.569441\pi$
$367$	14.1244	−	24.4641i	0.737285	−	1.27702i	0.953713	−	0.300717i	$-0.0972260\pi$
$368$		−	18.9282i		−	0.986701i
$369$	7.79423	+	4.50000i	0.405751	+	0.234261i
$370$	6.92820	−	6.92820i	0.360180	−	0.360180i
$371$	7.46410	+	27.8564i	0.387517	+	1.44623i
$372$	0.928203	+	1.60770i	0.0481251	+	0.0833551i
$373$	−7.36603	+	27.4904i	−0.381398	+	1.42340i	0.462368	+	0.886688i	$0.347000\pi$
$373$	−7.36603	+	27.4904i	−0.381398	+	1.42340i	−0.843767	+	0.536710i	$0.819667\pi$
$374$	−30.7583	+	17.7583i	−1.59048	+	0.918261i
$375$	15.4641	−	4.14359i	0.798563	−	0.213974i
$376$	5.60770	+	20.9282i	0.289195	+	1.07929i
$377$			8.53590i			0.439621i
$378$	5.19615	−	19.3923i	0.267261	−	0.997433i
$379$	3.75833	+	3.75833i	0.193052	+	0.193052i	0.797014	−	0.603961i	$-0.206412\pi$
$379$	3.75833	+	3.75833i	0.193052	+	0.193052i	−0.603961	+	0.797014i	$0.706412\pi$
$380$	−6.00000	−	3.46410i	−0.307794	−	0.177705i
$381$	−6.29423	−	3.63397i	−0.322463	−	0.186174i
$382$	8.80385	−	32.8564i	0.450444	−	1.68108i
$383$	−6.73205	−	11.6603i	−0.343992	−	0.595811i	0.641178	−	0.767392i	$-0.278446\pi$
$383$	−6.73205	−	11.6603i	−0.343992	−	0.595811i	−0.985170	+	0.171581i	$0.945113\pi$
$384$	5.07180	−	18.9282i	0.258819	−	0.965926i
$385$	−6.19615	+	10.7321i	−0.315785	+	0.546956i
$386$	21.7321	+	21.7321i	1.10613	+	1.10613i
$387$	−18.2942	−	18.2942i	−0.929948	−	0.929948i
$388$			23.4641i			1.19121i
$389$	19.7583	−	5.29423i	1.00179	−	0.268428i	0.279593	−	0.960119i	$-0.409800\pi$
$389$	19.7583	−	5.29423i	1.00179	−	0.268428i	0.722194	+	0.691691i	$0.243134\pi$
$390$	6.24871	−	6.24871i	0.316416	−	0.316416i
$391$	−23.4904	+	13.5622i	−1.18796	+	0.685869i
$392$	−1.26795	−	0.339746i	−0.0640411	−	0.0171598i
$393$	9.92820	+	9.92820i	0.500812	+	0.500812i
$394$	−23.6603	−	13.6603i	−1.19199	−	0.688194i
$395$	−8.78461	−	8.78461i	−0.442002	−	0.442002i
$396$	−25.3923	−	6.80385i	−1.27601	−	0.341906i
$397$	−9.26795	+	9.26795i	−0.465145	+	0.465145i	−0.900337	−	0.435192i	$-0.856680\pi$
$397$	−9.26795	+	9.26795i	−0.465145	+	0.465145i	0.435192	+	0.900337i	$0.356680\pi$
$398$	9.19615	+	34.3205i	0.460961	+	1.72033i
$399$	−15.2942	−	4.09808i	−0.765669	−	0.205160i
$400$	13.6077	−	7.85641i	0.680385	−	0.392820i
$401$	−1.79423	−	3.10770i	−0.0895995	−	0.155191i	0.817742	−	0.575584i	$-0.195225\pi$
$401$	−1.79423	−	3.10770i	−0.0895995	−	0.155191i	−0.907342	+	0.420393i	$0.861892\pi$
$402$	14.4904	+	8.36603i	0.722715	+	0.417259i
$403$	0.483340	+	1.80385i	0.0240769	+	0.0898560i
$404$	−2.92820	+	2.92820i	−0.145684	+	0.145684i
$405$	−6.58846	−	6.58846i	−0.327383	−	0.327383i
$406$		−	9.46410i		−	0.469695i
$407$	−25.3923	−	14.6603i	−1.25865	−	0.726682i
$408$	−27.1244	+	7.26795i	−1.34286	+	0.359817i
$409$	−27.8660	+	16.0885i	−1.37789	+	0.795523i	−0.991905	−	0.126984i	$-0.959470\pi$
$409$	−27.8660	+	16.0885i	−1.37789	+	0.795523i	−0.385981	+	0.922507i	$0.626137\pi$
$410$	−2.19615	−	3.80385i	−0.108460	−	0.187859i
$411$	8.25833	+	14.3038i	0.407353	+	0.705557i
$412$	−15.1244	+	26.1962i	−0.745124	+	1.29059i
$413$	14.6603	−	14.6603i	0.721384	−	0.721384i
$414$	−19.3923	−	5.19615i	−0.953080	−	0.255377i
$415$	−1.46410			−0.0718699
$416$	9.85641	−	17.0718i	0.483250	−	0.837014i
$417$	−14.4904	+	14.4904i	−0.709597	+	0.709597i
$418$	−5.36603	+	20.0263i	−0.262461	+	0.979517i
$419$	−6.63397	−	1.77757i	−0.324091	−	0.0868399i	0.0931055	−	0.995656i	$-0.470321\pi$
$419$	−6.63397	−	1.77757i	−0.324091	−	0.0868399i	−0.417196	+	0.908816i	$0.636987\pi$
$420$	−6.92820	+	6.92820i	−0.338062	+	0.338062i
