LMFDB - Embedded newform 315.2.cg.b.283.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(157,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3, 2]))

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

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

chi := DirichletCharacter("315.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			283.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.283
Dual form			315.2.cg.b.187.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 1.86603i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(1.00000 + 2.00000i) q^{5} +(3.23205 + 0.866025i) q^{6} +(-2.59808 - 0.500000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 1.86603i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(1.00000 + 2.00000i) q^{5} +(3.23205 + 0.866025i) q^{6} +(-2.59808 - 0.500000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(3.23205 - 2.86603i) q^{10} -2.00000 q^{11} -3.00000i q^{12} +(1.36603 + 5.09808i) q^{13} +(0.366025 + 5.09808i) q^{14} +(-3.86603 - 0.232051i) q^{15} +(-2.23205 + 3.86603i) q^{16} +(-7.46410 + 2.00000i) q^{17} +(-4.09808 + 4.09808i) q^{18} +(1.36603 + 2.36603i) q^{19} +(-3.23205 - 2.13397i) q^{20} +(3.00000 - 3.46410i) q^{21} +(1.00000 + 3.73205i) q^{22} +(-2.46410 - 2.46410i) q^{23} +(0.866025 - 0.232051i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(8.83013 - 5.09808i) q^{26} +5.19615 q^{27} +(4.33013 - 1.50000i) q^{28} +(3.40192 - 1.96410i) q^{29} +(1.50000 + 7.33013i) q^{30} +(-1.26795 + 0.732051i) q^{31} +(7.33013 + 1.96410i) q^{32} +(1.73205 - 3.00000i) q^{33} +(7.46410 + 12.9282i) q^{34} +(-1.59808 - 5.69615i) q^{35} +(4.50000 + 2.59808i) q^{36} +(-0.633975 - 0.169873i) q^{37} +(3.73205 - 3.73205i) q^{38} +(-8.83013 - 2.36603i) q^{39} +(0.366025 - 1.09808i) q^{40} +(2.59808 + 1.50000i) q^{41} +(-7.96410 - 3.86603i) q^{42} +(-0.866025 + 3.23205i) q^{43} +(3.00000 - 1.73205i) q^{44} +(3.69615 - 5.59808i) q^{45} +(-3.36603 + 5.83013i) q^{46} +(-7.33013 + 1.96410i) q^{47} +(-3.86603 - 6.69615i) q^{48} +(6.50000 + 2.59808i) q^{49} +(8.96410 + 3.59808i) q^{50} +(3.46410 - 12.9282i) q^{51} +(-6.46410 - 6.46410i) q^{52} +(3.73205 - 1.00000i) q^{53} +(-2.59808 - 9.69615i) q^{54} +(-2.00000 - 4.00000i) q^{55} +(0.767949 + 1.13397i) q^{56} -4.73205 q^{57} +(-5.36603 - 5.36603i) q^{58} +(-7.56218 - 13.0981i) q^{59} +(6.00000 - 3.00000i) q^{60} +(2.53590 + 1.46410i) q^{61} +(2.00000 + 2.00000i) q^{62} +(2.59808 + 7.50000i) q^{63} -5.73205i q^{64} +(-8.83013 + 7.83013i) q^{65} +(-6.46410 - 1.73205i) q^{66} +(6.09808 + 1.63397i) q^{67} +(9.46410 - 9.46410i) q^{68} +(5.83013 - 1.56218i) q^{69} +(-9.83013 + 5.83013i) q^{70} +4.73205 q^{71} +(-0.401924 + 1.50000i) q^{72} +(0.928203 + 3.46410i) q^{73} +1.26795i q^{74} +(-3.40192 - 7.96410i) q^{75} +(-4.09808 - 2.36603i) q^{76} +(5.19615 + 1.00000i) q^{77} +17.6603i q^{78} +(-3.92820 - 2.26795i) q^{79} +(-9.96410 - 0.598076i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(1.50000 - 5.59808i) q^{82} +(-11.3301 - 3.03590i) q^{83} +(-1.50000 + 7.79423i) q^{84} +(-11.4641 - 12.9282i) q^{85} +6.46410 q^{86} +6.80385i q^{87} +(0.732051 + 0.732051i) q^{88} +(7.46410 + 12.9282i) q^{89} +(-12.2942 - 4.09808i) q^{90} +(-1.00000 - 13.9282i) q^{91} +(5.83013 + 1.56218i) q^{92} -2.53590i q^{93} +(7.33013 + 12.6962i) q^{94} +(-3.36603 + 5.09808i) q^{95} +(-9.29423 + 9.29423i) q^{96} +(3.90192 - 14.5622i) q^{97} +(1.59808 - 13.4282i) q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{4} + 4 q^{5} + 6 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^4 + 4 * q^5 + 6 * q^6 + 2 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} - 6 q^{4} + 4 q^{5} + 6 q^{6} + 2 q^{8} - 6 q^{9} + 6 q^{10} - 8 q^{11} + 2 q^{13} - 2 q^{14} - 12 q^{15} - 2 q^{16} - 16 q^{17} - 6 q^{18} + 2 q^{19} - 6 q^{20} + 12 q^{21} + 4 q^{22} + 4 q^{23} - 12 q^{25} + 18 q^{26} + 24 q^{29} + 6 q^{30} - 12 q^{31} + 12 q^{32} + 16 q^{34} + 4 q^{35} + 18 q^{36} - 6 q^{37} + 8 q^{38} - 18 q^{39} - 2 q^{40} - 18 q^{42} + 12 q^{44} - 6 q^{45} - 10 q^{46} - 12 q^{47} - 12 q^{48} + 26 q^{49} + 22 q^{50} - 12 q^{52} + 8 q^{53} - 8 q^{55} + 10 