LMFDB - Embedded newform 144.2.x.c.61.1

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:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			61.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	144.61
Dual form			144.2.x.c.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.00000 + 0.267949i) q^{5} +(2.36603 + 0.633975i) q^{6} +(2.36603 + 1.36603i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.366025 + 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.00000 + 0.267949i) 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} +(1.13397 + 4.23205i) q^{11} +3.46410i q^{12} +(0.901924 - 3.36603i) q^{13} +(-1.00000 + 3.73205i) 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} +(-2.00000 + 0.535898i) q^{20} +(4.09808 - 2.36603i) 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} -5.19615 q^{27} -5.46410 q^{28} +(2.36603 - 0.633975i) q^{29} +(2.19615 + 1.26795i) q^{30} +(-0.267949 - 0.464102i) q^{31} +(5.46410 + 1.46410i) q^{32} +(7.33013 + 1.96410i) q^{33} +(-2.09808 - 7.83013i) 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} +(2.23205 + 8.33013i) q^{43} +(-6.19615 - 6.19615i) q^{44} +(-0.803848 - 3.00000i) q^{45} +(-4.73205 - 4.73205i) q^{46} +(3.83013 - 6.63397i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(0.232051 + 0.401924i) q^{49} +(1.43782 - 5.36603i) q^{50} +(-4.96410 + 8.59808i) q^{51} +(1.80385 + 6.73205i) q^{52} +(-7.46410 + 7.46410i) q^{53} +(-1.90192 - 7.09808i) q^{54} +4.53590i q^{55} +(-2.00000 - 7.46410i) q^{56} +(-5.59808 + 1.50000i) q^{57} +(1.73205 + 3.00000i) q^{58} +(7.33013 + 1.96410i) q^{59} +(-0.928203 + 3.46410i) q^{60} +(11.1962 - 3.00000i) q^{61} +(0.535898 - 0.535898i) q^{62} -8.19615i q^{63} +8.00000i q^{64} +(1.80385 - 3.12436i) q^{65} +10.7321i q^{66} +(-1.76795 + 6.59808i) q^{67} +(9.92820 - 5.73205i) q^{68} +8.19615i q^{69} +(-2.00000 + 3.46410i) q^{70} +2.92820i q^{71} +(-2.19615 + 8.19615i) q^{72} -6.26795i q^{73} +(8.19615 + 4.73205i) q^{74} +(-5.89230 + 3.40192i) q^{75} +(6.46410 + 1.73205i) q^{76} +(-3.09808 + 11.5622i) q^{77} +(4.26795 - 7.39230i) 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} +(-1.36603 + 0.366025i) q^{83} +(-4.73205 + 8.19615i) q^{84} +(-5.73205 - 1.53590i) 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} -0.928203 q^{93} +(10.4641 + 2.80385i) 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} + 4 q^{5} + 6 q^{6} + 6 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 4 * q^5 + 6 * q^6 + 6 * q^7 - 8 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} + 4 q^{5} + 6 q^{6} + 6 q^{7} - 8 q^{8} - 6 q^{9} + 8 q^{11} + 14 q^{13} - 4 q^{14} + 12 q^{15} + 8 q^{16} - 16 q^{17} + 12 q^{18} - 6 q^{19} - 8 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} + 2 q^{34} + 8 q^{35} + 12 q^{37} + 6 q^{38} - 24 q^{39} + 8 q^{40} + 12 q^{42} + 2 q^{43} - 4 q^{44} - 24 q^{45} - 12 q^{46} - 2 q^{47} - 6 q^{49} + 30 q^{50} - 6 q^{51} + 28 q^{52} - 16 q^{53} - 18 q^{54} - 8 q^{56} - 12 q^{57} + 12 q^{59} + 24 q^{60} + 24 q^{61} + 16 q^{62} + 28 q^{65} - 14 q^{67} + 12 q^{68} - 8 q^{70} + 12 q^{72} + 12 q^{74} + 18 q^{75} + 12 q^{76} - 2 q^{77} + 24 q^{78} - 24 q^{79} - 16 q^{80} - 18 q^{81} - 12 q^{82} - 2 q^{83} - 12 q^{84} - 16 q^{85} - 18 q^{86} - 6 q^{87} + 4 q^{88} + 36 q^{90} + 20 q^{91} + 12 q^{92} + 24 q^{93} + 28 q^{94} - 20 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^5 + 6 * q^6 + 6 * q^7 - 8 * q^8 - 6 * q^9 + 8 * q^11 + 14 * q^13 - 4 * q^14 + 12 * q^15 + 8 * q^16 - 16 * q^17 + 12 * q^18 - 6 * q^19 - 8 * 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 + 2 * q^34 + 8 * q^35 + 12 * q^37 + 6 * q^38 - 24 * q^39 + 8 * q^40 + 12 * q^42 + 2 * q^43 - 4 * q^44 - 24 * q^45 - 12 * q^46 - 2 * q^47 - 6 * q^49 + 30 * q^50 - 6 * q^51 + 28 * q^52 - 16 * q^53 - 18 * q^54 - 8 * q^56 - 12 * q^57 + 12 * q^59 + 24 * q^60 + 24 * q^61 + 16 * q^62 + 28 * q^65 - 14 * q^67 + 12 * q^68 - 8 * q^70 + 12 * q^72 + 12 * q^74 + 18 * q^75 + 12 * q^76 - 2 * q^77 + 24 * q^78 - 24 * q^79 - 16 * q^80 - 18 * q^81 - 12 * q^82 - 2 * q^83 - 12 * q^84 - 16 * q^85 - 18 * q^86 - 6 * q^87 + 4 * q^88 + 36 * q^90 + 20 * q^91 + 12 * q^92 + 24 * q^93 + 28 * 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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	1.00000	+	0.267949i	0.447214	+	0.119831i	0.475395	−	0.879772i	$-0.342305\pi$
$5$	1.00000	+	0.267949i	0.447214	+	0.119831i	−0.0281817	+	0.999603i	$0.508972\pi$
$6$	2.36603	+	0.633975i	0.965926	+	0.258819i
$7$	2.36603	+	1.36603i	0.894274	+	0.516309i	0.875338	−	0.483512i	$-0.160639\pi$
$7$	2.36603	+	1.36603i	0.894274	+	0.516309i	0.0189356	+	0.999821i	$0.493972\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$			1.46410i			0.462990i
$11$	1.13397	+	4.23205i	0.341906	+	1.27601i	0.896185	+	0.443680i	$0.146327\pi$
$11$	1.13397	+	4.23205i	0.341906	+	1.27601i	−0.554279	+	0.832331i	$0.687006\pi$
$12$			3.46410i			1.00000i
$13$	0.901924	−	3.36603i	0.250149	−	0.933567i	−0.720577	−	0.693375i	$-0.756123\pi$
$13$	0.901924	−	3.36603i	0.250149	−	0.933567i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$	−1.00000	+	3.73205i	−0.267261	+	0.997433i
$15$	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	0.381546	−	0.924350i	$-0.375392\pi$
$19$	−2.36603	−	2.36603i	−0.542803	−	0.542803i	−0.924350	+	0.381546i	$0.875392\pi$
$20$	−2.00000	+	0.535898i	−0.447214	+	0.119831i
$21$	4.09808	−	2.36603i	0.894274	−	0.516309i
$22$	−5.36603	+	3.09808i	−1.14404	+	0.660512i
$23$	−4.09808	+	2.36603i	−0.854508	+	0.493350i	−0.862169	−	0.506620i	$-0.830895\pi$
$23$	−4.09808	+	2.36603i	−0.854508	+	0.493350i	0.00766135	+	0.999971i	$0.497561\pi$
$24$	−4.73205	+	1.26795i	−0.965926	+	0.258819i
$25$	−3.40192	−	1.96410i	−0.680385	−	0.392820i
$26$	4.92820			0.966500
$27$	−5.19615			−1.00000
$28$	−5.46410			−1.03262
$29$	2.36603	−	0.633975i	0.439360	−	0.117726i	−0.0323566	−	0.999476i	$-0.510301\pi$
$29$	2.36603	−	0.633975i	0.439360	−	0.117726i	0.471717	+	0.881750i	$0.343635\pi$
$30$	2.19615	+	1.26795i	0.400961	+	0.231495i
$31$	−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	$0.848658\pi$
$32$	5.46410	+	1.46410i	0.965926	+	0.258819i
$33$	7.33013	+	1.96410i	1.27601	+	0.341906i
$34$	−2.09808	−	7.83013i	−0.359817	−	1.34286i
$35$	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	−0.201537	−	0.979481i	$-0.564594\pi$
$37$	4.73205	−	4.73205i	0.777944	−	0.777944i	0.979481	+	0.201537i	$0.0645935\pi$
$38$	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	−0.688963	−	0.724797i	$-0.741934\pi$
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	0.283211	+	0.959058i	$0.408600\pi$
$42$	4.73205	+	4.73205i	0.730171	+	0.730171i
$43$	2.23205	+	8.33013i	0.340385	+	1.27033i	0.897912	+	0.440174i	$0.145083\pi$
$43$	2.23205	+	8.33013i	0.340385	+	1.27033i	−0.557528	+	0.830158i	$0.688250\pi$
$44$	−6.19615	−	6.19615i	−0.934105	−	0.934105i
$45$	−0.803848	−	3.00000i	−0.119831	−	0.447214i
$46$	−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	$-0.0220259\pi$
$48$	−3.46410	−	6.00000i	−0.500000	−	0.866025i
$49$	0.232051	+	0.401924i	0.0331501	+	0.0574177i
$50$	1.43782	−	5.36603i	0.203339	−	0.758871i
$51$	−4.96410	+	8.59808i	−0.695113	+	1.20397i
$52$	1.80385	+	6.73205i	0.250149	+	0.933567i
$53$	−7.46410	+	7.46410i	−1.02527	+	1.02527i	−0.0256010	+	0.999672i	$0.508150\pi$
$53$	−7.46410	+	7.46410i	−1.02527	+	1.02527i	−0.999672	+	0.0256010i	$0.991850\pi$
$54$	−1.90192	−	7.09808i	−0.258819	−	0.965926i
$55$			4.53590i			0.611620i
$56$	−2.00000	−	7.46410i	−0.267261	−	0.997433i
$57$	−5.59808	+	1.50000i	−0.741483	+	0.198680i
$58$	1.73205	+	3.00000i	0.227429	+	0.393919i
$59$	7.33013	+	1.96410i	0.954301	+	0.255704i	0.702186	−	0.711993i	$-0.252207\pi$
$59$	7.33013	+	1.96410i	0.954301	+	0.255704i	0.252115	+	0.967697i	$0.418874\pi$
$60$	−0.928203	+	3.46410i	−0.119831	+	0.447214i
$61$	11.1962	−	3.00000i	1.43352	−	0.384111i	0.543261	−	0.839564i	$-0.317189\pi$