$421$	−30.5885	+	8.19615i	−1.49079	+	0.399456i	−0.910004	−	0.414600i	$-0.863922\pi$
$421$	−30.5885	+	8.19615i	−1.49079	+	0.399456i	−0.580786	+	0.814056i	$0.697255\pi$
$422$	−6.00000			−0.292075
$423$	22.9808			1.11736
$424$	29.8564			1.44996
$425$	−19.5000	−	11.2583i	−0.945889	−	0.546109i
$426$	1.85641	−	6.92820i	0.0899432	−	0.335673i
$427$	−8.19615	+	30.5885i	−0.396640	+	1.48028i
$428$	34.1244	+	9.14359i	1.64946	+	0.441972i
$429$	−22.9019	−	13.2224i	−1.10572	−	0.638385i
$430$	3.26795	+	12.1962i	0.157595	+	0.588151i
$431$	−16.1962			−0.780141			−0.390071	−	0.920785i	$-0.627549\pi$
$431$	−16.1962			−0.780141			−0.390071	+	0.920785i	$0.627549\pi$
$432$	−18.0000	−	10.3923i	−0.866025	−	0.500000i
$433$	−5.73205			−0.275465			−0.137732	−	0.990469i	$-0.543981\pi$
$433$	−5.73205			−0.275465			−0.137732	+	0.990469i	$0.543981\pi$
$434$	−0.535898	−	2.00000i	−0.0257239	−	0.0960031i
$435$	−3.80385	−	2.19615i	−0.182381	−	0.105297i
$436$	7.85641	−	29.3205i	0.376254	−	1.40420i
$437$	−4.09808	+	15.2942i	−0.196038	+	0.731622i
$438$	−3.97372	+	14.8301i	−0.189872	+	0.708611i
$439$	22.8564	+	13.1962i	1.09088	+	0.629818i	0.933810	−	0.357770i	$-0.116463\pi$
$439$	22.8564	+	13.1962i	1.09088	+	0.629818i	0.157067	+	0.987588i	$0.449796\pi$
$440$	9.07180	+	9.07180i	0.432481	+	0.432481i
$441$	−0.696152	+	1.20577i	−0.0331501	+	0.0574177i
$442$	−28.2487			−1.34365
$443$	17.2583	−	4.62436i	0.819968	−	0.219710i	0.175636	−	0.984455i	$-0.443802\pi$
$443$	17.2583	−	4.62436i	0.819968	−	0.219710i	0.644332	+	0.764745i	$0.277135\pi$
$444$	−16.3923	−	16.3923i	−0.777944	−	0.777944i
$445$	−2.00000	−	0.535898i	−0.0948091	−	0.0254040i
$446$	5.87564	−	21.9282i	0.278220	−	1.03833i
$447$	9.92820	−	9.92820i	0.469588	−	0.469588i
$448$	−10.9282	+	18.9282i	−0.516309	+	0.894274i
$449$	−3.33975			−0.157612			−0.0788062	−	0.996890i	$-0.525111\pi$
$449$	−3.33975			−0.157612			−0.0788062	+	0.996890i	$0.525111\pi$
$450$	−4.31347	−	16.0981i	−0.203339	−	0.758871i
$451$	−9.29423	+	9.29423i	−0.437648	+	0.437648i
$452$	−24.0000	−	13.8564i	−1.12887	−	0.651751i
$453$	0.633975	+	1.09808i	0.0297867	+	0.0515921i
$454$	1.56218	+	2.70577i	0.0733166	+	0.126988i
$455$	−8.53590	+	4.92820i	−0.400169	+	0.231038i
$456$	−8.19615	+	14.1962i	−0.383820	+	0.664796i
$457$	−2.25833	−	1.30385i	−0.105640	−	0.0609914i	0.446249	−	0.894909i	$-0.352760\pi$
$457$	−2.25833	−	1.30385i	−0.105640	−	0.0609914i	−0.551889	+	0.833917i	$0.686093\pi$
$458$		−	10.0000i		−	0.467269i
$459$			29.7846i			1.39023i
$460$	6.92820	+	6.92820i	0.323029	+	0.323029i
$461$	−9.56218	−	35.6865i	−0.445355	−	1.66209i	−0.714997	−	0.699127i	$-0.753572\pi$
$461$	−9.56218	−	35.6865i	−0.445355	−	1.66209i	0.269642	−	0.962961i	$-0.413094\pi$
$462$	25.3923	+	14.6603i	1.18136	+	0.682057i
$463$	1.19615	+	2.07180i	0.0555899	+	0.0962846i	0.892481	−	0.451085i	$-0.148963\pi$
$463$	1.19615	+	2.07180i	0.0555899	+	0.0962846i	−0.836891	+	0.547369i	$0.815629\pi$
$464$	−9.46410	−	2.53590i	−0.439360	−	0.117726i
$465$	−0.928203	−	0.248711i	−0.0430444	−	0.0115337i
$466$	−1.16987	−	4.36603i	−0.0541933	−	0.202252i
$467$	2.63397	−	2.63397i	0.121886	−	0.121886i	−0.643533	−	0.765419i	$-0.722532\pi$
$467$	2.63397	−	2.63397i	0.121886	−	0.121886i	0.765419	+	0.643533i	$0.222532\pi$
$468$	−14.7846	−	14.7846i	−0.683419	−	0.683419i
$469$	−13.1962	−	13.1962i	−0.609342	−	0.609342i
$470$	−9.71281	−	5.60770i	−0.448019	−	0.258664i
$471$	6.00000	+	6.00000i	0.276465	+	0.276465i
$472$	−10.7321	−	18.5885i	−0.493983	−	0.855603i
$473$	32.7224	−	18.8923i	1.50458	−	0.868669i