q^{56} - 12 q^{57} - 18 q^{58} - 6 q^{59} + 24 q^{60} + 24 q^{61} + 8 q^{62} - 18 q^{65} - 12 q^{66} + 14 q^{67} + 24 q^{68} + 6 q^{69} - 22 q^{70} + 12 q^{71} - 12 q^{72} - 24 q^{73} - 24 q^{75} - 6 q^{76} + 12 q^{79} - 26 q^{80} - 18 q^{81} + 6 q^{82} - 28 q^{83} - 6 q^{84} - 32 q^{85} + 12 q^{86} - 4 q^{88} + 16 q^{89} - 18 q^{90} - 4 q^{91} + 6 q^{92} + 12 q^{94} - 10 q^{95} - 6 q^{96} + 26 q^{97} - 4 q^{98} + 12 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^4 + 4 * q^5 + 6 * q^6 + 2 * q^8 - 6 * q^9 + 6 * q^10 - 8 * q^11 + 2 * q^13 - 2 * q^14 - 12 * q^15 - 2 * q^16 - 16 * q^17 - 6 * q^18 + 2 * q^19 - 6 * q^20 + 12 * q^21 + 4 * q^22 + 4 * q^23 - 12 * q^25 + 18 * q^26 + 24 * q^29 + 6 * q^30 - 12 * q^31 + 12 * q^32 + 16 * q^34 + 4 * q^35 + 18 * q^36 - 6 * q^37 + 8 * q^38 - 18 * q^39 - 2 * q^40 - 18 * q^42 + 12 * q^44 - 6 * q^45 - 10 * q^46 - 12 * q^47 - 12 * q^48 + 26 * q^49 + 22 * q^50 - 12 * q^52 + 8 * q^53 - 8 * q^55 + 10 * q^56 - 12 * q^57 - 18 * q^58 - 6 * q^59 + 24 * q^60 + 24 * q^61 + 8 * q^62 - 18 * q^65 - 12 * q^66 + 14 * q^67 + 24 * q^68 + 6 * q^69 - 22 * q^70 + 12 * q^71 - 12 * q^72 - 24 * q^73 - 24 * q^75 - 6 * q^76 + 12 * q^79 - 26 * q^80 - 18 * q^81 + 6 * q^82 - 28 * q^83 - 6 * q^84 - 32 * q^85 + 12 * q^86 - 4 * q^88 + 16 * q^89 - 18 * q^90 - 4 * q^91 + 6 * q^92 + 12 * q^94 - 10 * q^95 - 6 * q^96 + 26 * q^97 - 4 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	1.86603i	−0.353553	−	1.31948i	−0.882295	−	0.470696i	$-0.844003\pi$
$2$	−0.500000	−	1.86603i	−0.353553	−	1.31948i	0.528742	−	0.848783i	$-0.322664\pi$
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$4$	−1.50000	+	0.866025i	−0.750000	+	0.433013i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$	3.23205	+	0.866025i	1.31948	+	0.353553i
$7$	−2.59808	−	0.500000i	−0.981981	−	0.188982i
$7$	−2.59808	−	0.500000i	−0.981981	−	0.188982i
$8$	−0.366025	−	0.366025i	−0.129410	−	0.129410i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	3.23205	−	2.86603i	1.02206	−	0.906317i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		−	3.00000i		−	0.866025i
$13$	1.36603	+	5.09808i	0.378867	+	1.41395i	0.847611	+	0.530618i	$0.178040\pi$
$13$	1.36603	+	5.09808i	0.378867	+	1.41395i	−0.468744	+	0.883334i	$0.655293\pi$
$14$	0.366025	+	5.09808i	0.0978244	+	1.36252i
$15$	−3.86603	−	0.232051i	−0.998203	−	0.0599153i
$16$	−2.23205	+	3.86603i	−0.558013	+	0.966506i
$17$	−7.46410	+	2.00000i	−1.81031	+	0.485071i	−0.995509	−	0.0946685i	$-0.969821\pi$
$17$	−7.46410	+	2.00000i	−1.81031	+	0.485071i	−0.814802	+	0.579740i	$0.803154\pi$
$18$	−4.09808	+	4.09808i	−0.965926	+	0.965926i
$19$	1.36603	+	2.36603i	0.313388	+	0.542803i	0.979093	−	0.203411i	$-0.0652027\pi$
$19$	1.36603	+	2.36603i	0.313388	+	0.542803i	−0.665706	+	0.746214i	$0.731869\pi$
$20$	−3.23205	−	2.13397i	−0.722709	−	0.477171i
$21$	3.00000	−	3.46410i	0.654654	−	0.755929i
$22$	1.00000	+	3.73205i	0.213201	+	0.795676i
$23$	−2.46410	−	2.46410i	−0.513801	−	0.513801i	0.401888	−	0.915689i	$-0.368354\pi$
$23$	−2.46410	−	2.46410i	−0.513801	−	0.513801i	−0.915689	+	0.401888i	$0.868354\pi$
$24$	0.866025	−	0.232051i	0.176777	−	0.0473672i
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	8.83013	−	5.09808i	1.73173	−	0.999815i
$27$	5.19615			1.00000
$28$	4.33013	−	1.50000i	0.818317	−	0.283473i
$29$	3.40192	−	1.96410i	0.631721	−	0.364725i	−0.149697	−	0.988732i	$-0.547830\pi$
$29$	3.40192	−	1.96410i	0.631721	−	0.364725i	0.781418	+	0.624007i	$0.214497\pi$
$30$	1.50000	+	7.33013i	0.273861	+	1.33829i
$31$	−1.26795	+	0.732051i	−0.227730	+	0.131480i	−0.609525	−	0.792767i	$-0.708640\pi$
$31$	−1.26795	+	0.732051i	−0.227730	+	0.131480i	0.381794	+	0.924247i	$0.375306\pi$
$32$	7.33013	+	1.96410i	1.29580	+	0.347207i
$33$	1.73205	−	3.00000i	0.301511	−	0.522233i
$34$	7.46410	+	12.9282i	1.28008	+	2.21717i
$35$	−1.59808	−	5.69615i	−0.270124	−	0.962825i
$36$	4.50000	+	2.59808i	0.750000	+	0.433013i
$37$	−0.633975	−	0.169873i	−0.104225	−	0.0279269i	0.206330	−	0.978483i	$-0.433848\pi$
$37$	−0.633975	−	0.169873i	−0.104225	−	0.0279269i	−0.310554	+	0.950556i	$0.600515\pi$
$38$	3.73205	−	3.73205i	0.605419	−	0.605419i
$39$	−8.83013	−	2.36603i	−1.41395	−	0.378867i