$61$	11.1962	−	3.00000i	1.43352	−	0.384111i	0.890260	+	0.455453i	$0.150523\pi$
$62$	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
$66$			10.7321i			1.32102i
$67$	−1.76795	+	6.59808i	−0.215989	+	0.806083i	0.769827	+	0.638253i	$0.220343\pi$
$67$	−1.76795	+	6.59808i	−0.215989	+	0.806083i	−0.985816	+	0.167830i	$0.946324\pi$
$68$	9.92820	−	5.73205i	1.20397	−	0.695113i
$69$			8.19615i			0.986701i
$70$	−2.00000	+	3.46410i	−0.239046	+	0.414039i
$71$			2.92820i			0.347514i	0.984789	+	0.173757i	$0.0555907\pi$
$71$			2.92820i			0.347514i	−0.984789	+	0.173757i	$0.944409\pi$
$72$	−2.19615	+	8.19615i	−0.258819	+	0.965926i
$73$		−	6.26795i		−	0.733608i	−0.930298	−	0.366804i	$-0.880452\pi$
$73$		−	6.26795i		−	0.733608i	0.930298	−	0.366804i	$-0.119548\pi$
$74$	8.19615	+	4.73205i	0.952783	+	0.550090i
$75$	−5.89230	+	3.40192i	−0.680385	+	0.392820i
$76$	6.46410	+	1.73205i	0.741483	+	0.198680i
$77$	−3.09808	+	11.5622i	−0.353059	+	1.31763i
$78$	4.26795	−	7.39230i	0.483250	−	0.837014i
$79$	−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
$83$	−1.36603	+	0.366025i	−0.149941	+	0.0401765i	−0.333009	−	0.942924i	$-0.608064\pi$
$83$	−1.36603	+	0.366025i	−0.149941	+	0.0401765i	0.183068	+	0.983100i	$0.441397\pi$
$84$	−4.73205	+	8.19615i	−0.516309	+	0.894274i
$85$	−5.73205	−	1.53590i	−0.621728	−	0.166592i
$86$	−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	$-0.966196\pi$
$89$		−	2.00000i		−	0.212000i	0.994366	−	0.106000i	$-0.0338043\pi$
$90$	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
$93$	−0.928203			−0.0962502
$94$	10.4641	+	2.80385i	1.07929	+	0.289195i
$95$	−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
$101$	0.535898	+	2.00000i	0.0533239	+	0.199007i	0.987449	−	0.157938i	$-0.0504847\pi$
$101$	0.535898	+	2.00000i	0.0533239	+	0.199007i	−0.934125	+	0.356946i	$0.883818\pi$
$102$	−13.5622	−	3.63397i	−1.34286	−	0.359817i
$103$	13.0981	−	7.56218i	1.29059	−	0.745124i	0.311833	−	0.950137i	$-0.399057\pi$
$103$	13.0981	−	7.56218i	1.29059	−	0.745124i	0.978759	+	0.205014i	$0.0657238\pi$
$104$	−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	0.235654	−	0.971837i	$-0.424277\pi$
$107$	12.4904	−	12.4904i	1.20749	−	1.20749i	0.971837	−	0.235654i	$-0.0757231\pi$
$108$	9.00000	−	5.19615i	0.866025	−	0.500000i
$109$	10.7321	+	10.7321i	1.02794	+	1.02794i	0.999598	+	0.0283459i	$0.00902398\pi$
$109$	10.7321	+	10.7321i	1.02794	+	1.02794i	0.0283459	+	0.999598i	$0.490976\pi$
$110$	−6.19615	+	1.66025i	−0.590780	+	0.158299i
$111$	−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	$-0.392632\pi$
$114$	−4.09808	−	7.09808i	−0.383820	−	0.664796i
$115$	−4.73205	+	1.26795i	−0.441266	+	0.118237i
$116$	−3.46410	+	3.46410i	−0.321634	+	0.321634i
$117$	−10.0981	+	2.70577i	−0.933567	+	0.250149i
$118$			10.7321i			0.987965i
$119$	−13.5622	−	7.83013i	−1.24324	−	0.717787i
$120$	−5.07180			−0.462990
$121$	−7.09808	+	4.09808i	−0.645280	+	0.372552i
$122$	8.19615	+	14.1962i	0.742045	+	1.28526i
$123$			5.19615i			0.468521i
$124$	0.928203	+	0.535898i	0.0833551	+	0.0481251i
$125$	−6.53590	−	6.53590i	−0.584589	−	0.584589i
$126$	11.1962	−	3.00000i	0.997433	−	0.267261i
$127$	4.19615			0.372348			0.186174	−	0.982517i	$-0.440391\pi$
$127$	4.19615			0.372348			0.186174	+	0.982517i	$0.440391\pi$
$128$	−10.9282	+	2.92820i	−0.965926	+	0.258819i
$129$	14.4282	+	3.86603i	1.27033	+	0.340385i
$130$	4.92820	+	1.32051i	0.432232	+	0.115816i
$131$	2.09808	−	7.83013i	0.183310	−	0.684121i	−0.811676	−	0.584108i	$-0.801445\pi$
$131$	2.09808	−	7.83013i	0.183310	−	0.684121i	0.994986	−	0.100014i	$-0.0318887\pi$
$132$	−14.6603	+	3.92820i	−1.27601	+	0.341906i
$133$	−2.36603	−	8.83013i	−0.205160	−	0.765669i
$134$	−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	0.809414	−	0.587239i	$-0.199785\pi$
$137$	8.25833	+	4.76795i	0.705557	+	0.407353i	−0.103857	+	0.994592i	$0.533118\pi$
$138$	−11.1962	+	3.00000i	−0.953080	+	0.255377i
$139$	−11.4282	−	3.06218i	−0.969328	−	0.259731i	−0.260784	−	0.965397i	$-0.583981\pi$
$139$	−11.4282	−	3.06218i	−0.969328	−	0.259731i	−0.708544	+	0.705667i	$0.750648\pi$
$140$	−5.46410	−	1.46410i	−0.461801	−	0.123739i
$141$	−6.63397	−	11.4904i	−0.558681	−	0.967665i
$142$	−4.00000	+	1.07180i	−0.335673	+	0.0899432i
$143$	15.2679			1.27677
$144$	−12.0000			−1.00000
$145$	2.53590			0.210595
$146$	8.56218	−	2.29423i	0.708611	−	0.189872i
$147$	0.803848			0.0663002
$148$	−3.46410	+	12.9282i	−0.284747	+	1.06269i
$149$	7.83013	+	2.09808i	0.641469	+	0.171881i	0.564869	−	0.825181i	$-0.308927\pi$
$149$	7.83013	+	2.09808i	0.641469	+	0.171881i	0.0766003	+	0.997062i	$0.475593\pi$
$150$	−6.80385	−	6.80385i	−0.555532	−	0.555532i
$151$	0.633975	+	0.366025i	0.0515921	+	0.0297867i	0.525574	−	0.850748i	$-0.323851\pi$
$151$	0.633975	+	0.366025i	0.0515921	+	0.0297867i	−0.473982	+	0.880534i	$0.657184\pi$
$152$			9.46410i			0.767640i
$153$	8.59808	+	14.8923i	0.695113	+	1.20397i
$154$	−16.9282			−1.36411
$155$	−0.143594	−	0.535898i	−0.0115337	−	0.0430444i
$156$	11.6603	+	3.12436i	0.933567	+	0.250149i
$157$	1.26795	−	4.73205i	0.101193	−	0.377659i	−0.896692	−	0.442655i	$-0.854037\pi$
$157$	1.26795	−	4.73205i	0.101193	−	0.377659i	0.997886	+	0.0649959i	$0.0207034\pi$
$158$	−16.3923	−	4.39230i	−1.30410	−	0.349433i
$159$	4.73205	+	17.6603i	0.375276	+	1.40055i
$160$	5.07180	+	2.92820i	0.400961	+	0.231495i
$161$	−12.9282			−1.01889
$162$	−12.2942	−	3.29423i	−0.965926	−	0.258819i
$163$	−7.00000	−	7.00000i	−0.548282	−	0.548282i	0.377661	−	0.925944i	$-0.376728\pi$
$163$	−7.00000	−	7.00000i	−0.548282	−	0.548282i	−0.925944	+	0.377661i	$0.876728\pi$
$164$	3.00000	−	5.19615i	0.234261	−	0.405751i
$165$	6.80385	+	3.92820i	0.529679	+	0.305810i
$166$	−1.00000	−	1.73205i	−0.0776151	−	0.134433i
$167$	6.46410	−	3.73205i	0.500207	−	0.288795i	−0.228592	−	0.973522i	$-0.573412\pi$
$167$	6.46410	−	3.73205i	0.500207	−	0.288795i	0.728799	+	0.684728i	$0.240079\pi$
$168$	−12.9282	−	3.46410i	−0.997433	−	0.267261i
$169$	0.741670	+	0.428203i	0.0570515	+	0.0329387i
$170$		−	8.39230i		−	0.643660i
$171$	−2.59808	+	9.69615i	−0.198680	+	0.741483i
$172$	−12.1962	−	12.1962i	−0.929948	−	0.929948i
$173$	1.63397	−	0.437822i	0.124229	−	0.0332870i	−0.196169	−	0.980570i	$-0.562850\pi$
$173$	1.63397	−	0.437822i	0.124229	−	0.0332870i	0.320398	+	0.947283i	$0.396183\pi$
$174$	6.00000			0.454859
$175$	−5.36603	−	9.29423i	−0.405633	−	0.702578i
$176$	16.9282	+	4.53590i	1.27601	+	0.341906i
$177$	9.29423	−	9.29423i	0.698597	−	0.698597i
$178$	2.73205	−	0.732051i	0.204776	−	0.0548695i
$179$	−1.92820	−	1.92820i	−0.144121	−	0.144121i	0.631365	−	0.775486i	$-0.282495\pi$
$179$	−1.92820	−	1.92820i	−0.144121	−	0.144121i	−0.775486	+	0.631365i	$0.782495\pi$
$180$	4.39230	+	4.39230i	0.327383	+	0.327383i
$181$	−7.39230	+	7.39230i	−0.549466	+	0.549466i	−0.926286	−	0.376821i	$-0.877017\pi$
$181$	−7.39230	+	7.39230i	−0.549466	+	0.549466i	0.376821	+	0.926286i	$0.377017\pi$
$182$	11.6603	+	6.73205i	0.864316	+	0.499013i
$183$	5.19615	−	19.3923i	0.384111	−	1.43352i
$184$	12.9282	+	3.46410i	0.953080	+	0.255377i
$185$	6.00000	−	3.46410i	0.441129	−	0.254686i
$186$	−0.339746	−	1.26795i	−0.0249114	−	0.0929705i
$187$	−6.50000	−	24.2583i	−0.475327	−	1.77394i
$188$			15.3205i			1.11736i
$189$	−12.2942	−	7.09808i	−0.894274	−	0.516309i
$190$	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	$0.830662\pi$
$192$	12.0000	+	6.92820i	0.866025	+	0.500000i
$193$	−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	$-0.452545\pi$
$194$	−16.0263	−	4.29423i	−1.15062	−	0.308308i
$195$	−3.12436	−	5.41154i	−0.223740	−	0.387529i
$196$	−0.803848	−	0.464102i	−0.0574177	−	0.0331501i
$197$	13.6603	−	13.6603i	0.973253	−	0.973253i	−0.0263987	−	0.999651i	$-0.508404\pi$
$197$	13.6603	−	13.6603i	0.973253	−	0.973253i	0.999651	+	0.0263987i	$0.00840394\pi$
$198$	16.0981	+	9.29423i	1.14404	+	0.660512i
$199$			25.1244i			1.78102i	0.454965	+	0.890509i	$0.349652\pi$
$199$			25.1244i			1.78102i	−0.454965	+	0.890509i	$0.650348\pi$