$474$	−20.7846	+	20.7846i	−0.954669	+	0.954669i
$475$	−12.6962	+	3.40192i	−0.582539	+	0.156091i
$476$	31.3205			1.43557
$477$	8.19615	−	30.5885i	0.375276	−	1.40055i
$478$	15.8038	+	15.8038i	0.722851	+	0.722851i
$479$	4.16987	−	7.22243i	0.190526	−	0.330001i	−0.754898	−	0.655842i	$-0.772314\pi$
$479$	4.16987	−	7.22243i	0.190526	−	0.330001i	0.945425	+	0.325840i	$0.105647\pi$
$480$	5.07180	+	8.78461i	0.231495	+	0.400961i
$481$	−11.6603	−	20.1962i	−0.531662	−	0.920865i
$482$	8.49038	−	31.6865i	0.386726	−	1.44328i
$483$	19.3923	+	11.1962i	0.882380	+	0.509443i
$484$	8.19615	−	14.1962i	0.372552	−	0.645280i
$485$	−8.58846	−	8.58846i	−0.389982	−	0.389982i
$486$	−15.5885	+	15.5885i	−0.707107	+	0.707107i
$487$		−	5.80385i		−	0.262997i	−0.991316	−	0.131499i	$-0.958021\pi$
$487$		−	5.80385i		−	0.262997i	0.991316	−	0.131499i	$-0.0419789\pi$
$488$	28.3923	+	16.3923i	1.28526	+	0.742045i
$489$	16.5622	−	4.43782i	0.748968	−	0.200685i
$490$	0.588457	−	0.339746i	0.0265838	−	0.0153482i
$491$	3.72243	−	13.8923i	0.167991	−	0.626951i	−0.829649	−	0.558286i	$-0.811459\pi$
$491$	3.72243	−	13.8923i	0.167991	−	0.626951i	0.997640	−	0.0686652i	$-0.0218740\pi$
$492$	−9.00000	+	5.19615i	−0.405751	+	0.234261i
$493$	3.63397	+	13.5622i	0.163666	+	0.610810i
$494$	−11.6603	+	11.6603i	−0.524620	+	0.524620i
$495$	11.7846	−	6.80385i	0.529679	−	0.305810i
$496$	−2.14359			−0.0962502
$497$	−4.00000	+	6.92820i	−0.179425	+	0.310772i
$498$			3.46410i			0.155230i
$499$	8.69615	+	2.33013i	0.389293	+	0.104311i	0.448156	−	0.893955i	$-0.352081\pi$
$499$	8.69615	+	2.33013i	0.389293	+	0.104311i	−0.0588630	+	0.998266i	$0.518748\pi$
$500$	−4.78461	+	17.8564i	−0.213974	+	0.798563i
$501$	12.9282			0.577590
$502$	10.0981	+	5.83013i	0.450699	+	0.260211i
$503$			27.7128i			1.23565i	0.786314	+	0.617827i	$0.211987\pi$
$503$			27.7128i			1.23565i	−0.786314	+	0.617827i	$0.788013\pi$
$504$	16.3923	+	16.3923i	0.730171	+	0.730171i
$505$		−	2.14359i		−	0.0953887i
$506$	14.6603	−	25.3923i	0.651728	−	1.12883i
$507$	0.741670	+	1.28461i	0.0329387	+	0.0570515i
$508$	7.26795	−	4.19615i	0.322463	−	0.186174i
$509$	−11.4641	−	3.07180i	−0.508137	−	0.136155i	−0.00436335	−	0.999990i	$-0.501389\pi$
$509$	−11.4641	−	3.07180i	−0.508137	−	0.136155i	−0.503774	+	0.863835i	$0.668056\pi$
$510$	7.26795	−	12.5885i	0.321830	−	0.557426i
$511$	8.56218	−	14.8301i	0.378768	−	0.656046i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	12.2942	+	12.2942i	0.542803	+	0.542803i
$514$	−18.8564	−	18.8564i	−0.831720	−	0.831720i
$515$	−4.05256	−	15.1244i	−0.178577	−	0.666459i
$516$	28.8564	−	7.73205i	1.27033	−	0.340385i
$517$	−8.68653	+	32.4186i	−0.382033	+	1.42577i
$518$	12.9282	+	22.3923i	0.568033	+	0.983861i
$519$	−0.758330	+	2.83013i	−0.0332870	+	0.124229i
$520$	2.64102	+	9.85641i	0.115816	+	0.432232i
$521$		−	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
$523$	−7.53590	−	7.53590i	−0.329522	−	0.329522i	0.522883	−	0.852405i	$-0.324857\pi$
$523$	−7.53590	−	7.53590i	−0.329522	−	0.329522i	−0.852405	+	0.522883i	$0.824857\pi$
$524$	−15.6603	+	4.19615i	−0.684121	+	0.183310i
$525$			18.5885i			0.811267i
$526$	−3.92820	−	1.05256i	−0.171278	−	0.0458937i
$527$	1.53590	+	2.66025i	0.0669048	+	0.115882i
$528$	21.4641	−	21.4641i	0.934105	−	0.934105i
$529$	−0.303848	+	0.526279i	−0.0132108	+	0.0228817i
$530$	−10.9282	+	10.9282i	−0.474691	+	0.474691i
$531$	−21.9904	+	5.89230i	−0.954301	+	0.255704i
$532$	12.9282	−	12.9282i	0.560509	−	0.560509i
$533$	−10.0981	+	2.70577i	−0.437396	+	0.117200i