$40$	0.366025	−	1.09808i	0.0578737	−	0.173621i
$41$	2.59808	+	1.50000i	0.405751	+	0.234261i	0.688963	−	0.724797i	$-0.258066\pi$
$41$	2.59808	+	1.50000i	0.405751	+	0.234261i	−0.283211	+	0.959058i	$0.591400\pi$
$42$	−7.96410	−	3.86603i	−1.22889	−	0.596541i
$43$	−0.866025	+	3.23205i	−0.132068	+	0.492883i	−0.999993	−	0.00381197i	$-0.998787\pi$
$43$	−0.866025	+	3.23205i	−0.132068	+	0.492883i	0.867925	+	0.496695i	$0.165453\pi$
$44$	3.00000	−	1.73205i	0.452267	−	0.261116i
$45$	3.69615	−	5.59808i	0.550990	−	0.834512i
$46$	−3.36603	+	5.83013i	−0.496293	+	0.859605i
$47$	−7.33013	+	1.96410i	−1.06921	+	0.286494i	−0.750168	−	0.661247i	$-0.770027\pi$
$47$	−7.33013	+	1.96410i	−1.06921	+	0.286494i	−0.319041	+	0.947741i	$0.603361\pi$
$48$	−3.86603	−	6.69615i	−0.558013	−	0.966506i
$49$	6.50000	+	2.59808i	0.928571	+	0.371154i
$50$	8.96410	+	3.59808i	1.26772	+	0.508845i
$51$	3.46410	−	12.9282i	0.485071	−	1.81031i
$52$	−6.46410	−	6.46410i	−0.896410	−	0.896410i
$53$	3.73205	−	1.00000i	0.512637	−	0.137361i	0.00677809	−	0.999977i	$-0.497842\pi$
$53$	3.73205	−	1.00000i	0.512637	−	0.137361i	0.505859	+	0.862616i	$0.331176\pi$
$54$	−2.59808	−	9.69615i	−0.353553	−	1.31948i
$55$	−2.00000	−	4.00000i	−0.269680	−	0.539360i
$56$	0.767949	+	1.13397i	0.102622	+	0.151534i
$57$	−4.73205			−0.626775
$58$	−5.36603	−	5.36603i	−0.704594	−	0.704594i
$59$	−7.56218	−	13.0981i	−0.984512	−	1.70522i	−0.644086	−	0.764953i	$-0.722762\pi$
$59$	−7.56218	−	13.0981i	−0.984512	−	1.70522i	−0.340425	−	0.940272i	$-0.610571\pi$
$60$	6.00000	−	3.00000i	0.774597	−	0.387298i
$61$	2.53590	+	1.46410i	0.324689	+	0.187459i	0.653480	−	0.756943i	$-0.273308\pi$
$61$	2.53590	+	1.46410i	0.324689	+	0.187459i	−0.328792	+	0.944402i	$0.606641\pi$
$62$	2.00000	+	2.00000i	0.254000	+	0.254000i
$63$	2.59808	+	7.50000i	0.327327	+	0.944911i
$64$		−	5.73205i		−	0.716506i
$65$	−8.83013	+	7.83013i	−1.09524	+	0.971208i
$66$	−6.46410	−	1.73205i	−0.795676	−	0.213201i
$67$	6.09808	+	1.63397i	0.744999	+	0.199622i	0.611299	−	0.791400i	$-0.290647\pi$
$67$	6.09808	+	1.63397i	0.744999	+	0.199622i	0.133700	+	0.991022i	$0.457314\pi$
$68$	9.46410	−	9.46410i	1.14769	−	1.14769i
$69$	5.83013	−	1.56218i	0.701865	−	0.188064i
$70$	−9.83013	+	5.83013i	−1.17492	+	0.696833i
$71$	4.73205			0.561591			0.280796	−	0.959768i	$-0.409402\pi$
$71$	4.73205			0.561591			0.280796	+	0.959768i	$0.409402\pi$
$72$	−0.401924	+	1.50000i	−0.0473672	+	0.176777i
$73$	0.928203	+	3.46410i	0.108638	+	0.405442i	0.998732	−	0.0503336i	$-0.0160285\pi$
$73$	0.928203	+	3.46410i	0.108638	+	0.405442i	−0.890094	+	0.455776i	$0.849362\pi$
$74$			1.26795i			0.147396i
$75$	−3.40192	−	7.96410i	−0.392820	−	0.919615i
$76$	−4.09808	−	2.36603i	−0.470082	−	0.271402i
$77$	5.19615	+	1.00000i	0.592157	+	0.113961i
$78$			17.6603i			1.99963i
$79$	−3.92820	−	2.26795i	−0.441957	−	0.255164i	0.262470	−	0.964940i	$-0.415463\pi$
$79$	−3.92820	−	2.26795i	−0.441957	−	0.255164i	−0.704428	+	0.709776i	$0.748796\pi$
$80$	−9.96410	−	0.598076i	−1.11402	−	0.0668670i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	1.50000	−	5.59808i	0.165647	−	0.618204i
$83$	−11.3301	−	3.03590i	−1.24364	−	0.333233i	−0.423765	−	0.905772i	$-0.639292\pi$
$83$	−11.3301	−	3.03590i	−1.24364	−	0.333233i	−0.819878	+	0.572539i	$0.805959\pi$
$84$	−1.50000	+	7.79423i	−0.163663	+	0.850420i
$85$	−11.4641	−	12.9282i	−1.24346	−	1.40226i
$86$	6.46410			0.697042
$87$			6.80385i			0.729449i
$88$	0.732051	+	0.732051i	0.0780369	+	0.0780369i
$89$	7.46410	+	12.9282i	0.791193	+	1.37039i	0.925229	+	0.379410i	$0.123873\pi$
$89$	7.46410	+	12.9282i	0.791193	+	1.37039i	−0.134035	+	0.990977i	$0.542794\pi$
$90$	−12.2942	−	4.09808i	−1.29593	−	0.431975i
$91$	−1.00000	−	13.9282i	−0.104828	−	1.46007i
$92$	5.83013	+	1.56218i	0.607833	+	0.162868i
$93$		−	2.53590i		−	0.262960i
$94$	7.33013	+	12.6962i	0.756045	+	1.30951i
$95$	−3.36603	+	5.09808i	−0.345347	+	0.523052i
$96$	−9.29423	+	9.29423i	−0.948588	+	0.948588i
$97$	3.90192	−	14.5622i	0.396180	−	1.47857i	−0.423580	−	0.905859i	$-0.639227\pi$
$97$	3.90192	−	14.5622i	0.396180	−	1.47857i	0.819760	−	0.572707i	$-0.194107\pi$
$98$	1.59808	−	13.4282i	0.161430	−	1.35645i