$200$	2.87564	+	10.7321i	0.203339	+	0.758871i
$201$	8.36603	+	8.36603i	0.590094	+	0.590094i
$202$	−2.53590	+	1.46410i	−0.178425	+	0.103014i
$203$	6.46410	+	1.73205i	0.453691	+	0.121566i
$204$		−	19.8564i		−	1.39023i
$205$	−3.00000	+	0.803848i	−0.209529	+	0.0561432i
$206$	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
$210$	3.46410	+	6.00000i	0.239046	+	0.414039i
$211$	−1.09808	+	4.09808i	−0.0755947	+	0.282123i	−0.993367	−	0.114983i	$-0.963319\pi$
$211$	−1.09808	+	4.09808i	−0.0755947	+	0.282123i	0.917773	+	0.397106i	$0.129985\pi$
$212$	5.46410	−	20.3923i	0.375276	−	1.40055i
$213$	4.39230	+	2.53590i	0.300956	+	0.173757i
$214$	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
$219$	−9.40192	−	5.42820i	−0.635323	−	0.366804i
$220$	−4.53590	−	7.85641i	−0.305810	−	0.529679i
$221$	−5.16987	+	19.2942i	−0.347763	+	1.29787i
$222$	14.1962	−	8.19615i	0.952783	−	0.550090i
$223$	−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
$227$	2.13397	−	0.571797i	0.141637	−	0.0379515i	−0.187304	−	0.982302i	$-0.559975\pi$
$227$	2.13397	−	0.571797i	0.141637	−	0.0379515i	0.328941	+	0.944351i	$0.393308\pi$
$228$	8.19615	−	8.19615i	0.542803	−	0.542803i
$229$	6.83013	+	1.83013i	0.451347	+	0.120938i	0.477330	−	0.878724i	$-0.341605\pi$
$229$	6.83013	+	1.83013i	0.451347	+	0.120938i	−0.0259823	+	0.999662i	$0.508271\pi$
$230$	−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	$-0.966614\pi$
$233$		−	3.19615i		−	0.209387i	0.994505	−	0.104693i	$-0.0333861\pi$
$234$	−7.39230	−	12.8038i	−0.483250	−	0.837014i
$235$	5.60770	−	5.60770i	0.365806	−	0.365806i
$236$	−14.6603	+	3.92820i	−0.954301	+	0.255704i
$237$	10.3923	+	18.0000i	0.675053	+	1.16923i
$238$	5.73205	−	21.3923i	0.371554	−	1.38666i
$239$	−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
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$	−16.3923	+	16.3923i	−1.04941	+	1.04941i
$245$	0.124356	+	0.464102i	0.00794479	+	0.0296504i
$246$	−7.09808	+	1.90192i	−0.452557	+	0.121262i
$247$	−10.0981	+	5.83013i	−0.642525	+	0.370962i
$248$	−0.392305	+	1.46410i	−0.0249114	+	0.0929705i
$249$	−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	−0.866745	−	0.498751i	$-0.833792\pi$
$251$	−5.83013	+	5.83013i	−0.367994	+	0.367994i	0.498751	+	0.866745i	$0.333792\pi$
$252$	8.19615	+	14.1962i	0.516309	+	0.894274i
$253$	−14.6603	−	14.6603i	−0.921682	−	0.921682i
$254$	1.53590	+	5.73205i	0.0963708	+	0.359661i
$255$	−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	$0.633204\pi$
$258$			21.1244i			1.31514i
$259$	17.6603	−	4.73205i	1.09735	−	0.294035i
$260$			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	0.421249	−	0.906945i	$-0.361592\pi$
$263$	−2.49038	−	1.43782i	−0.153563	−	0.0886599i	−0.574813	+	0.818285i	$0.694925\pi$
$264$	−10.7321	−	18.5885i	−0.660512	−	1.14404i
$265$	−9.46410	+	5.46410i	−0.581375	+	0.335657i
$266$	11.1962	−	6.46410i	0.686480	−	0.396339i
$267$	−3.00000	−	1.73205i	−0.183597	−	0.106000i
$268$	−3.53590	−	13.1962i	−0.215989	−	0.806083i
$269$	1.26795	+	1.26795i	0.0773082	+	0.0773082i	0.744704	−	0.667395i	$-0.232591\pi$
$269$	1.26795	+	1.26795i	0.0773082	+	0.0773082i	−0.667395	+	0.744704i	$0.732591\pi$
$270$		−	7.60770i		−	0.462990i
$271$	−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
$274$	−3.49038	+	13.0263i	−0.210862	+	0.786946i
$275$	4.45448	−	16.6244i	0.268615	−	1.00249i
$276$	−8.19615	−	14.1962i	−0.493350	−	0.854508i
$277$	−6.75833	−	25.2224i	−0.406069	−	1.51547i	−0.802076	−	0.597222i	$-0.796271\pi$
$277$	−6.75833	−	25.2224i	−0.406069	−	1.51547i	0.396007	−	0.918247i	$-0.370395\pi$
$278$		−	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	0.218926	−	0.975741i	$-0.429745\pi$
$281$	−8.66025	−	5.00000i	−0.516627	−	0.298275i	−0.735554	+	0.677466i	$0.763078\pi$
$282$	13.2679	−	13.2679i	0.790095	−	0.790095i
$283$	−19.5622	−	5.24167i	−1.16285	−	0.311585i	−0.374747	−	0.927127i	$-0.622270\pi$
$283$	−19.5622	−	5.24167i	−1.16285	−	0.311585i	−0.788104	+	0.615542i	$0.788937\pi$
$284$	−2.92820	−	5.07180i	−0.173757	−	0.300956i
$285$	−6.00000			−0.355409
$286$	5.58846	+	20.8564i	0.330452	+	1.23327i
$287$	−8.19615			−0.483804
$288$	−4.39230	−	16.3923i	−0.258819	−	0.965926i
$289$	15.8564			0.932730
$290$	0.928203	+	3.46410i	0.0545060	+	0.203419i
$291$	10.1603	+	17.5981i	0.595605	+	1.03162i
$292$	6.26795	+	10.8564i	0.366804	+	0.635323i
$293$	−5.36603	−	1.43782i	−0.313487	−	0.0839985i	0.0986454	−	0.995123i	$-0.468549\pi$
$293$	−5.36603	−	1.43782i	−0.313487	−	0.0839985i	−0.412132	+	0.911124i	$0.635216\pi$
$294$	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
$299$	4.26795	+	15.9282i	0.246822	+	0.921152i
$300$	6.80385	−	11.7846i	0.392820	−	0.680385i
$301$	−6.09808	+	22.7583i	−0.351487	+	1.31177i
$302$	−0.267949	+	1.00000i	−0.0154187	+	0.0575435i
$303$	3.46410	+	0.928203i	0.199007	+	0.0533239i
$304$	−12.9282	+	3.46410i	−0.741483	+	0.198680i
$305$	12.0000			0.687118
$306$	−17.1962	+	17.1962i	−0.983039	+	0.983039i
$307$	3.02628	+	3.02628i	0.172719	+	0.172719i	0.788173	−	0.615454i	$-0.211027\pi$
$307$	3.02628	+	3.02628i	0.172719	+	0.172719i	−0.615454	+	0.788173i	$0.711027\pi$
$308$	−6.19615	−	23.1244i	−0.353059	−	1.31763i
$309$		−	26.1962i		−	1.49025i
$310$	0.679492	−	0.392305i	0.0385925	−	0.0222814i
$311$	−19.0981	+	11.0263i	−1.08295	+	0.625243i	−0.931691	−	0.363251i	$-0.881667\pi$
$311$	−19.0981	+	11.0263i	−1.08295	+	0.625243i	−0.151261	+	0.988494i	$0.548333\pi$
$312$			17.0718i			0.966500i
$313$	18.6506	+	10.7679i	1.05420	+	0.608640i	0.923821	−	0.382824i	$-0.125049\pi$
$313$	18.6506	+	10.7679i	1.05420	+	0.608640i	0.130375	+	0.991465i	$0.458382\pi$
$314$	6.92820			0.390981
$315$	2.19615	−	8.19615i	0.123739	−	0.461801i
$316$		−	24.0000i		−	1.35011i
$317$	−20.5622	+	5.50962i	−1.15489	+	0.309451i	−0.784922	−	0.619595i	$-0.787297\pi$
$317$	−20.5622	+	5.50962i	−1.15489	+	0.309451i	−0.369965	+	0.929046i	$0.620630\pi$
$318$	−22.3923	+	12.9282i	−1.25570	+	0.724978i
$319$	5.36603	+	9.29423i	0.300440	+	0.520377i
$320$	−2.14359	+	8.00000i	−0.119831	+	0.447214i
$321$	−7.91858	−	29.5526i	−0.441972	−	1.64946i
$322$	−4.73205	−	17.6603i	−0.263707	−	0.984167i
$323$	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
$328$	8.19615	+	2.19615i	0.452557	+	0.121262i
$329$	18.1244	−	10.4641i	0.999228	−	0.576905i
$330$	−2.87564	+	10.7321i	−0.158299	+	0.590780i
$331$	0.0262794	+	0.0980762i	0.00144445	+	0.00539076i	0.966644	−	0.256123i	$-0.0824451\pi$
$331$	0.0262794	+	0.0980762i	0.00144445	+	0.00539076i	−0.965200	+	0.261513i	$0.915778\pi$
$332$	2.00000	−	2.00000i	0.109764	−	0.109764i
$333$	−19.3923	−	5.19615i	−1.06269	−	0.284747i
$334$	7.46410	+	7.46410i	0.408417	+	0.408417i
$335$	−3.53590	+	6.12436i	−0.193187	+	0.334609i
$336$		−	18.9282i		−	1.03262i
$337$	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	$0.672373\pi$
$338$	−0.313467	+	1.16987i	−0.0170503	+	0.0636327i
$339$	−24.0000			−1.30350
$340$	11.4641	−	3.07180i	0.621728	−	0.166592i
$341$	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
$347$	−17.6244	−	4.72243i	−0.946125	−	0.253513i	−0.247408	−	0.968911i	$-0.579579\pi$
$347$	−17.6244	−	4.72243i	−0.946125	−	0.253513i	−0.698717	+	0.715398i	$0.746245\pi$
$348$	2.19615	+	8.19615i	0.117726	+	0.439360i
$349$	15.9282	−	4.26795i	0.852617	−	0.228458i	0.194061	−	0.980989i	$-0.437834\pi$
$349$	15.9282	−	4.26795i	0.852617	−	0.228458i	0.658556	+	0.752531i	$0.271167\pi$
$350$	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	$0.0422114\pi$
$354$	16.0981	+	9.29423i	0.855603	+	0.493983i
$355$	−0.784610	+	2.92820i	−0.0416428	+	0.155413i
$356$	2.00000	+	3.46410i	0.106000	+	0.183597i
$357$	−23.4904	+	13.5622i	−1.24324	+	0.717787i
$358$	1.92820	−	3.33975i	0.101909	−	0.176511i
$359$			11.2679i			0.594700i	0.954769	+	0.297350i	$0.0961028\pi$
$359$			11.2679i			0.594700i	−0.954769	+	0.297350i	$0.903897\pi$
$360$	−4.39230	+	7.60770i	−0.231495	+	0.400961i
$361$		−	7.80385i		−	0.410729i