$534$	−1.26795	+	4.73205i	−0.0548695	+	0.204776i
$535$	−15.8372	+	9.14359i	−0.684701	+	0.395312i
$536$	−16.7321	+	9.66025i	−0.722715	+	0.417259i
$537$	4.56218	−	1.22243i	0.196873	−	0.0527518i
$538$	−1.26795	+	2.19615i	−0.0546652	+	0.0946829i
$539$	−1.43782	−	1.43782i	−0.0619314	−	0.0619314i
$540$	10.3923	−	2.78461i	0.447214	−	0.119831i
$541$	2.19615	−	2.19615i	0.0944200	−	0.0944200i	−0.658319	−	0.752739i	$-0.728732\pi$
$541$	2.19615	−	2.19615i	0.0944200	−	0.0944200i	0.752739	+	0.658319i	$0.228732\pi$
$542$	0.535898	−	0.143594i	0.0230188	−	0.00616787i
$543$	4.68653	+	17.4904i	0.201118	+	0.750584i
$544$	8.39230	−	31.3205i	0.359817	−	1.34286i
$545$	7.85641	+	13.6077i	0.336531	+	0.582890i
$546$	11.6603	+	20.1962i	0.499013	+	0.864316i
$547$	−8.74167	−	32.6244i	−0.373767	−	1.39492i	−0.855138	−	0.518400i	$-0.826528\pi$
$547$	−8.74167	−	32.6244i	−0.373767	−	1.39492i	0.481371	−	0.876517i	$-0.340139\pi$
$548$	−19.0718			−0.814707
$549$	24.5885	−	24.5885i	1.04941	−	1.04941i
$550$	24.3397			1.03785
$551$	7.09808	+	4.09808i	0.302388	+	0.174584i
$552$	16.3923	−	16.3923i	0.697703	−	0.697703i
$553$	28.3923	−	16.3923i	1.20736	−	0.697072i
$554$	−31.9808	+	18.4641i	−1.35873	+	0.784465i
$555$	12.0000			0.509372
$556$	−6.12436	−	22.8564i	−0.259731	−	0.969328i
$557$	−14.8038	+	14.8038i	−0.627259	+	0.627259i	−0.947378	−	0.320118i	$-0.896277\pi$
$557$	−14.8038	+	14.8038i	−0.627259	+	0.627259i	0.320118	+	0.947378i	$0.396277\pi$
$558$	−0.588457	+	2.19615i	−0.0249114	+	0.0929705i
$559$	30.0526			1.27109
$560$	−2.92820	−	10.9282i	−0.123739	−	0.461801i
$561$	−42.0167	−	11.2583i	−1.77394	−	0.475327i
$562$	−13.6603	−	3.66025i	−0.576223	−	0.154398i
$563$	26.9904	+	7.23205i	1.13751	+	0.304795i	0.777949	−	0.628327i	$-0.216260\pi$
$563$	26.9904	+	7.23205i	1.13751	+	0.304795i	0.359560	+	0.933122i	$0.382927\pi$
$564$	−13.2679	+	22.9808i	−0.558681	+	0.967665i
$565$	13.8564	−	3.71281i	0.582943	−	0.156199i
$566$			28.6410i			1.20387i
$567$	21.2942	−	12.2942i	0.894274	−	0.516309i
$568$	5.85641	+	5.85641i	0.245729	+	0.245729i
$569$	18.4019	+	10.6244i	0.771449	+	0.445396i	0.833391	−	0.552684i	$-0.186396\pi$
$569$	18.4019	+	10.6244i	0.771449	+	0.445396i	−0.0619424	+	0.998080i	$0.519730\pi$
$570$	−2.19615	−	8.19615i	−0.0919867	−	0.343299i
$571$	0.892305	−	3.33013i	0.0373418	−	0.139361i	−0.944738	−	0.327825i	$-0.893684\pi$
$571$	0.892305	−	3.33013i	0.0373418	−	0.139361i	0.982080	+	0.188464i	$0.0603509\pi$
$572$	26.4449	−	15.2679i	1.10572	−	0.638385i
$573$	36.0788	−	20.8301i	1.50722	−	0.870191i
$574$	11.1962	−	3.00000i	0.467318	−	0.125218i
$575$	18.5885			0.775192
$576$	20.7846	−	12.0000i	0.866025	−	0.500000i
$577$	−5.78461			−0.240816			−0.120408	−	0.992724i	$-0.538420\pi$
$577$	−5.78461			−0.240816			−0.120408	+	0.992724i	$0.538420\pi$
$578$	−21.6603	+	5.80385i	−0.900948	+	0.241408i
$579$			37.6410i			1.56431i
$580$	4.39230	−	2.53590i	0.182381	−	0.105297i
$581$	1.00000	−	3.73205i	0.0414870	−	0.154832i
$582$	−20.3205	+	20.3205i	−0.842312	+	0.842312i
$583$	40.0526	+	23.1244i	1.65881	+	0.957713i
$584$	−12.5359	−	12.5359i	−0.518739	−	0.518739i
$585$	10.8231			0.447480
$586$			7.85641i			0.324545i
$587$	−26.9904	+	7.23205i	−1.11401	+	0.298499i	−0.768458	−	0.639900i	$-0.778976\pi$
$587$	−26.9904	+	7.23205i	−1.11401	+	0.298499i	−0.345554	+	0.938399i	$0.612309\pi$
$588$	−0.803848	−	1.39230i	−0.0331501	−	0.0574177i
$589$	1.73205	+	0.464102i	0.0713679	+	0.0191230i
$590$	10.7321	+	2.87564i	0.441832	+	0.118388i
$591$	−8.66025	−	32.3205i	−0.356235	−	1.32949i