$99$	3.00000	+	5.19615i	0.301511	+	0.522233i
$100$	1.03590	−	8.59808i	0.103590	−	0.859808i
$101$			3.73205i			0.371353i	0.982611	+	0.185676i	$0.0594476\pi$
$101$			3.73205i			0.371353i	−0.982611	+	0.185676i	$0.940552\pi$
$102$	−25.8564			−2.56017
$103$	6.36603	−	6.36603i	0.627263	−	0.627263i	−0.320115	−	0.947379i	$-0.603722\pi$
$103$	6.36603	−	6.36603i	0.627263	−	0.627263i	0.947379	+	0.320115i	$0.103722\pi$
$104$	1.36603	−	2.36603i	0.133950	−	0.232008i
$105$	9.92820	+	2.53590i	0.968893	+	0.247478i
$106$	−3.73205	−	6.46410i	−0.362489	−	0.627849i
$107$	11.4282	+	3.06218i	1.10481	+	0.296032i	0.764720	−	0.644362i	$-0.222877\pi$
$107$	11.4282	+	3.06218i	1.10481	+	0.296032i	0.340086	+	0.940394i	$0.389544\pi$
$108$	−7.79423	+	4.50000i	−0.750000	+	0.433013i
$109$	5.42820	+	3.13397i	0.519928	+	0.300180i	0.736905	−	0.675996i	$-0.236286\pi$
$109$	5.42820	+	3.13397i	0.519928	+	0.300180i	−0.216977	+	0.976177i	$0.569620\pi$
$110$	−6.46410	+	5.73205i	−0.616328	+	0.546530i
$111$	0.803848	−	0.803848i	0.0762978	−	0.0762978i
$112$	7.73205	−	8.92820i	0.730610	−	0.843636i
$113$	−9.46410	+	2.53590i	−0.890308	+	0.238557i	−0.674849	−	0.737956i	$-0.735791\pi$
$113$	−9.46410	+	2.53590i	−0.890308	+	0.238557i	−0.215459	+	0.976513i	$0.569125\pi$
$114$	2.36603	+	8.83013i	0.221599	+	0.827017i
$115$	2.46410	−	7.39230i	0.229779	−	0.689336i
$116$	−3.40192	+	5.89230i	−0.315861	+	0.547087i
$117$	11.1962	−	11.1962i	1.03508	−	1.03508i
$118$	−20.6603	+	20.6603i	−1.90193	+	1.90193i
$119$	20.3923	−	1.46410i	1.86936	−	0.134214i
$120$	1.33013	+	1.50000i	0.121423	+	0.136931i
$121$	−7.00000			−0.636364
$122$	1.46410	−	5.46410i	0.132554	−	0.494697i
$123$	−4.50000	+	2.59808i	−0.405751	+	0.234261i
$124$	1.26795	−	2.19615i	0.113865	−	0.197220i
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$	12.6962	−	8.59808i	1.13106	−	0.765978i
$127$	9.63397	−	9.63397i	0.854877	−	0.854877i	−0.135852	−	0.990729i	$-0.543377\pi$
$127$	9.63397	−	9.63397i	0.854877	−	0.854877i	0.990729	+	0.135852i	$0.0433772\pi$
$128$	3.96410	−	1.06218i	0.350380	−	0.0938841i
$129$	−4.09808	−	4.09808i	−0.360815	−	0.360815i
$130$	19.0263	+	12.5622i	1.66872	+	1.10178i
$131$			5.07180i			0.443125i	0.975146	+	0.221562i	$0.0711157\pi$
$131$			5.07180i			0.443125i	−0.975146	+	0.221562i	$0.928884\pi$
$132$			6.00000i			0.522233i
$133$	−2.36603	−	6.83013i	−0.205160	−	0.592247i
$134$		−	12.1962i		−	1.05359i
$135$	5.19615	+	10.3923i	0.447214	+	0.894427i
$136$	3.46410	+	2.00000i	0.297044	+	0.171499i
$137$	1.00000	−	1.00000i	0.0854358	−	0.0854358i	−0.663097	−	0.748533i	$-0.730758\pi$
$137$	1.00000	−	1.00000i	0.0854358	−	0.0854358i	0.748533	+	0.663097i	$0.230758\pi$
$138$	−5.83013	−	10.0981i	−0.496293	−	0.859605i
$139$	−6.29423	+	10.9019i	−0.533870	+	0.924689i	0.465348	+	0.885128i	$0.345929\pi$
$139$	−6.29423	+	10.9019i	−0.533870	+	0.924689i	−0.999217	+	0.0395611i	$0.987404\pi$
$140$	7.33013	+	7.16025i	0.619509	+	0.605152i
$141$	3.40192	−	12.6962i	0.286494	−	1.06921i
$142$	−2.36603	−	8.83013i	−0.198552	−	0.741008i
$143$	−2.73205	−	10.1962i	−0.228466	−	0.852645i
$144$	13.3923			1.11603
$145$	7.33013	+	4.83975i	0.608734	+	0.401919i
$146$	6.00000	−	3.46410i	0.496564	−	0.286691i
$147$	−9.52628	+	7.50000i	−0.785714	+	0.618590i
$148$	1.09808	−	0.294229i	0.0902613	−	0.0241854i
$149$			15.4641i			1.26687i	0.773796	+	0.633434i	$0.218355\pi$
$149$			15.4641i			1.26687i	−0.773796	+	0.633434i	$0.781645\pi$
$150$	−13.1603	+	10.3301i	−1.07453	+	0.843451i
$151$	−17.6603			−1.43717			−0.718586	−	0.695439i	$-0.755210\pi$
$151$	−17.6603			−1.43717			−0.718586	+	0.695439i	$0.755210\pi$
$152$	0.366025	−	1.36603i	0.0296886	−	0.110799i
$153$	16.3923	+	16.3923i	1.32524	+	1.32524i
$154$	−0.732051	−	10.1962i	−0.0589903	−	0.821629i
$155$	−2.73205	−	1.80385i	−0.219444	−	0.144889i
$156$	15.2942	−	4.09808i	1.22452	−	0.328109i
$157$	−2.63397	+	9.83013i	−0.210214	+	0.784530i	0.777583	+	0.628781i	$0.216446\pi$
$157$	−2.63397	+	9.83013i	−0.210214	+	0.784530i	−0.987797	+	0.155749i	$0.950221\pi$
$158$	−2.26795	+	8.46410i	−0.180428	+	0.673368i
$159$	−1.73205	+	6.46410i	−0.137361	+	0.512637i
$160$	3.40192	+	16.6244i	0.268946	+	1.31427i