$362$	−12.8038	−	7.39230i	−0.672955	−	0.388531i
$363$			14.1962i			0.745105i
$364$	−4.92820	+	18.3923i	−0.258308	+	0.964019i
$365$	1.67949	−	6.26795i	0.0879086	−	0.328079i
$366$	28.3923			1.48409
$367$	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
$371$	−27.8564	+	7.46410i	−1.44623	+	0.387517i
$372$	1.60770	−	0.928203i	0.0833551	−	0.0481251i
$373$	27.4904	+	7.36603i	1.42340	+	0.381398i	0.886688	−	0.462368i	$-0.153000\pi$
$373$	27.4904	+	7.36603i	1.42340	+	0.381398i	0.536710	+	0.843767i	$0.319667\pi$
$374$	30.7583	−	17.7583i	1.59048	−	0.918261i
$375$	−15.4641	+	4.14359i	−0.798563	+	0.213974i
$376$	−20.9282	+	5.60770i	−1.07929	+	0.289195i
$377$		−	8.53590i		−	0.439621i
$378$	5.19615	−	19.3923i	0.267261	−	0.997433i
$379$	3.75833	−	3.75833i	0.193052	−	0.193052i	−0.603961	−	0.797014i	$-0.706412\pi$
$379$	3.75833	−	3.75833i	0.193052	−	0.193052i	0.797014	+	0.603961i	$0.206412\pi$
$380$	6.00000	+	3.46410i	0.307794	+	0.177705i
$381$	3.63397	−	6.29423i	0.186174	−	0.322463i
$382$	−32.8564	−	8.80385i	−1.68108	−	0.450444i
$383$	−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
$389$	−5.29423	−	19.7583i	−0.268428	−	1.00179i	−0.960119	−	0.279593i	$-0.909800\pi$
$389$	−5.29423	−	19.7583i	−0.268428	−	1.00179i	0.691691	−	0.722194i	$-0.256866\pi$
$390$	6.24871	−	6.24871i	0.316416	−	0.316416i
$391$	23.4904	−	13.5622i	1.18796	−	0.685869i
$392$	0.339746	−	1.26795i	0.0171598	−	0.0640411i
$393$	−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
$396$	−6.80385	+	25.3923i	−0.341906	+	1.27601i
$397$	−9.26795	−	9.26795i	−0.465145	−	0.465145i	0.435192	−	0.900337i	$-0.356680\pi$
$397$	−9.26795	−	9.26795i	−0.465145	−	0.465145i	−0.900337	+	0.435192i	$0.856680\pi$
$398$	−34.3205	+	9.19615i	−1.72033	+	0.460961i
$399$	−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	$0.861892\pi$
$402$	−8.36603	+	14.4904i	−0.417259	+	0.722715i
$403$	−1.80385	+	0.483340i	−0.0898560	+	0.0240769i
$404$	−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	0.385981	−	0.922507i	$-0.373863\pi$
$409$	27.8660	−	16.0885i	1.37789	−	0.795523i	0.991905	+	0.126984i	$0.0405295\pi$
$410$	−2.19615	−	3.80385i	−0.108460	−	0.187859i
$411$	14.3038	−	8.25833i	0.705557	−	0.407353i
$412$	−15.1244	+	26.1962i	−0.745124	+	1.29059i
$413$	14.6603	+	14.6603i	0.721384	+	0.721384i
$414$	−5.19615	+	19.3923i	−0.255377	+	0.953080i
$415$	−1.46410			−0.0718699
$416$	9.85641	−	17.0718i	0.483250	−	0.837014i
$417$	−14.4904	+	14.4904i	−0.709597	+	0.709597i
$418$	20.0263	+	5.36603i	0.979517	+	0.262461i
$419$	1.77757	−	6.63397i	0.0868399	−	0.324091i	−0.908816	−	0.417196i	$-0.863013\pi$
$419$	1.77757	−	6.63397i	0.0868399	−	0.324091i	0.995656	+	0.0931055i	$0.0296794\pi$
$420$	−6.92820	+	6.92820i	−0.338062	+	0.338062i
$421$	8.19615	+	30.5885i	0.399456	+	1.49079i	0.814056	+	0.580786i	$0.197255\pi$
$421$	8.19615	+	30.5885i	0.399456	+	1.49079i	−0.414600	+	0.910004i	$0.636078\pi$
$422$	−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
$427$	30.5885	+	8.19615i	1.48028	+	0.396640i
$428$	−9.14359	+	34.1244i	−0.441972	+	1.64946i
$429$	13.2224	−	22.9019i	0.638385	−	1.10572i
$430$	−12.1962	+	3.26795i	−0.588151	+	0.157595i
$431$	−16.1962			−0.780141			−0.390071	−	0.920785i	$-0.627549\pi$
$431$	−16.1962			−0.780141			−0.390071	+	0.920785i	$0.627549\pi$
$432$	−10.3923	+	18.0000i	−0.500000	+	0.866025i
$433$	−5.73205			−0.275465			−0.137732	−	0.990469i	$-0.543981\pi$
$433$	−5.73205			−0.275465			−0.137732	+	0.990469i	$0.543981\pi$
$434$	2.00000	−	0.535898i	0.0960031	−	0.0257239i
$435$	2.19615	−	3.80385i	0.105297	−	0.182381i
$436$	−29.3205	−	7.85641i	−1.40420	−	0.376254i
$437$	15.2942	+	4.09808i	0.731622	+	0.196038i
$438$	3.97372	−	14.8301i	0.189872	−	0.708611i
$439$	−22.8564	−	13.1962i	−1.09088	−	0.629818i	−0.157067	−	0.987588i	$-0.550204\pi$
$439$	−22.8564	−	13.1962i	−1.09088	−	0.629818i	−0.933810	+	0.357770i	$0.883537\pi$
$440$	9.07180	−	9.07180i	0.432481	−	0.432481i
$441$	0.696152	−	1.20577i	0.0331501	−	0.0574177i
$442$	−28.2487			−1.34365
$443$	−4.62436	−	17.2583i	−0.219710	−	0.819968i	−0.984455	−	0.175636i	$-0.943802\pi$
$443$	−4.62436	−	17.2583i	−0.219710	−	0.819968i	0.764745	−	0.644332i	$-0.222865\pi$
$444$	16.3923	+	16.3923i	0.777944	+	0.777944i
$445$	0.535898	−	2.00000i	0.0254040	−	0.0948091i
$446$	−21.9282	−	5.87564i	−1.03833	−	0.278220i
$447$	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	$0.525111\pi$
$450$	−16.0981	+	4.31347i	−0.758871	+	0.203339i
$451$	−9.29423	−	9.29423i	−0.437648	−	0.437648i
$452$	24.0000	+	13.8564i	1.12887	+	0.651751i
$453$	1.09808	−	0.633975i	0.0515921	−	0.0297867i
$454$	1.56218	+	2.70577i	0.0733166	+	0.126988i
$455$	8.53590	−	4.92820i	0.400169	−	0.231038i
$456$	14.1962	+	8.19615i	0.664796	+	0.383820i
$457$	2.25833	+	1.30385i	0.105640	+	0.0609914i	0.551889	−	0.833917i	$-0.313907\pi$
$457$	2.25833	+	1.30385i	0.105640	+	0.0609914i	−0.446249	+	0.894909i	$0.647240\pi$
$458$			10.0000i			0.467269i
$459$	29.7846			1.39023
$460$	6.92820	−	6.92820i	0.323029	−	0.323029i
$461$	35.6865	−	9.56218i	1.66209	−	0.445355i	0.699127	−	0.714997i	$-0.253572\pi$
$461$	35.6865	−	9.56218i	1.66209	−	0.445355i	0.962961	+	0.269642i	$0.0869055\pi$
$462$	−14.6603	+	25.3923i	−0.682057	+	1.18136i
$463$	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	$0.815629\pi$
$464$	2.53590	−	9.46410i	0.117726	−	0.439360i
$465$	−0.928203	−	0.248711i	−0.0430444	−	0.0115337i
$466$	4.36603	−	1.16987i	0.202252	−	0.0541933i
$467$	2.63397	+	2.63397i	0.121886	+	0.121886i	0.765419	−	0.643533i	$-0.222532\pi$
$467$	2.63397	+	2.63397i	0.121886	+	0.121886i	−0.643533	+	0.765419i	$0.722532\pi$
$468$	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
$475$	3.40192	+	12.6962i	0.156091	+	0.582539i
$476$	31.3205			1.43557
$477$	30.5885	+	8.19615i	1.40055	+	0.375276i
$478$	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	$0.105647\pi$
$480$	8.78461	−	5.07180i	0.400961	−	0.231495i
$481$	−11.6603	−	20.1962i	−0.531662	−	0.920865i
$482$	−31.6865	−	8.49038i	−1.44328	−	0.386726i
$483$	−11.1962	+	19.3923i	−0.509443	+	0.882380i
$484$	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	$0.0419789\pi$
$487$			5.80385i			0.262997i	−0.991316	+	0.131499i	$0.958021\pi$
$488$	−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
$491$	−13.8923	−	3.72243i	−0.626951	−	0.167991i	−0.0686652	−	0.997640i	$-0.521874\pi$
$491$	−13.8923	−	3.72243i	−0.626951	−	0.167991i	−0.558286	+	0.829649i	$0.688541\pi$
$492$	−5.19615	−	9.00000i	−0.234261	−	0.405751i
$493$	−13.5622	+	3.63397i	−0.610810	+	0.163666i
$494$	−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
$498$	−3.46410			−0.155230
$499$	−2.33013	+	8.69615i	−0.104311	+	0.389293i	−0.998266	−	0.0588630i	$-0.981252\pi$
$499$	−2.33013	+	8.69615i	−0.104311	+	0.389293i	0.893955	+	0.448156i	$0.147919\pi$
$500$	17.8564	+	4.78461i	0.798563	+	0.213974i
$501$		−	12.9282i		−	0.577590i
$502$	−10.0981	−	5.83013i	−0.450699	−	0.260211i
$503$		−	27.7128i		−	1.23565i	−0.786314	−	0.617827i	$-0.788013\pi$
$503$		−	27.7128i		−	1.23565i	0.786314	−	0.617827i	$-0.211987\pi$
$504$	−16.3923	+	16.3923i	−0.730171	+	0.730171i
$505$			2.14359i			0.0953887i
$506$	14.6603	−	25.3923i	0.651728	−	1.12883i
$507$	1.28461	−	0.741670i	0.0570515	−	0.0329387i
$508$	−7.26795	+	4.19615i	−0.322463	+	0.186174i
$509$	3.07180	−	11.4641i	0.136155	−	0.508137i	−0.863835	−	0.503774i	$-0.831944\pi$
$509$	3.07180	−	11.4641i	0.136155	−	0.508137i	0.999990	−	0.00436335i	$-0.00138890\pi$
$510$	−12.5885	−	7.26795i	−0.557426	−	0.321830i
$511$	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
$515$	15.1244	−	4.05256i	0.666459	−	0.178577i
$516$	−28.8564	+	7.73205i	−1.27033	+	0.340385i
$517$	32.4186	+	8.68653i	1.42577	+	0.382033i
$518$	12.9282	+	22.3923i	0.568033	+	0.983861i
$519$	0.758330	−	2.83013i	0.0332870	−	0.124229i
$520$	−9.85641	+	2.64102i	−0.432232	+	0.115816i
$521$			13.0000i			0.569540i	0.958596	+	0.284770i	$0.0919173\pi$