$592$	25.8564	−	6.92820i	1.06269	−	0.284747i
$593$	17.4641			0.717165			0.358582	−	0.933498i	$-0.383260\pi$
$593$	17.4641			0.717165			0.358582	+	0.933498i	$0.383260\pi$
$594$	−16.0981	−	27.8827i	−0.660512	−	1.14404i
$595$	−11.4641	+	11.4641i	−0.469982	+	0.469982i
$596$	4.19615	+	15.6603i	0.171881	+	0.641469i
$597$	−21.7583	+	37.6865i	−0.890509	+	1.54241i
$598$	20.1962	−	11.6603i	0.825882	−	0.476823i
$599$	−11.3205	+	6.53590i	−0.462543	+	0.267050i	−0.713113	−	0.701049i	$-0.752715\pi$
$599$	−11.3205	+	6.53590i	−0.462543	+	0.267050i	0.250570	+	0.968099i	$0.419382\pi$
$600$	18.5885	+	4.98076i	0.758871	+	0.203339i
$601$	20.5526	+	11.8660i	0.838356	+	0.484025i	0.856705	−	0.515806i	$-0.172508\pi$
$601$	20.5526	+	11.8660i	0.838356	+	0.484025i	−0.0183488	+	0.999832i	$0.505841\pi$
$602$	−33.3205			−1.35804
$603$	5.30385	+	19.7942i	0.215989	+	0.806083i
$604$	−1.46410			−0.0595734
$605$	2.19615	+	8.19615i	0.0892863	+	0.333221i
$606$	−5.07180			−0.206028
$607$	−8.58846	−	14.8756i	−0.348595	−	0.603784i	0.637405	−	0.770529i	$-0.280008\pi$
$607$	−8.58846	−	14.8756i	−0.348595	−	0.603784i	−0.986000	+	0.166745i	$0.946674\pi$
$608$	−9.46410	−	16.3923i	−0.383820	−	0.664796i
$609$	8.19615	−	8.19615i	0.332125	−	0.332125i
$610$	−16.3923	+	4.39230i	−0.663705	+	0.177839i
$611$	−18.8756	+	18.8756i	−0.763627	+	0.763627i
$612$	−29.7846	−	17.1962i	−1.20397	−	0.695113i
$613$	−15.6603	−	15.6603i	−0.632512	−	0.632512i	0.316186	−	0.948697i	$-0.397598\pi$
$613$	−15.6603	−	15.6603i	−0.632512	−	0.632512i	−0.948697	+	0.316186i	$0.897598\pi$
$614$	−3.02628	+	5.24167i	−0.122131	+	0.211537i
$615$	1.39230	−	5.19615i	0.0561432	−	0.209529i
$616$	−29.3205	+	16.9282i	−1.18136	+	0.682057i
$617$	35.0885	−	20.2583i	1.41261	−	0.815570i	0.416975	−	0.908918i	$-0.363090\pi$
$617$	35.0885	−	20.2583i	1.41261	−	0.815570i	0.995633	+	0.0933485i	$0.0297571\pi$
$618$	−35.7846	+	9.58846i	−1.43947	+	0.385704i
$619$	−15.5981	+	4.17949i	−0.626940	+	0.167988i	−0.558281	−	0.829652i	$-0.688539\pi$
$619$	−15.5981	+	4.17949i	−0.626940	+	0.167988i	−0.0686590	+	0.997640i	$0.521872\pi$
$620$	0.784610	−	0.784610i	0.0315107	−	0.0315107i
$621$	−12.2942	−	21.2942i	−0.493350	−	0.854508i
$622$	−22.0526	+	22.0526i	−0.884227	+	0.884227i
$623$	2.73205	−	4.73205i	0.109457	−	0.189586i
$624$	23.3205	−	6.24871i	0.933567	−	0.250149i
$625$	5.03590	+	8.72243i	0.201436	+	0.348897i
$626$	29.4186	+	7.88269i	1.17580	+	0.315055i
$627$	−21.9904	+	12.6962i	−0.878211	+	0.507035i
$628$	−9.46410	+	2.53590i	−0.377659	+	0.101193i
$629$	−27.1244	−	27.1244i	−1.08152	−	1.08152i
$630$	−12.0000			−0.478091
$631$		−	17.6077i		−	0.700951i	−0.936572	−	0.350476i	$-0.886020\pi$
$631$		−	17.6077i		−	0.700951i	0.936572	−	0.350476i	$-0.113980\pi$
$632$	−8.78461	−	32.7846i	−0.349433	−	1.30410i
$633$	−5.19615	−	5.19615i	−0.206529	−	0.206529i
$634$	−15.0526	−	26.0718i	−0.597813	−	1.03544i
$635$	−1.12436	+	4.19615i	−0.0446187	+	0.166519i
$636$	25.8564	+	25.8564i	1.02527	+	1.02527i
$637$	−0.418584	−	1.56218i	−0.0165849	−	0.0618957i
$638$	−10.7321	−	10.7321i	−0.424886	−	0.424886i
$639$	7.60770	−	4.39230i	0.300956	−	0.173757i
$640$	−11.7128			−0.462990
$641$	−19.7942	+	34.2846i	−0.781825	+	1.35416i	0.149053	+	0.988829i	$0.452378\pi$
$641$	−19.7942	+	34.2846i	−0.781825	+	1.35416i	−0.930878	+	0.365331i	$0.880956\pi$
$642$	21.6340	+	37.4711i	0.853825	+	1.47887i
$643$	8.76795	+	2.34936i	0.345774	+	0.0926499i	0.427527	−	0.904003i	$-0.359385\pi$
$643$	8.76795	+	2.34936i	0.345774	+	0.0926499i	−0.0817525	+	0.996653i	$0.526052\pi$