$161$	5.16987	+	7.63397i	0.407443	+	0.601641i
$162$	16.7942	+	4.50000i	1.31948	+	0.353553i
$163$	−2.49038	+	9.29423i	−0.195062	+	0.727980i	0.797189	+	0.603730i	$0.206319\pi$
$163$	−2.49038	+	9.29423i	−0.195062	+	0.727980i	−0.992251	+	0.124251i	$0.960347\pi$
$164$	−5.19615			−0.405751
$165$	7.73205	+	0.464102i	0.601939	+	0.0361303i
$166$			22.6603i			1.75878i
$167$	−3.36603	+	0.901924i	−0.260471	+	0.0697930i	−0.386691	−	0.922209i	$-0.626382\pi$
$167$	−3.36603	+	0.901924i	−0.260471	+	0.0697930i	0.126220	+	0.992002i	$0.459715\pi$
$168$	−2.36603	+	0.169873i	−0.182543	+	0.0131060i
$169$	−12.8660	+	7.42820i	−0.989694	+	0.571400i
$170$	−18.3923	+	27.8564i	−1.41063	+	2.13649i
$171$	4.09808	−	7.09808i	0.313388	−	0.542803i
$172$	−1.50000	−	5.59808i	−0.114374	−	0.426849i
$173$	5.85641	+	21.8564i	0.445254	+	1.66171i	0.715264	+	0.698854i	$0.246306\pi$
$173$	5.85641	+	21.8564i	0.445254	+	1.66171i	−0.270010	+	0.962858i	$0.587027\pi$
$174$	12.6962	−	3.40192i	0.962493	−	0.257899i
$175$	9.79423	−	8.89230i	0.740374	−	0.672195i
$176$	4.46410	−	7.73205i	0.336494	−	0.582825i
$177$	26.1962			1.96902
$178$	20.3923	−	20.3923i	1.52847	−	1.52847i
$179$	−1.09808	−	0.633975i	−0.0820741	−	0.0473855i	0.458401	−	0.888745i	$-0.348422\pi$
$179$	−1.09808	−	0.633975i	−0.0820741	−	0.0473855i	−0.540475	+	0.841360i	$0.681756\pi$
$180$	−0.696152	+	11.5981i	−0.0518881	+	0.864470i
$181$		−	20.1244i		−	1.49583i	−0.663794	−	0.747916i	$-0.731055\pi$
$181$		−	20.1244i		−	1.49583i	0.663794	−	0.747916i	$-0.268945\pi$
$182$	−25.4904	+	8.83013i	−1.88947	+	0.654533i
$183$	−4.39230	+	2.53590i	−0.324689	+	0.187459i
$184$			1.80385i			0.132981i
$185$	−0.294229	−	1.43782i	−0.0216321	−	0.105711i
$186$	−4.73205	+	1.26795i	−0.346971	+	0.0929705i
$187$	14.9282	−	4.00000i	1.09166	−	0.292509i
$188$	9.29423	−	9.29423i	0.677851	−	0.677851i
$189$	−13.5000	−	2.59808i	−0.981981	−	0.188982i
$190$	11.1962	+	3.73205i	0.812254	+	0.270751i
$191$	4.90192	−	8.49038i	0.354691	−	0.614342i	−0.632374	−	0.774663i	$-0.717919\pi$
$191$	4.90192	−	8.49038i	0.354691	−	0.614342i	0.987065	+	0.160321i	$0.0512528\pi$
$192$	8.59808	+	4.96410i	0.620513	+	0.358253i
$193$	0.0717968	−	0.267949i	0.00516804	−	0.0192874i	−0.963294	−	0.268450i	$-0.913489\pi$
$193$	0.0717968	−	0.267949i	0.00516804	−	0.0192874i	0.968462	+	0.249162i	$0.0801553\pi$
$194$	−29.1244			−2.09101
$195$	−4.09808	−	20.0263i	−0.293469	−	1.43411i
$196$	−12.0000	+	1.73205i	−0.857143	+	0.123718i
$197$	4.00000	−	4.00000i	0.284988	−	0.284988i	−0.550106	−	0.835095i	$-0.685413\pi$
$197$	4.00000	−	4.00000i	0.284988	−	0.284988i	0.835095	+	0.550106i	$0.185413\pi$
$198$	8.19615	−	8.19615i	0.582475	−	0.582475i
$199$	−2.19615	+	3.80385i	−0.155681	+	0.269648i	−0.933307	−	0.359080i	$-0.883091\pi$
$199$	−2.19615	+	3.80385i	−0.155681	+	0.269648i	0.777626	+	0.628727i	$0.216424\pi$
$200$	2.56218	−	0.366025i	0.181173	−	0.0258819i
$201$	−7.73205	+	7.73205i	−0.545377	+	0.545377i
$202$	6.96410	−	1.86603i	0.489992	−	0.131293i
$203$	−9.82051	+	3.40192i	−0.689265	+	0.238768i
$204$	6.00000	+	22.3923i	0.420084	+	1.56777i
$205$	−0.401924	+	6.69615i	−0.0280716	+	0.467680i
$206$	−15.0622	−	8.69615i	−1.04943	−	0.605890i
$207$	−2.70577	+	10.0981i	−0.188064	+	0.701865i
$208$	−22.7583	−	6.09808i	−1.57801	−	0.422826i
$209$	−2.73205	−	4.73205i	−0.188980	−	0.327323i
$210$	−0.232051	−	19.7942i	−0.0160130	−	1.36593i
$211$	−6.53590	+	11.3205i	−0.449950	+	0.779336i	−0.998382	−	0.0568590i	$-0.981891\pi$
$211$	−6.53590	+	11.3205i	−0.449950	+	0.779336i	0.548432	+	0.836195i	$0.315225\pi$
$212$	−4.73205	+	4.73205i	−0.324999	+	0.324999i
$213$	−4.09808	+	7.09808i	−0.280796	+	0.486352i
$214$		−	22.8564i		−	1.56243i
$215$	−7.33013	+	1.50000i	−0.499911	+	0.102299i
$216$	−1.90192	−	1.90192i	−0.129410	−	0.129410i
$217$	3.66025	−	1.26795i	0.248474	−	0.0860740i
$218$	3.13397	−	11.6962i	0.212260	−	0.792163i
$219$	−6.00000	−	1.60770i	−0.405442	−	0.108638i
$220$	6.46410	+	4.26795i	0.435810	+	0.287745i
$221$	−20.3923	−	35.3205i	−1.37173	−	2.37591i
$222$	−1.90192	−	1.09808i	−0.127649	−	0.0736980i
$223$	7.33013	+	1.96410i	0.490862	+	0.131526i	0.495756	−	0.868462i	$-0.334891\pi$