$521$			13.0000i			0.569540i	−0.958596	+	0.284770i	$0.908083\pi$
$522$	5.19615	−	9.00000i	0.227429	−	0.393919i
$523$	−7.53590	+	7.53590i	−0.329522	+	0.329522i	−0.852405	−	0.522883i	$-0.824857\pi$
$523$	−7.53590	+	7.53590i	−0.329522	+	0.329522i	0.522883	+	0.852405i	$0.324857\pi$
$524$	4.19615	+	15.6603i	0.183310	+	0.684121i
$525$	−18.5885			−0.811267
$526$	1.05256	−	3.92820i	0.0458937	−	0.171278i
$527$	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
$531$	−5.89230	−	21.9904i	−0.255704	−	0.954301i
$532$	12.9282	+	12.9282i	0.560509	+	0.560509i
$533$	2.70577	+	10.0981i	0.117200	+	0.437396i
$534$	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	0.752739	−	0.658319i	$-0.228732\pi$
$541$	2.19615	+	2.19615i	0.0944200	+	0.0944200i	−0.658319	+	0.752739i	$0.728732\pi$
$542$	−0.143594	−	0.535898i	−0.00616787	−	0.0230188i
$543$	4.68653	+	17.4904i	0.201118	+	0.750584i
$544$	−31.3205	−	8.39230i	−1.34286	−	0.359817i
$545$	7.85641	+	13.6077i	0.336531	+	0.582890i
$546$	20.1962	−	11.6603i	0.864316	−	0.499013i
$547$	32.6244	−	8.74167i	1.39492	−	0.373767i	0.518400	−	0.855138i	$-0.326528\pi$
$547$	32.6244	−	8.74167i	1.39492	−	0.373767i	0.876517	+	0.481371i	$0.159861\pi$
$548$	−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
$555$		−	12.0000i		−	0.509372i
$556$	22.8564	−	6.12436i	0.969328	−	0.259731i
$557$	−14.8038	−	14.8038i	−0.627259	−	0.627259i	0.320118	−	0.947378i	$-0.396277\pi$
$557$	−14.8038	−	14.8038i	−0.627259	−	0.627259i	−0.947378	+	0.320118i	$0.896277\pi$
$558$	−2.19615	−	0.588457i	−0.0929705	−	0.0249114i
$559$	30.0526			1.27109
$560$	10.9282	−	2.92820i	0.461801	−	0.123739i
$561$	−42.0167	−	11.2583i	−1.77394	−	0.475327i
$562$	3.66025	−	13.6603i	0.154398	−	0.576223i
$563$	−7.23205	+	26.9904i	−0.304795	+	1.13751i	0.628327	+	0.777949i	$0.283740\pi$
$563$	−7.23205	+	26.9904i	−0.304795	+	1.13751i	−0.933122	+	0.359560i	$0.882927\pi$
$564$	22.9808	+	13.2679i	0.967665	+	0.558681i
$565$	−3.71281	−	13.8564i	−0.156199	−	0.582943i
$566$		−	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	0.0619424	−	0.998080i	$-0.480270\pi$
$569$	−18.4019	−	10.6244i	−0.771449	−	0.445396i	−0.833391	+	0.552684i	$0.813604\pi$
$570$	−2.19615	−	8.19615i	−0.0919867	−	0.343299i
$571$	−3.33013	−	0.892305i	−0.139361	−	0.0373418i	0.188464	−	0.982080i	$-0.439649\pi$
$571$	−3.33013	−	0.892305i	−0.139361	−	0.0373418i	−0.327825	+	0.944738i	$0.606316\pi$
$572$	−26.4449	+	15.2679i	−1.10572	+	0.638385i
$573$	20.8301	+	36.0788i	0.870191	+	1.50722i
$574$	−3.00000	−	11.1962i	−0.125218	−	0.467318i
$575$	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	$0.538420\pi$
$578$	5.80385	+	21.6603i	0.241408	+	0.900948i
$579$	−37.6410			−1.56431
$580$	−4.39230	+	2.53590i	−0.182381	+	0.105297i
$581$	−3.73205	−	1.00000i	−0.154832	−	0.0414870i
$582$	−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
$587$	7.23205	+	26.9904i	0.298499	+	1.11401i	0.938399	+	0.345554i	$0.112309\pi$
$587$	7.23205	+	26.9904i	0.298499	+	1.11401i	−0.639900	+	0.768458i	$0.721024\pi$
$588$	−1.39230	+	0.803848i	−0.0574177	+	0.0331501i
$589$	−0.464102	+	1.73205i	−0.0191230	+	0.0713679i
$590$	−2.87564	+	10.7321i	−0.118388	+	0.441832i
$591$	−8.66025	−	32.3205i	−0.356235	−	1.32949i
$592$	−6.92820	−	25.8564i	−0.284747	−	1.06269i
$593$	17.4641			0.717165			0.358582	−	0.933498i	$-0.383260\pi$
$593$	17.4641			0.717165			0.358582	+	0.933498i	$0.383260\pi$
$594$	27.8827	−	16.0981i	1.14404	−	0.660512i
$595$	−11.4641	−	11.4641i	−0.469982	−	0.469982i
$596$	−15.6603	+	4.19615i	−0.641469	+	0.171881i
$597$	37.6865	+	21.7583i	1.54241	+	0.890509i
$598$	−20.1962	+	11.6603i	−0.825882	+	0.476823i
$599$	11.3205	−	6.53590i	0.462543	−	0.267050i	−0.250570	−	0.968099i	$-0.580618\pi$
$599$	11.3205	−	6.53590i	0.462543	−	0.267050i	0.713113	+	0.701049i	$0.247285\pi$
$600$	18.5885	+	4.98076i	0.758871	+	0.203339i
$601$	−20.5526	−	11.8660i	−0.838356	−	0.484025i	0.0183488	−	0.999832i	$-0.494159\pi$
$601$	−20.5526	−	11.8660i	−0.838356	−	0.484025i	−0.856705	+	0.515806i	$0.827492\pi$
$602$	−33.3205			−1.35804
$603$	19.7942	−	5.30385i	0.806083	−	0.215989i
$604$	−1.46410			−0.0595734
$605$	−8.19615	+	2.19615i	−0.333221	+	0.0892863i
$606$			5.07180i			0.206028i
$607$	−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
$610$	4.39230	+	16.3923i	0.177839	+	0.663705i
$611$	−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	−0.948697	−	0.316186i	$-0.897598\pi$
$613$	−15.6603	+	15.6603i	−0.632512	+	0.632512i	0.316186	+	0.948697i	$0.397598\pi$
$614$	−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	−0.995633	−	0.0933485i	$-0.970243\pi$
$617$	−35.0885	+	20.2583i	−1.41261	+	0.815570i	−0.416975	+	0.908918i	$0.636910\pi$
$618$	35.7846	−	9.58846i	1.43947	−	0.385704i
$619$	4.17949	+	15.5981i	0.167988	+	0.626940i	0.997640	+	0.0686590i	$0.0218721\pi$
$619$	4.17949	+	15.5981i	0.167988	+	0.626940i	−0.829652	+	0.558281i	$0.811461\pi$
$620$	0.784610	+	0.784610i	0.0315107	+	0.0315107i
$621$	21.2942	−	12.2942i	0.854508	−	0.493350i
$622$	−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
$626$	−7.88269	+	29.4186i	−0.315055	+	1.17580i
$627$	−12.6962	−	21.9904i	−0.507035	−	0.878211i
$628$	2.53590	+	9.46410i	0.101193	+	0.377659i
$629$	−27.1244	+	27.1244i	−1.08152	+	1.08152i
$630$	12.0000			0.478091
$631$			17.6077i			0.700951i	0.936572	+	0.350476i	$0.113980\pi$
$631$			17.6077i			0.700951i	−0.936572	+	0.350476i	$0.886020\pi$
$632$	32.7846	−	8.78461i	1.30410	−	0.349433i
$633$	5.19615	+	5.19615i	0.206529	+	0.206529i
$634$	−15.0526	−	26.0718i	−0.597813	−	1.03544i
$635$	4.19615	+	1.12436i	0.166519	+	0.0446187i
$636$	−25.8564	−	25.8564i	−1.02527	−	1.02527i
$637$	1.56218	−	0.418584i	0.0618957	−	0.0165849i
$638$	−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	$0.880956\pi$
$642$	37.4711	−	21.6340i	1.47887	−	0.853825i
$643$	−2.34936	+	8.76795i	−0.0926499	+	0.345774i	−0.996653	−	0.0817525i	$-0.973948\pi$
$643$	−2.34936	+	8.76795i	−0.0926499	+	0.345774i	0.904003	+	0.427527i	$0.140615\pi$
$644$	22.3923	−	12.9282i	0.882380	−	0.509443i
$645$	13.3923	+	7.73205i	0.527321	+	0.304449i
$646$	−13.5622	+	23.4904i	−0.533597	+	0.924217i
$647$			16.7321i			0.657805i	0.944364	+	0.328902i	$0.106679\pi$
$647$			16.7321i			0.657805i	−0.944364	+	0.328902i	$0.893321\pi$
$648$	24.5885	−	6.58846i	0.965926	−	0.258819i
$649$			33.2487i			1.30513i
$650$	−16.7654	−	9.67949i	−0.657592	−	0.379661i
$651$	−2.19615	−	1.26795i	−0.0860740	−	0.0496948i
$652$	19.1244	+	5.12436i	0.748968	+	0.200685i
$653$	7.36603	−	27.4904i	0.288255	−	1.07578i	−0.658173	−	0.752867i	$-0.728671\pi$
$653$	7.36603	−	27.4904i	0.288255	−	1.07578i	0.946428	−	0.322915i	$-0.104663\pi$
$654$	18.5885	+	32.1962i	0.726866	+	1.25897i
$655$	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
$659$	−15.0263	+	4.02628i	−0.585341	+	0.156842i	−0.539323	−	0.842099i	$-0.681320\pi$
$659$	−15.0263	+	4.02628i	−0.585341	+	0.156842i	−0.0460178	+	0.998941i	$0.514653\pi$
$660$	−15.7128			−0.611620
$661$	−8.19615	−	2.19615i	−0.318793	−	0.0854204i	0.0958740	−	0.995393i	$-0.469435\pi$
$661$	−8.19615	−	2.19615i	−0.318793	−	0.0854204i	−0.414667	+	0.909973i	$0.636102\pi$
$662$	−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
$669$	13.9019	+	24.0788i	0.537479	+	0.930942i
$670$	−9.66025	−	2.58846i	−0.373208	−	0.100001i
$671$	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
$675$	17.6769	+	10.2058i	0.680385	+	0.392820i
$676$	−1.71281			−0.0658774
$677$	1.26795	+	4.73205i	0.0487312	+	0.181867i	0.986002	−	0.166736i	$-0.0533227\pi$
$677$	1.26795	+	4.73205i	0.0487312	+	0.181867i	−0.937270	+	0.348603i	$0.886656\pi$
$678$	−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	−0.979240	−	0.202703i	$-0.935027\pi$
$683$	−20.2942	+	20.2942i	−0.776537	+	0.776537i	0.202703	+	0.979240i	$0.435027\pi$
$684$	−5.19615	−	19.3923i	−0.198680	−	0.741483i
$685$	6.98076	+	6.98076i	0.266721	+	0.266721i
$686$	24.3923	−	6.53590i	0.931303	−	0.249542i
$687$	8.66025	−	8.66025i	0.330409	−	0.330409i