$644$	−22.3923	+	12.9282i	−0.882380	+	0.509443i
$645$	−7.73205	+	13.3923i	−0.304449	+	0.527321i
$646$	−13.5622	+	23.4904i	−0.533597	+	0.924217i
$647$		−	16.7321i		−	0.657805i	−0.944364	−	0.328902i	$-0.893321\pi$
$647$		−	16.7321i		−	0.657805i	0.944364	−	0.328902i	$-0.106679\pi$
$648$	−6.58846	−	24.5885i	−0.258819	−	0.965926i
$649$		−	33.2487i		−	1.30513i
$650$	16.7654	+	9.67949i	0.657592	+	0.379661i
$651$	1.26795	−	2.19615i	0.0496948	−	0.0860740i
$652$	−5.12436	+	19.1244i	−0.200685	+	0.748968i
$653$	−27.4904	−	7.36603i	−1.07578	−	0.288255i	−0.322915	−	0.946428i	$-0.604663\pi$
$653$	−27.4904	−	7.36603i	−1.07578	−	0.288255i	−0.752867	+	0.658173i	$0.771329\pi$
$654$	32.1962	−	18.5885i	1.25897	−	0.726866i
$655$	4.19615	−	7.26795i	0.163957	−	0.283982i
$656$		−	12.0000i		−	0.468521i
$657$	−16.2846	+	9.40192i	−0.635323	+	0.366804i
$658$	20.9282	−	20.9282i	0.815866	−	0.815866i
$659$	4.02628	+	15.0263i	0.156842	+	0.585341i	0.998941	+	0.0460178i	$0.0146531\pi$
$659$	4.02628	+	15.0263i	0.156842	+	0.585341i	−0.842099	+	0.539323i	$0.818680\pi$
$660$			15.7128i			0.611620i
$661$	2.19615	−	8.19615i	0.0854204	−	0.318793i	−0.909973	−	0.414667i	$-0.863898\pi$
$661$	2.19615	−	8.19615i	0.0854204	−	0.318793i	0.995393	+	0.0958740i	$0.0305646\pi$
$662$	0.124356	−	0.0717968i	0.00483322	−	0.00279046i
$663$	−24.4641	−	24.4641i	−0.950107	−	0.950107i
$664$	−3.46410	−	2.00000i	−0.134433	−	0.0776151i
$665$			9.46410i			0.367002i
$666$		−	28.3923i		−	1.10018i
$667$	−8.19615	−	8.19615i	−0.317356	−	0.317356i
$668$	−7.46410	+	12.9282i	−0.288795	+	0.500207i
$669$	24.0788	−	13.9019i	0.930942	−	0.537479i
$670$	2.58846	−	9.66025i	0.100001	−	0.373208i
$671$	25.3923	+	43.9808i	0.980259	+	1.69786i
$672$	−25.8564	+	6.92820i	−0.997433	+	0.267261i
$673$	19.1962	−	33.2487i	0.739957	−	1.28164i	−0.212557	−	0.977149i	$-0.568179\pi$
$673$	19.1962	−	33.2487i	0.739957	−	1.28164i	0.952514	−	0.304495i	$-0.0984877\pi$
$674$	−17.7846	−	17.7846i	−0.685038	−	0.685038i
$675$	10.2058	−	17.6769i	0.392820	−	0.680385i
$676$	−1.71281			−0.0658774
$677$	−4.73205	+	1.26795i	−0.181867	+	0.0487312i	−0.348603	−	0.937270i	$-0.613344\pi$
$677$	−4.73205	+	1.26795i	−0.181867	+	0.0487312i	0.166736	+	0.986002i	$0.446677\pi$
$678$	−8.78461	−	32.7846i	−0.337371	−	1.25909i
$679$	27.7583	−	16.0263i	1.06527	−	0.615032i
$680$	8.39230	+	14.5359i	0.321830	+	0.557426i
$681$	−0.990381	+	3.69615i	−0.0379515	+	0.141637i
$682$	−2.87564	−	1.66025i	−0.110114	−	0.0635744i
$683$	−20.2942	−	20.2942i	−0.776537	−	0.776537i	0.202703	−	0.979240i	$-0.435027\pi$
$683$	−20.2942	−	20.2942i	−0.776537	−	0.776537i	−0.979240	+	0.202703i	$0.935027\pi$
$684$	−19.3923	+	5.19615i	−0.741483	+	0.198680i
$685$	6.98076	−	6.98076i	0.266721	−	0.266721i
$686$	−6.53590	−	24.3923i	−0.249542	−	0.931303i
$687$	8.66025	−	8.66025i	0.330409	−	0.330409i
$688$	−8.92820	+	33.3205i	−0.340385	+	1.27033i
$689$	18.3923	+	31.8564i	0.700691	+	1.21363i
$690$			12.0000i			0.456832i
$691$	−2.49038	−	9.29423i	−0.0947386	−	0.353569i	0.902241	−	0.431232i	$-0.141921\pi$
$691$	−2.49038	−	9.29423i	−0.0947386	−	0.353569i	−0.996980	+	0.0776628i	$0.975254\pi$
$692$	−2.39230	−	2.39230i	−0.0909418	−	0.0909418i
$693$	9.29423	+	34.6865i	0.353059	+	1.31763i
$694$			25.8038i			0.979501i
$695$	10.6077	+	6.12436i	0.402373	+	0.232310i
$696$	−6.00000	−	10.3923i	−0.227429	−	0.393919i
$697$	−14.8923	+	8.59808i	−0.564086	+	0.325675i
$698$	11.6603	+	20.1962i	0.441347	+	0.764436i
$699$	2.76795	−	4.79423i	0.104693	−	0.181334i
$700$	−18.5885	−	10.7321i	−0.702578	−	0.405633i