$223$	7.33013	+	1.96410i	0.490862	+	0.131526i	−0.00489404	+	0.999988i	$0.501558\pi$
$224$	−18.0622	−	8.76795i	−1.20683	−	0.585833i
$225$	14.8923	+	1.79423i	0.992820	+	0.119615i
$226$	9.46410	+	16.3923i	0.629543	+	1.09040i
$227$	13.5885	+	13.5885i	0.901898	+	0.901898i	0.995600	−	0.0937026i	$-0.0298703\pi$
$227$	13.5885	+	13.5885i	0.901898	+	0.901898i	−0.0937026	+	0.995600i	$0.529870\pi$
$228$	7.09808	−	4.09808i	0.470082	−	0.271402i
$229$	−5.33975			−0.352860			−0.176430	−	0.984313i	$-0.556455\pi$
$229$	−5.33975			−0.352860			−0.176430	+	0.984313i	$0.556455\pi$
$230$	−15.0263	−	0.901924i	−0.990804	−	0.0594711i
$231$	−6.00000	+	6.92820i	−0.394771	+	0.455842i
$232$	−1.96410	−	0.526279i	−0.128950	−	0.0345519i
$233$	−3.33975	+	12.4641i	−0.218794	+	0.816550i	0.766002	+	0.642838i	$0.222243\pi$
$233$	−3.33975	+	12.4641i	−0.218794	+	0.816550i	−0.984796	+	0.173713i	$0.944424\pi$
$234$	−26.4904	−	15.2942i	−1.73173	−	0.999815i
$235$	−11.2583	−	12.6962i	−0.734412	−	0.828206i
$236$	22.6865	+	13.0981i	1.47677	+	0.852612i
$237$	6.80385	−	3.92820i	0.441957	−	0.255164i
$238$	−12.9282	−	37.3205i	−0.838011	−	2.41913i
$239$	1.73205	+	1.00000i	0.112037	+	0.0646846i	0.554971	−	0.831869i	$-0.312729\pi$
$239$	1.73205	+	1.00000i	0.112037	+	0.0646846i	−0.442934	+	0.896554i	$0.646063\pi$
$240$	9.52628	−	14.4282i	0.614919	−	0.931337i
$241$			22.4641i			1.44704i	0.690303	+	0.723520i	$0.257477\pi$
$241$			22.4641i			1.44704i	−0.690303	+	0.723520i	$0.742523\pi$
$242$	3.50000	+	13.0622i	0.224989	+	0.839669i
$243$	−7.79423	−	13.5000i	−0.500000	−	0.866025i
$244$	−5.07180			−0.324689
$245$	1.30385	+	15.5981i	0.0832998	+	0.996525i
$246$	7.09808	+	7.09808i	0.452557	+	0.452557i
$247$	−10.1962	+	10.1962i	−0.648766	+	0.648766i
$248$	0.732051	+	0.196152i	0.0464853	+	0.0124557i
$249$	14.3660	−	14.3660i	0.910410	−	0.910410i
$250$	1.76795	+	21.5263i	0.111815	+	1.36144i
$251$			3.66025i			0.231033i	0.993306	+	0.115517i	$0.0368523\pi$
$251$			3.66025i			0.231033i	−0.993306	+	0.115517i	$0.963148\pi$
$252$	−10.3923	−	9.00000i	−0.654654	−	0.566947i
$253$	4.92820	+	4.92820i	0.309833	+	0.309833i
$254$	−22.7942	−	13.1603i	−1.43024	−	0.825748i
$255$	29.3205	−	6.00000i	1.83612	−	0.375735i
$256$	−9.69615	−	16.7942i	−0.606010	−	1.04964i
$257$	0.196152	+	0.196152i	0.0122357	+	0.0122357i	0.713198	−	0.700962i	$-0.247246\pi$
$257$	0.196152	+	0.196152i	0.0122357	+	0.0122357i	−0.700962	+	0.713198i	$0.747246\pi$
$258$	−5.59808	+	9.69615i	−0.348521	+	0.603656i
$259$	1.56218	+	0.758330i	0.0970690	+	0.0471203i
$260$	6.46410	−	19.3923i	0.400887	−	1.20266i
$261$	−10.2058	−	5.89230i	−0.631721	−	0.364725i
$262$	9.46410	−	2.53590i	0.584694	−	0.156668i
$263$	3.90192	+	3.90192i	0.240603	+	0.240603i	0.817100	−	0.576497i	$-0.195581\pi$
$263$	3.90192	+	3.90192i	0.240603	+	0.240603i	−0.576497	+	0.817100i	$0.695581\pi$
$264$	−1.73205	+	0.464102i	−0.106600	+	0.0285635i
$265$	5.73205	+	6.46410i	0.352117	+	0.397087i
$266$	−11.5622	+	7.83013i	−0.708923	+	0.480096i
$267$	−25.8564			−1.58239
$268$	−10.5622	+	2.83013i	−0.645188	+	0.172878i
$269$	−14.1962	+	24.5885i	−0.865555	+	1.49918i	0.000940662		1.00000i	$0.499701\pi$
$269$	−14.1962	+	24.5885i	−0.865555	+	1.49918i	−0.866495	+	0.499185i	$0.833633\pi$
$270$	16.7942	−	14.8923i	1.02206	−	0.906317i
$271$	−28.2224	+	16.2942i	−1.71439	+	0.989804i	−0.785977	+	0.618256i	$0.787840\pi$
$271$	−28.2224	+	16.2942i	−1.71439	+	0.989804i	−0.928414	+	0.371548i	$0.878827\pi$
$272$	8.92820	−	33.3205i	0.541352	−	2.02035i
$273$	21.7583	+	10.5622i	1.31687	+	0.639252i
$274$	−2.36603	−	1.36603i	−0.142937	−	0.0825246i
$275$	6.00000	−	8.00000i	0.361814	−	0.482418i
$276$	−7.39230	+	7.39230i	−0.444964	+	0.444964i
$277$	−8.19615	+	8.19615i	−0.492459	+	0.492459i	−0.909080	−	0.416621i	$-0.863214\pi$
$277$	−8.19615	+	8.19615i	−0.492459	+	0.492459i	0.416621	+	0.909080i	$0.363214\pi$
$278$	23.4904	+	6.29423i	1.40886	+	0.377503i
$279$	3.80385	+	2.19615i	0.227730	+	0.131480i
$280$	−1.50000	+	2.66987i	−0.0896421	+	0.159555i
$281$	−11.1340	−	19.2846i	−0.664197	−	1.15042i	−0.979502	−	0.201433i	$-0.935440\pi$
$281$	−11.1340	−	19.2846i	−0.664197	−	1.15042i	0.315305	−	0.948990i	$-0.397893\pi$
$282$	−25.3923			−1.51209