$688$	33.3205	+	8.92820i	1.27033	+	0.340385i
$689$	18.3923	+	31.8564i	0.700691	+	1.21363i
$690$	−12.0000			−0.456832
$691$	9.29423	−	2.49038i	0.353569	−	0.0947386i	−0.0776628	−	0.996980i	$-0.524746\pi$
$691$	9.29423	−	2.49038i	0.353569	−	0.0947386i	0.431232	+	0.902241i	$0.358079\pi$
$692$	−2.39230	+	2.39230i	−0.0909418	+	0.0909418i
$693$	34.6865	−	9.29423i	1.31763	−	0.353059i
$694$		−	25.8038i		−	0.979501i
$695$	−10.6077	−	6.12436i	−0.402373	−	0.232310i
$696$	−10.3923	+	6.00000i	−0.393919	+	0.227429i
$697$	14.8923	−	8.59808i	0.564086	−	0.325675i
$698$	11.6603	+	20.1962i	0.441347	+	0.764436i
$699$	−4.79423	−	2.76795i	−0.181334	−	0.104693i
$700$	18.5885	+	10.7321i	0.702578	+	0.405633i
$701$	−6.66025	−	6.66025i	−0.251554	−	0.251554i	0.570053	−	0.821608i	$-0.306923\pi$
$701$	−6.66025	−	6.66025i	−0.251554	−	0.251554i	−0.821608	+	0.570053i	$0.806923\pi$
$702$	−25.6077			−0.966500
$703$	−22.3923			−0.844542
$704$	−33.8564	+	9.07180i	−1.27601	+	0.341906i
$705$	−3.55514	−	13.2679i	−0.133894	−	0.499700i
$706$	19.5622	+	5.24167i	0.736232	+	0.197273i
$707$	−1.46410	+	5.46410i	−0.0550632	+	0.205499i
$708$	−6.80385	+	25.3923i	−0.255704	+	0.954301i
$709$	−9.80385	−	36.5885i	−0.368191	−	1.37411i	−0.863043	−	0.505131i	$-0.831444\pi$
$709$	−9.80385	−	36.5885i	−0.368191	−	1.37411i	0.494852	−	0.868978i	$-0.335222\pi$
$710$	−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
$715$	15.2679	+	4.09103i	0.570989	+	0.152996i
$716$	5.26795	+	1.41154i	0.196873	+	0.0527518i
$717$	−27.3731			−1.02227
$718$	−15.3923	+	4.12436i	−0.574436	+	0.153920i
$719$	4.39230			0.163805			0.0819027	−	0.996640i	$-0.473900\pi$
$719$	4.39230			0.163805			0.0819027	+	0.996640i	$0.473900\pi$
$720$	−12.0000	−	3.21539i	−0.447214	−	0.119831i
$721$	41.3205			1.53886
$722$	10.6603	−	2.85641i	0.396734	−	0.106304i
$723$	20.0885	+	34.7942i	0.747098	+	1.29401i
$724$	5.41154	−	20.1962i	0.201118	−	0.750584i
$725$	−9.29423	−	2.49038i	−0.345179	−	0.0924904i
$726$	−19.3923	+	5.19615i	−0.719716	+	0.192847i
$727$	−28.8109	−	16.6340i	−1.06854	−	0.616920i	−0.140755	−	0.990044i	$-0.544953\pi$
$727$	−28.8109	−	16.6340i	−1.06854	−	0.616920i	−0.927781	+	0.373124i	$0.878286\pi$
$728$	−26.9282			−0.998026
$729$	27.0000			1.00000
$730$	9.17691			0.339653
$731$	−12.7942	−	47.7487i	−0.473212	−	1.76605i
$732$	10.3923	+	38.7846i	0.384111	+	1.43352i
$733$	2.95448	−	11.0263i	0.109126	−	0.407265i	−0.889654	−	0.456635i	$-0.849055\pi$
$733$	2.95448	−	11.0263i	0.109126	−	0.407265i	0.998781	+	0.0493698i	$0.0157213\pi$
$734$	38.5885	+	10.3397i	1.42433	+	0.381647i
$735$	0.803848	+	0.215390i	0.0296504	+	0.00794479i
$736$	−25.8564	+	6.92820i	−0.953080	+	0.255377i
$737$	−29.9282			−1.10242
$738$	−3.29423	+	12.2942i	−0.121262	+	0.452557i
$739$	−8.22243	−	8.22243i	−0.302467	−	0.302467i	0.539511	−	0.841978i	$-0.318609\pi$
$739$	−8.22243	−	8.22243i	−0.302467	−	0.302467i	−0.841978	+	0.539511i	$0.818609\pi$
$740$	−6.92820	+	12.0000i	−0.254686	+	0.441129i
$741$			20.1962i			0.741924i
$742$	−20.3923	−	35.3205i	−0.748625	−	1.29666i
$743$	24.7583	−	14.2942i	0.908295	−	0.524404i	0.0284129	−	0.999596i	$-0.490955\pi$
$743$	24.7583	−	14.2942i	0.908295	−	0.524404i	0.879882	+	0.475192i	$0.157621\pi$
$744$	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
$749$	46.6147	−	12.4904i	1.70327	−	0.456389i
$750$	−11.3205	−	19.6077i	−0.413367	−	0.715972i
$751$	−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
$754$	11.6603	−	3.12436i	0.424641	−	0.113782i
$755$	0.535898	+	0.535898i	0.0195033	+	0.0195033i
$756$	28.3923			1.03262
$757$	−19.9282	+	19.9282i	−0.724303	+	0.724303i	−0.969479	−	0.245176i	$-0.921154\pi$
$757$	−19.9282	+	19.9282i	−0.724303	+	0.724303i	0.245176	+	0.969479i	$0.421154\pi$
$758$	6.50962	+	3.75833i	0.236440	+	0.136509i
$759$	−34.6865	+	9.29423i	−1.25904	+	0.337359i
$760$	−2.53590	+	9.46410i	−0.0919867	+	0.343299i
$761$	45.3731	−	26.1962i	1.64477	−	0.949610i	0.665669	−	0.746247i	$-0.268146\pi$
$761$	45.3731	−	26.1962i	1.64477	−	0.949610i	0.979104	−	0.203363i	$-0.0651870\pi$
$762$	9.92820	+	2.66025i	0.359661	+	0.0963708i
$763$	10.7321	+	40.0526i	0.388526	+	1.45000i
$764$		−	48.1051i		−	1.74038i
$765$	4.60770	+	17.1962i	0.166592	+	0.621728i
$766$	13.4641	−	13.4641i	0.486478	−	0.486478i
$767$	13.2224	−	22.9019i	0.477434	−	0.826941i
$768$	−27.7128			−1.00000
$769$	−14.1244	−	24.4641i	−0.509337	−	0.882198i	−0.999942	−	0.0108155i	$-0.996557\pi$
$769$	−14.1244	−	24.4641i	−0.509337	−	0.882198i	0.490604	−	0.871383i	$-0.336776\pi$
$770$	−16.9282	−	4.53590i	−0.610050	−	0.163462i
$771$	32.6603			1.17623
$772$	37.6410	+	21.7321i	1.35473	+	0.782154i
$773$	35.5885	−	35.5885i	1.28003	−	1.28003i	0.339378	−	0.940650i	$-0.389784\pi$
$773$	35.5885	−	35.5885i	1.28003	−	1.28003i	0.940650	−	0.339378i	$-0.110216\pi$
$774$	31.6865	+	18.2942i	1.13895	+	0.657572i
$775$			2.10512i			0.0756181i
$776$	32.0526	−	8.58846i	1.15062	−	0.308308i
$777$	8.19615	−	30.5885i	0.294035	−	1.09735i
$778$	25.0526	−	14.4641i	0.898178	−	0.518563i
$779$	9.69615	+	2.59808i	0.347401	+	0.0930857i
$780$	10.8231	+	6.24871i	0.387529	+	0.223740i
$781$	−12.3923	+	3.32051i	−0.443432	+	0.118817i
$782$	27.1244	+	27.1244i	0.969965	+	0.969965i
$783$	−12.2942	+	3.29423i	−0.439360	+	0.117726i
$784$	1.85641			0.0663002
$785$	2.53590	−	4.39230i	0.0905101	−	0.156768i
$786$	9.92820	−	17.1962i	0.354127	−	0.613366i
$787$	−10.8109	+	40.3468i	−0.385367	+	1.43821i	0.452222	+	0.891906i	$0.350632\pi$
$787$	−10.8109	+	40.3468i	−0.385367	+	1.43821i	−0.837588	+	0.546302i	$0.816035\pi$
$788$	−10.0000	+	37.3205i	−0.356235	+	1.32949i
$789$	−4.31347	+	2.49038i	−0.153563	+	0.0886599i
$790$	−15.2154	−	8.78461i	−0.541339	−	0.312542i
$791$		−	37.8564i		−	1.34602i
$792$	−37.1769			−1.32102
$793$		−	40.3923i		−	1.43437i
$794$	9.26795	−	16.0526i	0.328907	−	0.569684i
$795$			18.9282i			0.671314i
$796$	−25.1244	−	43.5167i	−0.890509	−	1.54241i
$797$	8.17691	−	30.5167i	0.289641	−	1.08096i	−0.655740	−	0.754987i	$-0.727643\pi$
$797$	8.17691	−	30.5167i	0.289641	−	1.08096i	0.945381	−	0.325968i	$-0.105690\pi$
$798$		−	22.3923i		−	0.792679i
$799$	−21.9545	+	38.0263i	−0.776694	+	1.34527i
$800$	−15.7128	−	15.7128i	−0.555532	−	0.555532i
$801$	−5.19615	+	3.00000i	−0.183597	+	0.106000i
$802$	3.58846	−	3.58846i	0.126713	−	0.126713i
$803$	26.5263	−	7.10770i	0.936092	−	0.250825i
$804$	−22.8564	−	6.12436i	−0.806083	−	0.215989i
$805$	−12.9282	−	3.46410i	−0.455659	−	0.122094i
$806$	−1.32051	−	2.28719i	−0.0465129	−	0.0805627i
$807$	3.00000	−	0.803848i	0.105605	−	0.0282968i
$808$	2.92820	−	5.07180i	0.103014	−	0.178425i
$809$		−	6.32051i		−	0.222217i	−0.993808	−	0.111109i	$-0.964560\pi$
$809$		−	6.32051i		−	0.222217i	0.993808	−	0.111109i	$-0.0354401\pi$
$810$	−11.4115	−	6.58846i	−0.400961	−	0.231495i
$811$	−14.0263	+	14.0263i	−0.492529	+	0.492529i	−0.909102	−	0.416573i	$-0.863231\pi$
$811$	−14.0263	+	14.0263i	−0.492529	+	0.492529i	0.416573	+	0.909102i	$0.363231\pi$
$812$	−12.9282	+	3.46410i	−0.453691	+	0.121566i
$813$	−0.339746	+	0.588457i	−0.0119154	+	0.0206381i
$814$	−10.7321	+	40.0526i	−0.376158	+	1.40384i
$815$	−5.12436	−	8.87564i	−0.179498	−	0.310900i
$816$	19.8564	+	34.3923i	0.695113	+	1.20397i
$817$	14.4282	−	24.9904i	0.504779	−	0.874303i
$818$	32.1769	+	32.1769i	1.12504	+	1.12504i
$819$	−27.5885	−	7.39230i	−0.964019	−	0.258308i
$820$	4.39230	−	4.39230i	0.153386	−	0.153386i
$821$	2.77757	+	10.3660i	0.0969378	+	0.361777i	0.997306	−	0.0733518i	$-0.0233696\pi$
$821$	2.77757	+	10.3660i	0.0969378	+	0.361777i	−0.900368	+	0.435129i	$0.856703\pi$
$822$	16.5167	+	16.5167i	0.576085	+	0.576085i
$823$	7.26795	−	4.19615i	0.253345	−	0.146269i	−0.367950	−	0.929846i	$-0.619940\pi$
$823$	7.26795	−	4.19615i	0.253345	−	0.146269i	0.621295	+	0.783577i	$0.286607\pi$
$824$	−41.3205	−	11.0718i	−1.43947	−	0.385704i
$825$	−21.0788	−	21.0788i	−0.733871	−	0.733871i
$826$	−14.6603	+	25.3923i	−0.510095	+	0.883511i