$701$	−6.66025	+	6.66025i	−0.251554	+	0.251554i	−0.821608	−	0.570053i	$-0.806923\pi$
$701$	−6.66025	+	6.66025i	−0.251554	+	0.251554i	0.570053	+	0.821608i	$0.306923\pi$
$702$		−	25.6077i		−	0.966500i
$703$	−22.3923			−0.844542
$704$	9.07180	+	33.8564i	0.341906	+	1.27601i
$705$	−3.55514	−	13.2679i	−0.133894	−	0.499700i
$706$	−5.24167	+	19.5622i	−0.197273	+	0.736232i
$707$	5.46410	+	1.46410i	0.205499	+	0.0550632i
$708$	6.80385	−	25.3923i	0.255704	−	0.954301i
$709$	36.5885	−	9.80385i	1.37411	−	0.368191i	0.505131	−	0.863043i	$-0.331444\pi$
$709$	36.5885	−	9.80385i	1.37411	−	0.368191i	0.868978	+	0.494852i	$0.164778\pi$
$710$	−4.28719			−0.160895
$711$	−36.0000			−1.35011
$712$	−4.00000	−	4.00000i	−0.149906	−	0.149906i
$713$	−2.19615	−	1.26795i	−0.0822466	−	0.0474851i
$714$	27.1244	+	27.1244i	1.01510	+	1.01510i
$715$	−4.09103	+	15.2679i	−0.152996	+	0.570989i
$716$	−1.41154	+	5.26795i	−0.0527518	+	0.196873i
$717$			27.3731i			1.02227i
$718$	4.12436	+	15.3923i	0.153920	+	0.574436i
$719$	4.39230			0.163805			0.0819027	−	0.996640i	$-0.473900\pi$
$719$	4.39230			0.163805			0.0819027	+	0.996640i	$0.473900\pi$
$720$	−3.21539	+	12.0000i	−0.119831	+	0.447214i
$721$	41.3205			1.53886
$722$	−2.85641	−	10.6603i	−0.106304	−	0.396734i
$723$	34.7942	−	20.0885i	1.29401	−	0.747098i
$724$	−20.1962	−	5.41154i	−0.750584	−	0.201118i
$725$	2.49038	−	9.29423i	0.0924904	−	0.345179i
$726$	19.3923	−	5.19615i	0.719716	−	0.192847i
$727$	28.8109	+	16.6340i	1.06854	+	0.616920i	0.927781	−	0.373124i	$-0.121714\pi$
$727$	28.8109	+	16.6340i	1.06854	+	0.616920i	0.140755	+	0.990044i	$0.455047\pi$
$728$	−26.9282			−0.998026
$729$	−27.0000			−1.00000
$730$	9.17691			0.339653
$731$	47.7487	−	12.7942i	1.76605	−	0.473212i
$732$	10.3923	+	38.7846i	0.384111	+	1.43352i
$733$	−11.0263	−	2.95448i	−0.407265	−	0.109126i	0.0493698	−	0.998781i	$-0.484279\pi$
$733$	−11.0263	−	2.95448i	−0.407265	−	0.109126i	−0.456635	+	0.889654i	$0.650945\pi$
$734$	−10.3397	+	38.5885i	−0.381647	+	1.42433i
$735$	0.803848	+	0.215390i	0.0296504	+	0.00794479i
$736$	6.92820	+	25.8564i	0.255377	+	0.953080i
$737$	−29.9282			−1.10242
$738$	−12.2942	−	3.29423i	−0.452557	−	0.121262i
$739$	−8.22243	+	8.22243i	−0.302467	+	0.302467i	−0.841978	−	0.539511i	$-0.818609\pi$
$739$	−8.22243	+	8.22243i	−0.302467	+	0.302467i	0.539511	+	0.841978i	$0.318609\pi$
$740$	−6.92820	+	12.0000i	−0.254686	+	0.441129i
$741$	−20.1962			−0.741924
$742$	−20.3923	−	35.3205i	−0.748625	−	1.29666i
$743$	−24.7583	+	14.2942i	−0.908295	+	0.524404i	−0.879882	−	0.475192i	$-0.842379\pi$
$743$	−24.7583	+	14.2942i	−0.908295	+	0.524404i	−0.0284129	+	0.999596i	$0.509045\pi$
$744$	−1.85641	−	1.85641i	−0.0680592	−	0.0680592i
$745$	−7.26795	−	4.19615i	−0.266277	−	0.153735i
$746$		−	40.2487i		−	1.47361i
$747$	−3.00000	+	3.00000i	−0.109764	+	0.109764i
$748$	35.5167	−	35.5167i	1.29862	−	1.29862i
$749$	−12.4904	−	46.6147i	−0.456389	−	1.70327i
$750$	−19.6077	+	11.3205i	−0.715972	+	0.413367i
$751$	−8.85641	−	15.3397i	−0.323175	−	0.559755i	0.657966	−	0.753047i	$-0.271417\pi$
$751$	−8.85641	−	15.3397i	−0.323175	−	0.559755i	−0.981141	+	0.193292i	$0.938084\pi$
$752$	−15.3205	−	26.5359i	−0.558681	−	0.967665i
$753$	3.69615	+	13.7942i	0.134695	+	0.502690i
$754$	−3.12436	−	11.6603i	−0.113782	−	0.424641i
$755$	0.535898	−	0.535898i	0.0195033	−	0.0195033i
$756$			28.3923i			1.03262i
$757$	−19.9282	−	19.9282i	−0.724303	−	0.724303i	0.245176	−	0.969479i	$-0.421154\pi$
$757$	−19.9282	−	19.9282i	−0.724303	−	0.724303i	−0.969479	+	0.245176i	$0.921154\pi$