$283$	13.1603	+	3.52628i	0.782296	+	0.209616i	0.627797	−	0.778377i	$-0.283957\pi$
$283$	13.1603	+	3.52628i	0.782296	+	0.209616i	0.154499	+	0.987993i	$0.450624\pi$
$284$	−7.09808	+	4.09808i	−0.421193	+	0.243176i
$285$	−4.73205	−	9.46410i	−0.280302	−	0.560605i
$286$	−17.6603	+	10.1962i	−1.04427	+	0.602911i
$287$	−6.00000	−	5.19615i	−0.354169	−	0.306719i
$288$	−5.89230	−	21.9904i	−0.347207	−	1.29580i
$289$	36.9904	−	21.3564i	2.17590	−	1.25626i
$290$	5.36603	−	16.0981i	0.315104	−	0.945312i
$291$	18.4641	+	18.4641i	1.08238	+	1.08238i
$292$	−4.39230	−	4.39230i	−0.257040	−	0.257040i
$293$	−1.80385	−	6.73205i	−0.105382	−	0.393291i	0.893006	−	0.450044i	$-0.148592\pi$
$293$	−1.80385	−	6.73205i	−0.105382	−	0.393291i	−0.998388	+	0.0567535i	$0.981925\pi$
$294$	18.7583	+	14.0263i	1.09401	+	0.818029i
$295$	18.6340	−	28.2224i	1.08491	−	1.64317i
$296$	0.169873	+	0.294229i	0.00987367	+	0.0171017i
$297$	−10.3923			−0.603023
$298$	28.8564	−	7.73205i	1.67161	−	0.447906i
$299$	9.19615	−	15.9282i	0.531827	−	0.921152i
$300$	12.0000	+	9.00000i	0.692820	+	0.519615i
$301$	3.86603	−	7.96410i	0.222834	−	0.459043i
$302$	8.83013	+	32.9545i	0.508117	+	1.89632i
$303$	−5.59808	−	3.23205i	−0.321601	−	0.185676i
$304$	−12.1962			−0.699497
$305$	−0.392305	+	6.53590i	−0.0224633	+	0.374244i
$306$	22.3923	−	38.7846i	1.28008	−	2.21717i
$307$	5.36603	+	5.36603i	0.306255	+	0.306255i	0.843455	−	0.537200i	$-0.180518\pi$
$307$	5.36603	+	5.36603i	0.306255	+	0.306255i	−0.537200	+	0.843455i	$0.680518\pi$
$308$	−8.66025	+	3.00000i	−0.493464	+	0.170941i
$309$	4.03590	+	15.0622i	0.229594	+	0.856857i
$310$	−2.00000	+	6.00000i	−0.113592	+	0.340777i
$311$	−6.16987	+	3.56218i	−0.349861	+	0.201993i	−0.664624	−	0.747178i	$-0.731408\pi$
$311$	−6.16987	+	3.56218i	−0.349861	+	0.201993i	0.314763	+	0.949170i	$0.398075\pi$
$312$	2.36603	+	4.09808i	0.133950	+	0.232008i
$313$	−0.588457	−	2.19615i	−0.0332616	−	0.124134i	0.947299	−	0.320351i	$-0.103801\pi$
$313$	−0.588457	−	2.19615i	−0.0332616	−	0.124134i	−0.980560	+	0.196217i	$0.937134\pi$
$314$	19.6603			1.10949
$315$	−12.4019	+	12.6962i	−0.698769	+	0.715347i
$316$	7.85641			0.441957
$317$	3.09808	+	11.5622i	0.174005	+	0.649397i	0.996719	+	0.0809406i	$0.0257924\pi$
$317$	3.09808	+	11.5622i	0.174005	+	0.649397i	−0.822714	+	0.568456i	$0.807541\pi$
$318$	12.9282			0.724978
$319$	−6.80385	+	3.92820i	−0.380942	+	0.219937i
$320$	11.4641	−	5.73205i	0.640863	−	0.320431i
$321$	−14.4904	+	14.4904i	−0.808774	+	0.808774i
$322$	11.6603	−	13.4641i	0.649801	−	0.750325i
$323$	−14.9282	−	14.9282i	−0.830627	−	0.830627i
$324$		−	15.5885i		−	0.866025i
$325$	−24.4904	−	9.83013i	−1.35848	−	0.545277i
$326$	18.5885			1.02952
$327$	−9.40192	+	5.42820i	−0.519928	+	0.300180i
$328$	−0.401924	−	1.50000i	−0.0221925	−	0.0828236i
$329$	20.0263	−	1.43782i	1.10408	−	0.0792697i
$330$	−3.00000	−	14.6603i	−0.165145	−	0.807020i
$331$	3.00000	−	5.19615i	0.164895	−	0.285606i	−0.771723	−	0.635959i	$-0.780605\pi$
$331$	3.00000	−	5.19615i	0.164895	−	0.285606i	0.936618	+	0.350352i	$0.113938\pi$
$332$	19.6244	−	5.25833i	1.07703	−	0.288588i
$333$	0.509619	+	1.90192i	0.0279269	+	0.104225i
$334$	3.36603	+	5.83013i	0.184181	+	0.319010i
$335$	2.83013	+	13.8301i	0.154626	+	0.755621i
$336$	6.69615	+	19.3301i	0.365305	+	1.05454i
$337$	1.97372	+	7.36603i	0.107515	+	0.401253i	0.998618	−	0.0525482i	$-0.0167343\pi$
$337$	1.97372	+	7.36603i	0.107515	+	0.401253i	−0.891103	+	0.453801i	$0.850068\pi$
$338$	20.2942	+	20.2942i	1.10386	+	1.10386i
$339$	4.39230	−	16.3923i	0.238557	−	0.890308i
$340$	28.3923	+	9.46410i	1.53979	+	0.513263i
$341$	2.53590	−	1.46410i	0.137327	−	0.0792855i
$342$	−15.2942	−	4.09808i	−0.827017	−	0.221599i
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$	1.50000	−	0.866025i	0.0808746	−	0.0466930i
$345$	8.95448	+	10.0981i	0.482093	+	0.543662i
$346$	37.8564	−	21.8564i	2.03517	−	1.17501i
$347$	−9.06218	−	2.42820i	−0.486483	−	0.130353i	0.00723662	−	0.999974i	$-0.497696\pi$
$347$	−9.06218	−	2.42820i	−0.486483	−	0.130353i	−0.493720	+	0.869621i	$0.664363\pi$
$348$	−5.89230	−	10.2058i	−0.315861	−	0.547087i
$349$	−5.00000	−	8.66025i	−0.267644	−	0.463573i	0.700609	−	0.713545i	$-0.252912\pi$