$827$	17.5359	−	17.5359i	0.609783	−	0.609783i	−0.333106	−	0.942889i	$-0.608097\pi$
$827$	17.5359	−	17.5359i	0.609783	−	0.609783i	0.942889	+	0.333106i	$0.108097\pi$
$828$	−28.3923			−0.986701
$829$	−20.5167	−	20.5167i	−0.712573	−	0.712573i	0.254500	−	0.967073i	$-0.418089\pi$
$829$	−20.5167	−	20.5167i	−0.712573	−	0.712573i	−0.967073	+	0.254500i	$0.918089\pi$
$830$	−0.535898	−	2.00000i	−0.0186013	−	0.0694210i
$831$	−43.6865	−	11.7058i	−1.51547	−	0.406069i
$832$	26.9282	+	7.21539i	0.933567	+	0.250149i
$833$	−1.33013	−	2.30385i	−0.0460862	−	0.0798236i
$834$	−25.0981	−	14.4904i	−0.869075	−	0.501761i
$835$	7.46410	−	2.00000i	0.258306	−	0.0692129i
$836$			29.3205i			1.01407i
$837$	1.39230	+	2.41154i	0.0481251	+	0.0833551i
$838$	9.71281			0.335524
$839$	23.4449	+	13.5359i	0.809407	+	0.467311i	0.846750	−	0.531991i	$-0.178556\pi$
$839$	23.4449	+	13.5359i	0.809407	+	0.467311i	−0.0373432	+	0.999303i	$0.511889\pi$
$840$	−12.0000	−	6.92820i	−0.414039	−	0.239046i
$841$	−19.9186	+	11.5000i	−0.686848	+	0.396552i
$842$	−38.7846	+	22.3923i	−1.33661	+	0.771690i
$843$	−15.0000	+	8.66025i	−0.516627	+	0.298275i
$844$	−2.19615	−	8.19615i	−0.0755947	−	0.282123i
$845$	0.626933	+	0.626933i	0.0215672	+	0.0215672i
$846$	−8.41154	−	31.3923i	−0.289195	−	1.07929i
$847$	−22.3923			−0.769409
$848$	10.9282	+	40.7846i	0.375276	+	1.40055i
$849$	−24.8038	+	24.8038i	−0.851266	+	0.851266i
$850$	−8.24167	+	30.7583i	−0.282687	+	1.05500i
$851$	−8.19615	+	30.5885i	−0.280960	+	1.04856i
$852$	−10.1436			−0.347514
$853$	−0.437822	−	1.63397i	−0.0149907	−	0.0559462i	0.958025	−	0.286684i	$-0.0925528\pi$
$853$	−0.437822	−	1.63397i	−0.0149907	−	0.0559462i	−0.973016	+	0.230737i	$0.925886\pi$
$854$			44.7846i			1.53250i
$855$	−5.19615	+	9.00000i	−0.177705	+	0.307794i
$856$	−49.9615			−1.70765
$857$	−44.9090	−	25.9282i	−1.53406	−	0.885691i	−0.999169	−	0.0407704i	$-0.987019\pi$
$857$	−44.9090	−	25.9282i	−1.53406	−	0.885691i	−0.534892	−	0.844920i	$-0.679648\pi$
$858$	36.1244	+	9.67949i	1.23327	+	0.330452i
$859$	14.2583	+	3.82051i	0.486488	+	0.130354i	0.493722	−	0.869620i	$-0.335636\pi$
$859$	14.2583	+	3.82051i	0.486488	+	0.130354i	−0.00723407	+	0.999974i	$0.502303\pi$
$860$	−8.92820	−	15.4641i	−0.304449	−	0.527321i
$861$	−7.09808	+	12.2942i	−0.241902	+	0.418986i
$862$	−5.92820	−	22.1244i	−0.201915	−	0.753559i
$863$	−15.4641			−0.526404			−0.263202	−	0.964741i	$-0.584779\pi$
$863$	−15.4641			−0.526404			−0.263202	+	0.964741i	$0.584779\pi$
$864$	−28.3923	−	7.60770i	−0.965926	−	0.258819i
$865$	1.75129			0.0595456
$866$	−2.09808	−	7.83013i	−0.0712955	−	0.266079i
$867$	13.7321	−	23.7846i	0.466365	−	0.807768i
$868$	1.46410	+	2.53590i	0.0496948	+	0.0860740i
$869$	−50.7846	−	13.6077i	−1.72275	−	0.461609i
$870$	6.00000	+	1.60770i	0.203419	+	0.0545060i
$871$	20.6147	+	11.9019i	0.698504	+	0.403281i
$872$		−	42.9282i		−	1.45373i
$873$	35.1962			1.19121
$874$			22.3923i			0.757431i
$875$	−6.53590	−	24.3923i	−0.220954	−	0.824610i
$876$	21.7128			0.733608
$877$	−8.46410	+	31.5885i	−0.285812	+	1.06667i	0.662431	+	0.749123i	$0.269525\pi$
$877$	−8.46410	+	31.5885i	−0.285812	+	1.06667i	−0.948244	+	0.317544i	$0.897142\pi$
$878$	9.66025	−	36.0526i	0.326018	−	1.21671i
$879$	−6.80385	+	6.80385i	−0.229488	+	0.229488i
$880$	15.7128	+	9.07180i	0.529679	+	0.305810i
$881$	27.3205			0.920451			0.460226	−	0.887802i	$-0.347769\pi$
$881$	27.3205			0.920451			0.460226	+	0.887802i	$0.347769\pi$
$882$	1.90192	+	0.509619i	0.0640411	+	0.0171598i
$883$	−12.6340	−	12.6340i	−0.425167	−	0.425167i	0.461811	−	0.886978i	$-0.347200\pi$
$883$	−12.6340	−	12.6340i	−0.425167	−	0.425167i	−0.886978	+	0.461811i	$0.847200\pi$
$884$	−10.3397	−	38.5885i	−0.347763	−	1.29787i
$885$	11.7846	−	6.80385i	0.396135	−	0.228709i
$886$	21.8827	−	12.6340i	0.735163	−	0.424447i
$887$	8.87564	−	5.12436i	0.298015	−	0.172059i	−0.343536	−	0.939140i	$-0.611625\pi$
$887$	8.87564	−	5.12436i	0.298015	−	0.172059i	0.641551	+	0.767081i	$0.278291\pi$
$888$	−16.3923	+	28.3923i	−0.550090	+	0.952783i
$889$	9.92820	+	5.73205i	0.332981	+	0.192247i
$890$	2.92820			0.0981536
$891$	−38.0885	−	10.2058i	−1.27601	−	0.341906i
$892$		−	32.1051i		−	1.07496i
$893$	−24.7583	+	6.63397i	−0.828506	+	0.221997i
$894$	17.1962	+	9.92820i	0.575125	+	0.332049i
$895$	−1.41154	−	2.44486i	−0.0471827	−	0.0817228i
$896$	−29.8564	−	8.00000i	−0.997433	−	0.267261i
$897$	27.5885	+	7.39230i	0.921152	+	0.246822i
$898$	−1.22243	−	4.56218i	−0.0407931	−	0.152242i
$899$	−0.928203	−	0.928203i	−0.0309573	−	0.0309573i
$900$	−11.7846	−	20.4115i	−0.392820	−	0.680385i
$901$	42.7846	−	42.7846i	1.42536	−	1.42536i
$902$	9.29423	−	16.0981i	0.309464	−	0.536007i
$903$	28.8564	+	28.8564i	0.960281	+	0.960281i
$904$	−10.1436	+	37.8564i	−0.337371	+	1.25909i
$905$	−9.37307	+	5.41154i	−0.311571	+	0.179886i
$906$	1.26795	+	1.26795i	0.0421248	+	0.0421248i
$907$	−1.20577	−	4.50000i	−0.0400370	−	0.149420i	0.943014	−	0.332754i	$-0.107978\pi$
$907$	−1.20577	−	4.50000i	−0.0400370	−	0.149420i	−0.983051	+	0.183334i	$0.941311\pi$
$908$	−3.12436	+	3.12436i	−0.103685	+	0.103685i
$909$	4.39230	−	4.39230i	0.145684	−	0.145684i
$910$	9.85641	+	9.85641i	0.326737	+	0.326737i
$911$	2.46410	−	4.26795i	0.0816393	−	0.141403i	−0.822315	−	0.569033i	$-0.807318\pi$
$911$	2.46410	−	4.26795i	0.0816393	−	0.141403i	0.903954	+	0.427629i	$0.140651\pi$
$912$	−6.00000	+	22.3923i	−0.198680	+	0.741483i
$913$	−3.09808	−	5.36603i	−0.102531	−	0.177590i
$914$	−0.954483	+	3.56218i	−0.0315715	+	0.117826i
$915$	10.3923	−	18.0000i	0.343559	−	0.595062i
$916$	−13.6603	+	3.66025i	−0.451347	+	0.120938i
$917$	15.6603	−	15.6603i	0.517147	−	0.517147i
$918$	10.9019	+	40.6865i	0.359817	+	1.34286i
$919$			18.9808i			0.626118i	0.949734	+	0.313059i	$0.101354\pi$
$919$			18.9808i			0.626118i	−0.949734	+	0.313059i	$0.898646\pi$
$920$	12.0000	+	6.92820i	0.395628	+	0.228416i
$921$	7.16025	−	1.91858i	0.235938	−	0.0632195i
$922$	26.1244	+	45.2487i	0.860360	+	1.49019i
$923$	9.85641	+	2.64102i	0.324428	+	0.0869301i
$924$	−40.0526	−	10.7321i	−1.31763	−	0.353059i
$925$	−25.3923	+	6.80385i	−0.834894	+	0.223709i
$926$	−2.39230	+	2.39230i	−0.0786160	+	0.0786160i
$927$	−39.2942	−	22.6865i	−1.29059	−	0.745124i
$928$	13.8564			0.454859
$929$	−11.5359	+	19.9808i	−0.378481	+	0.655548i	−0.990841	−	0.135031i	$-0.956887\pi$
$929$	−11.5359	+	19.9808i	−0.378481	+	0.655548i	0.612361	+	0.790578i	$0.290220\pi$
$930$		−	1.35898i		−	0.0445628i
$931$	0.401924	−	1.50000i	0.0131725	−	0.0491605i
$932$	3.19615	+	5.53590i	0.104693	+	0.181334i
$933$			38.1962i			1.25049i
$934$	−2.63397	+	4.56218i	−0.0861863	+	0.149279i
$935$		−	26.0000i		−	0.850291i
$936$	25.6077	+	14.7846i	0.837014	+	0.483250i
$937$		−	11.1769i		−	0.365134i	−0.983193	−	0.182567i	$-0.941559\pi$
$937$		−	11.1769i		−	0.365134i	0.983193	−	0.182567i	$-0.0584406\pi$
$938$	−22.8564	−	13.1962i	−0.746288	−	0.430870i
$939$	32.3038	−	18.6506i	1.05420	−	0.608640i
$940$	−4.10512	+	15.3205i	−0.133894	+	0.499700i
$941$	−1.80385	+	6.73205i	−0.0588038	+	0.219459i	−0.989075	−	0.147414i	$-0.952905\pi$
$941$	−1.80385	+	6.73205i	−0.0588038	+	0.219459i	0.930271	+	0.366873i	$0.119572\pi$
$942$	6.00000	−	10.3923i	0.195491	−	0.338600i
$943$	7.09808	−	12.2942i	0.231145	−	0.400355i
$944$	21.4641	−	21.4641i	0.698597	−	0.698597i
$945$	−10.3923	−	10.3923i	−0.338062	−	0.338062i
$946$	−37.7846	−	37.7846i	−1.22848	−	1.22848i
$947$	41.0167	−	10.9904i	1.33286	−	0.357139i	0.479081	−	0.877771i	$-0.340970\pi$
$947$	41.0167	−	10.9904i	1.33286	−	0.357139i	0.853782	+	0.520631i	$0.174303\pi$
$948$	−36.0000	−	20.7846i	−1.16923	−	0.675053i
$949$	−21.0981	−	5.65321i	−0.684873	−	0.183511i
$950$	−16.0981	+	9.29423i	−0.522291	+	0.301545i
$951$	−9.54294	+	35.6147i	−0.309451	+	1.15489i
$952$	11.4641	+	42.7846i	0.371554	+	1.38666i
$953$			17.1051i			0.554089i	0.960857	+	0.277045i	$0.0893550\pi$
$953$			17.1051i			0.554089i	−0.960857	+	0.277045i	$0.910645\pi$
$954$			44.7846i			1.44996i
$955$	−17.6077	+	17.6077i	−0.569772	+	0.569772i