$758$	−6.50962	−	3.75833i	−0.236440	−	0.136509i
$759$	34.6865	−	9.29423i	1.25904	−	0.337359i
$760$	9.46410	+	2.53590i	0.343299	+	0.0919867i
$761$	−45.3731	+	26.1962i	−1.64477	+	0.949610i	−0.665669	+	0.746247i	$0.731854\pi$
$761$	−45.3731	+	26.1962i	−1.64477	+	0.949610i	−0.979104	+	0.203363i	$0.934813\pi$
$762$	9.92820	+	2.66025i	0.359661	+	0.0963708i
$763$	−40.0526	+	10.7321i	−1.45000	+	0.388526i
$764$

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)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.267949 + 1.00000i) q^{5} +(2.36603 + 0.633975i) q^{6} +(-2.36603 - 1.36603i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.36603 + 0.366025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.267949 + 1.00000i) q^{5} +(2.36603 + 0.633975i) q^{6} +(-2.36603 - 1.36603i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.50000 + 2.59808i) q^{9} -1.46410i q^{10} +(-4.23205 + 1.13397i) q^{11} -3.46410 q^{12} +(-3.36603 - 0.901924i) q^{13} +(3.73205 + 1.00000i) q^{14} +(1.26795 - 1.26795i) q^{15} +(2.00000 - 3.46410i) q^{16} -5.73205 q^{17} +(-3.00000 - 3.00000i) q^{18} +(-2.36603 + 2.36603i) q^{19} +(0.535898 + 2.00000i) q^{20} +(2.36603 + 4.09808i) q^{21} +(5.36603 - 3.09808i) q^{22} +(4.09808 - 2.36603i) q^{23} +(4.73205 - 1.26795i) q^{24} +(3.40192 + 1.96410i) q^{25} +4.92820 q^{26} -5.19615i q^{27} -5.46410 q^{28} +(-0.633975 - 2.36603i) q^{29} +(-1.26795 + 2.19615i) q^{30} +(-0.267949 - 0.464102i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(7.33013 + 1.96410i) q^{33} +(7.83013 - 2.09808i) q^{34} +(2.00000 - 2.00000i) q^{35} +(5.19615 + 3.00000i) q^{36} +(4.73205 + 4.73205i) q^{37} +(2.36603 - 4.09808i) q^{38} +(4.26795 + 4.26795i) q^{39} +(-1.46410 - 2.53590i) q^{40} +(2.59808 - 1.50000i) q^{41} +(-4.73205 - 4.73205i) q^{42} +(-8.33013 + 2.23205i) q^{43} +(-6.19615 + 6.19615i) q^{44} +(-3.00000 + 0.803848i) q^{45} +(-4.73205 + 4.73205i) q^{46} +(3.83013 - 6.63397i) q^{47} +(-6.00000 + 3.46410i) q^{48} +(0.232051 + 0.401924i) q^{49} +(-5.36603 - 1.43782i) q^{50} +(8.59808 + 4.96410i) q^{51} +(-6.73205 + 1.80385i) q^{52} +(-7.46410 - 7.46410i) q^{53} +(1.90192 + 7.09808i) q^{54} -4.53590i q^{55} +(7.46410 - 2.00000i) q^{56} +(5.59808 - 1.50000i) q^{57} +(1.73205 + 3.00000i) q^{58} +(-1.96410 + 7.33013i) q^{59} +(0.928203 - 3.46410i) q^{60} +(-3.00000 - 11.1962i) q^{61} +(0.535898 + 0.535898i) q^{62} -8.19615i q^{63} -8.00000i q^{64} +(1.80385 - 3.12436i) q^{65} -10.7321 q^{66} +(6.59808 + 1.76795i) q^{67} +(-9.92820 + 5.73205i) q^{68} -8.19615 q^{69} +(-2.00000 + 3.46410i) q^{70} -2.92820i q^{71} +(-8.19615 - 2.19615i) q^{72} +6.26795i q^{73} +(-8.19615 - 4.73205i) q^{74} +(-3.40192 - 5.89230i) q^{75} +(-1.73205 + 6.46410i) q^{76} +(11.5622 + 3.09808i) q^{77} +(-7.39230 - 4.26795i) q^{78} +(-6.00000 + 10.3923i) q^{79} +(2.92820 + 2.92820i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.00000 + 3.00000i) q^{82} +(0.366025 + 1.36603i) q^{83} +(8.19615 + 4.73205i) q^{84} +(1.53590 - 5.73205i) q^{85} +(10.5622 - 6.09808i) q^{86} +(-1.09808 + 4.09808i) q^{87} +(6.19615 - 10.7321i) q^{88} +2.00000i q^{89} +(3.80385 - 2.19615i) q^{90} +(6.73205 + 6.73205i) q^{91} +(4.73205 - 8.19615i) q^{92} +0.928203i q^{93} +(-2.80385 + 10.4641i) q^{94} +(-1.73205 - 3.00000i) q^{95} +(6.92820 - 6.92820i) q^{96} +(-5.86603 + 10.1603i) q^{97} +(-0.464102 - 0.464102i) q^{98} +(-9.29423 - 9.29423i) 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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