$956$	27.3731	+	15.8038i	0.885308	+	0.511133i
$957$	18.5885			0.600879
$958$	11.3923	+	3.05256i	0.368069	+	0.0986237i
$959$	13.0263	+	22.5622i	0.420641	+	0.728571i
$960$	10.1436	+	10.1436i	0.327383	+	0.327383i
$961$	15.3564	−	26.5981i	0.495368	−	0.858002i
$962$	23.3205	−	23.3205i	0.751883	−	0.751883i
$963$	−51.1865	−	13.7154i	−1.64946	−	0.441972i
$964$		−	46.3923i		−	1.49420i
$965$	−5.82309	−	21.7321i	−0.187452	−	0.699579i
$966$	−30.5885	−	8.19615i	−0.984167	−	0.263707i
$967$	17.8301	−	10.2942i	0.573378	−	0.331040i	−0.185119	−	0.982716i	$-0.559267\pi$
$967$	17.8301	−	10.2942i	0.573378	−	0.331040i	0.758497	+	0.651676i	$0.225934\pi$
$968$	22.3923	+	6.00000i	0.719716	+	0.192847i
$969$	32.0885	−	8.59808i	1.03083	−	0.276210i
$970$	−14.8756	−	8.58846i	−0.477628	−	0.275759i
$971$	15.5359	−	15.5359i	0.498571	−	0.498571i	−0.412422	−	0.910993i	$-0.635317\pi$
$971$	15.5359	−	15.5359i	0.498571	−	0.498571i	0.910993	+	0.412422i	$0.135317\pi$
$972$	−27.0000	−	15.5885i	−0.866025	−	0.500000i
$973$	−22.8564	−	22.8564i	−0.732743	−	0.732743i
$974$	−7.92820	+	2.12436i	−0.254036	+	0.0680687i
$975$	6.13655	+	22.9019i	0.196527	+	0.733449i
$976$	12.0000	−	44.7846i	0.384111	−	1.43352i
$977$	−22.0622	−	38.2128i	−0.705832	−	1.22254i	−0.966391	−	0.257078i	$-0.917240\pi$
$977$	−22.0622	−	38.2128i	−0.705832	−	1.22254i	0.260559	−	0.965458i	$-0.416093\pi$
$978$	−12.1244	−	21.0000i	−0.387694	−	0.671506i
$979$	8.46410	−	2.26795i	0.270514	−	0.0724840i
$980$	−0.679492	−	0.679492i	−0.0217056	−	0.0217056i
$981$	11.7846	−	43.9808i	0.376254	−	1.40420i
$982$		−	20.3397i		−	0.649067i
$983$	13.8564	+	8.00000i	0.441951	+	0.255160i	0.704425	−	0.709779i	$-0.251205\pi$
$983$	13.8564	+	8.00000i	0.441951	+	0.255160i	−0.262474	+	0.964939i	$0.584538\pi$
$984$	10.3923	−	10.3923i	0.331295	−	0.331295i
$985$	17.3205	−	10.0000i	0.551877	−	0.318626i
$986$	−9.92820	−	17.1962i	−0.316178	−	0.547637i
$987$		−	36.2487i		−	1.15381i
$988$	11.6603	−	20.1962i	0.370962	−	0.642525i
$989$	−28.8564	−	28.8564i	−0.917580	−	0.917580i
$990$	13.6077	+	13.6077i	0.432481	+	0.432481i
$991$	36.6410			1.16394			0.581970	−	0.813210i	$-0.302282\pi$
$991$	36.6410			1.16394			0.581970	+	0.813210i	$0.302282\pi$
$992$	−0.784610	−	2.92820i	−0.0249114	−	0.0929705i
$993$	0.169873	+	0.0455173i	0.00539076	+	0.00144445i
$994$	−10.9282	−	2.92820i	−0.346622	−	0.0928770i
$995$	−6.73205	+	25.1244i	−0.213420	+	0.796496i
$996$	−1.26795	−	4.73205i	−0.0401765	−	0.149941i
$997$	7.87564	+	29.3923i	0.249424	+	0.930864i	0.971108	+	0.238641i	$0.0767018\pi$
$997$	7.87564	+	29.3923i	0.249424	+	0.930864i	−0.721684	+	0.692223i	$0.756632\pi$
$998$	−12.7321			−0.403026
$999$	−24.5885	+	24.5885i	−0.777944	+	0.777944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.x.c.61.1	yes	4
3.2	odd	2		432.2.y.b.397.1		4
4.3	odd	2		576.2.bb.c.529.1		4
9.4	even	3		144.2.x.b.13.1	✓	4
9.5	odd	6		432.2.y.c.253.1		4
12.11	even	2		1728.2.bc.a.721.1		4
16.5	even	4		144.2.x.b.133.1	yes	4
16.11	odd	4		576.2.bb.d.241.1		4
36.23	even	6		1728.2.bc.d.145.1		4
36.31	odd	6		576.2.bb.d.337.1		4
48.5	odd	4		432.2.y.c.181.1		4
48.11	even	4		1728.2.bc.d.1585.1		4
144.5	odd	12		432.2.y.b.37.1		4
144.59	even	12		1728.2.bc.a.1009.1		4
144.85	even	12	inner	144.2.x.c.85.1	yes	4
144.139	odd	12		576.2.bb.c.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.b.13.1	✓	4	9.4	even	3
144.2.x.b.133.1	yes	4	16.5	even	4
144.2.x.c.61.1	yes	4	1.1	even	1	trivial
144.2.x.c.85.1	yes	4	144.85	even	12	inner
432.2.y.b.37.1		4	144.5	odd	12
432.2.y.b.397.1		4	3.2	odd	2
432.2.y.c.181.1		4	48.5	odd	4
432.2.y.c.253.1		4	9.5	odd	6
576.2.bb.c.49.1		4	144.139	odd	12
576.2.bb.c.529.1		4	4.3	odd	2
576.2.bb.d.241.1		4	16.11	odd	4
576.2.bb.d.337.1		4	36.31	odd	6
1728.2.bc.a.721.1		4	12.11	even	2
1728.2.bc.a.1009.1		4	144.59	even	12
1728.2.bc.d.145.1		4	36.23	even	6
1728.2.bc.d.1585.1		4	48.11	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.00000 + 0.267949i) q^{5} +(2.36603 + 0.633975i) q^{6} +(2.36603 + 1.36603i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.00000 + 0.267949i) 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} +(1.13397 + 4.23205i) q^{11} +3.46410i q^{12} +(0.901924 - 3.36603i) q^{13} +(-1.00000 + 3.73205i) 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} +(-2.00000 + 0.535898i) q^{20} +(4.09808 - 2.36603i) 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} -5.19615 q^{27} -5.46410 q^{28} +(2.36603 - 0.633975i) q^{29} +(2.19615 + 1.26795i) q^{30} +(-0.267949 - 0.464102i) q^{31} +(5.46410 + 1.46410i) q^{32} +(7.33013 + 1.96410i) q^{33} +(-2.09808 - 7.83013i) 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} +(2.23205 + 8.33013i) q^{43} +(-6.19615 - 6.19615i) q^{44} +(-0.803848 - 3.00000i) q^{45} +(-4.73205 - 4.73205i) q^{46} +(3.83013 - 6.63397i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(0.232051 + 0.401924i) q^{49} +(1.43782 - 5.36603i) q^{50} +(-4.96410 + 8.59808i) q^{51} +(1.80385 + 6.73205i) q^{52} +(-7.46410 + 7.46410i) q^{53} +(-1.90192 - 7.09808i) q^{54} +4.53590i q^{55} +(-2.00000 - 7.46410i) q^{56} +(-5.59808 + 1.50000i) q^{57} +(1.73205 + 3.00000i) q^{58} +(7.33013 + 1.96410i) q^{59} +(-0.928203 + 3.46410i) q^{60} +(11.1962 - 3.00000i) q^{61} +(0.535898 - 0.535898i) q^{62} -8.19615i q^{63} +8.00000i q^{64} +(1.80385 - 3.12436i) q^{65} +10.7321i q^{66} +(-1.76795 + 6.59808i) q^{67} +(9.92820 - 5.73205i) q^{68} +8.19615i q^{69} +(-2.00000 + 3.46410i) q^{70} +2.92820i q^{71} +(-2.19615 + 8.19615i) q^{72} -6.26795i q^{73} +(8.19615 + 4.73205i) q^{74} +(-5.89230 + 3.40192i) q^{75} +(6.46410 + 1.73205i) q^{76} +(-3.09808 + 11.5622i) q^{77} +(4.26795 - 7.39230i) 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} +(-1.36603 + 0.366025i) q^{83} +(-4.73205 + 8.19615i) q^{84} +(-5.73205 - 1.53590i) 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} -0.928203 q^{93} +(10.4641 + 2.80385i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{5} + 6 q^{6} + 6 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 4 * q^5 + 6 * q^6 + 6 * q^7 - 8 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} + 4 q^{5} + 6 q^{6} + 6 q^{7} - 8 q^{8} - 6 q^{9} + 8 q^{11} + 14 q^{13} - 4 q^{14} + 12 q^{15} + 8 q^{16} - 16 q^{17} + 12 q^{18} - 6 q^{19} - 8 q^{20} + 6 q^{21} - 18 q^{22} - 6 q^{23} - 12 q^{24} - 24 q^{25} - 8 q^{26} - 8 q^{28} + 6 q^{29} - 12 q^{30} - 8 q^{31} + 8 q^{32} + 12 q^{33} + 2 q^{34} + 8 q^{35} + 12 q^{37} + 6 q^{38} - 24 q^{39} + 8 q^{40} + 12 q^{42} + 2 q^{43} - 4 q^{44} - 24 q^{45} - 12 q^{46} - 2 q^{47} - 6 q^{49} + 30 q^{50} - 6 q^{51} + 28 q^{52} - 16 q^{53} - 18 q^{54} - 8 q^{56} - 12 q^{57} + 12 q^{59} + 24 q^{60} + 24 q^{61} + 16 q^{62} + 28 q^{65} - 14 q^{67} + 12 q^{68} - 8 q^{70} + 12 q^{72} + 12 q^{74} + 18 q^{75} + 12 q^{76} - 2 q^{77} + 24 q^{78} - 24 q^{79} - 16 q^{80} - 18 q^{81} - 12 q^{82} - 2 q^{83} - 12 q^{84} - 16 q^{85} - 18 q^{86} - 6 q^{87} + 4 q^{88} + 36 q^{90} + 20 q^{91} + 12 q^{92} + 24 q^{93} + 28 q^{94} - 20 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^5 + 6 * q^6 + 6 * q^7 - 8 * q^8 - 6 * q^9 + 8 * q^11 + 14 * q^13 - 4 * q^14 + 12 * q^15 + 8 * q^16 - 16 * q^17 + 12 * q^18 - 6 * q^19 - 8 * 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 + 2 * q^34 + 8 * q^35 + 12 * q^37 + 6 * q^38 - 24 * q^39 + 8 * q^40 + 12 * q^42 + 2 * q^43 - 4 * q^44 - 24 * q^45 - 12 * q^46 - 2 * q^47 - 6 * q^49 + 30 * q^50 - 6 * q^51 + 28 * q^52 - 16 * q^53 - 18 * q^54 - 8 * q^56 - 12 * q^57 + 12 * q^59 + 24 * q^60 + 24 * q^61 + 16 * q^62 + 28 * q^65 - 14 * q^67 + 12 * q^68 - 8 * q^70 + 12 * q^72 + 12 * q^74 + 18 * q^75 + 12 * q^76 - 2 * q^77 + 24 * q^78 - 24 * q^79 - 16 * q^80 - 18 * q^81 - 12 * q^82 - 2 * q^83 - 12 * q^84 - 16 * q^85 - 18 * q^86 - 6 * q^87 + 4 * q^88 + 36 * q^90 + 20 * q^91 + 12 * q^92 + 24 * q^93 + 28 * q^94 - 20 * q^97 + 12 * q^98 + 6 * q^99

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