$349$	−5.00000	−	8.66025i	−0.267644	−	0.463573i	−0.968253	+	0.249973i	$0.919578\pi$
$350$	−21.4904	−	13.8301i	−1.14871	−	0.739251i
$351$	7.09808	+	26.4904i	0.378867	+	1.41395i
$352$	−14.6603	−	3.92820i	−0.781394	−	0.209374i
$353$	12.4641	−	12.4641i	0.663397	−	0.663397i	−0.292782	−	0.956179i	$-0.594581\pi$
$353$	12.4641	−	12.4641i	0.663397	−	0.663397i	0.956179	+	0.292782i	$0.0945810\pi$
$354$	−13.0981	−	48.8827i	−0.696155	−	2.59809i
$355$	4.73205	+	9.46410i	0.251151	+	0.502302i
$356$	−22.3923	−	12.9282i	−1.18679	−	0.685193i
$357$	−15.4641	+	31.8564i	−0.818447	+	1.68602i
$358$	−0.633975	+	2.36603i	−0.0335066	+	0.125048i
$359$	−9.46410	+	5.46410i	−0.499496	+	0.288384i	−0.728505	−	0.685040i	$-0.759785\pi$
$359$	−9.46410	+	5.46410i	−0.499496	+	0.288384i	0.229009	+	0.973424i	$0.426451\pi$
$360$	−3.40192	+	0.696152i	−0.179297	+	0.0366905i
$361$	5.76795	−	9.99038i	0.303576	−	0.525810i
$362$	−37.5526	+	10.0622i	−1.97372	+	0.528856i
$363$	6.06218	−	10.5000i	0.318182	−	0.551107i
$364$	13.5622	+	20.0263i	0.710851	+	1.04966i
$365$	−6.00000	+	5.32051i	−0.314054	+	0.278488i
$366$	6.92820	+	6.92820i	0.362143	+	0.362143i
$367$	−3.90192	−	3.90192i	−0.203679	−	0.203679i	0.597895	−	0.801574i	$-0.296004\pi$
$367$	−3.90192	−	3.90192i	−0.203679	−	0.203679i	−0.801574	+	0.597895i	$0.796004\pi$
$368$	15.0263	−	4.02628i	0.783299	−	0.209884i
$369$		−	9.00000i		−	0.468521i
$370$	−2.53590	+	1.26795i	−0.131835	+	0.0659175i
$371$	−10.1962	+	0.732051i	−0.529358	+	0.0380062i
$372$	2.19615	+	3.80385i	0.113865	+	0.197220i
$373$	−5.53590	−	5.53590i	−0.286638	−	0.286638i	0.549111	−	0.835749i	$-0.314966\pi$
$373$	−5.53590	−	5.53590i	−0.286638	−	0.286638i	−0.835749	+	0.549111i	$0.814966\pi$
$374$	−14.9282	−	25.8564i	−0.771919	−	1.33700i
$375$	12.5263	−	14.7679i	0.646854	−	0.762614i
$376$	3.40192	+	1.96410i	0.175441	+	0.101291i
$377$	14.6603	+	14.6603i	0.755041	+	0.755041i
$378$	1.90192	+	26.4904i	0.0978244	+	1.36252i
$379$			17.5167i			0.899770i	0.893086	+	0.449885i	$0.148535\pi$
$379$			17.5167i			0.899770i	−0.893086	+	0.449885i	$0.851465\pi$
$380$	0.633975	−	10.5622i	0.0325222	−	0.541828i
$381$	6.10770	+	22.7942i	0.312907	+	1.16778i
$382$	−18.2942	−	4.90192i	−0.936014	−	0.250804i
$383$	7.75833	−	7.75833i	0.396432	−	0.396432i	−0.480540	−	0.876973i	$-0.659559\pi$
$383$	7.75833	−	7.75833i	0.396432	−	0.396432i	0.876973	+	0.480540i	$0.159559\pi$
$384$	−1.83975	+	6.86603i	−0.0938841	+	0.350380i
$385$	3.19615	+	11.3923i	0.162891	+	0.580606i
$386$	−0.535898			−0.0272765
$387$	9.69615	−	2.59808i	0.492883	−	0.132068i
$388$	6.75833	+	25.2224i	0.343102	+	1.28047i
$389$			9.05256i			0.458983i	0.973311	+	0.229491i	$0.0737063\pi$
$389$			9.05256i			0.458983i	−0.973311	+	0.229491i	$0.926294\pi$
$390$	−35.3205	+	17.6603i	−1.78852	+	0.894262i
$391$	23.3205	+	13.4641i	1.17937	+	0.680909i
$392$	−1.42820	−	3.33013i	−0.0721352	−	0.168197i
$393$	−7.60770	−	4.39230i	−0.383757	−	0.221562i
$394$	−9.46410	−	5.46410i	−0.476795	−	0.275277i
$395$	0.607695	−	10.1244i	0.0305765	−	0.509412i
$396$	−9.00000	−	5.19615i	−0.452267	−	0.261116i
$397$	7.85641	−	29.3205i	0.394302	−	1.47155i	−0.428664	−	0.903464i	$-0.641016\pi$
$397$	7.85641	−	29.3205i	0.394302	−	1.47155i	0.822966	−	0.568090i	$-0.192318\pi$
$398$	8.19615	+	2.19615i	0.410836	+	0.110083i
$399$	12.2942	+	2.36603i	0.615481	+	0.118449i
$400$	−8.76795	−	20.5263i	−0.438397	−	1.02631i
$401$	−9.39230			−0.469029			−0.234515	−	0.972113i	$-0.575350\pi$
$401$	−9.39230			−0.469029			−0.234515	+	0.972113i	$0.575350\pi$
$402$	18.2942	+	10.5622i	0.912433	+	0.526794i
$403$	−5.46410	−	5.46410i	−0.272186	−	0.272186i
$404$	−3.23205	−	5.59808i	−0.160801	−	0.278515i
$405$	−20.0885	−	1.20577i	−0.998203	−	0.0599153i
$406$	11.2583	+	16.6244i	0.558742	+	0.825053i
$407$	1.26795	+	0.339746i	0.0628499	+	0.0168406i
$408$	−6.00000	+	3.46410i	−0.297044	+	0.171499i
$409$	−11.1603	−	19.3301i	−0.551839	−	0.955813i	−0.998142	−	0.0609313i	$-0.980593\pi$
$409$	−11.1603	−	19.3301i	−0.551839	−	0.955813i	0.446303	−	0.894882i	$-0.352740\pi$
$410$	12.6962	−	2.59808i	0.627018	−	0.128310i
$411$	0.633975	+	2.36603i	0.0312717	+	0.116707i
$412$	−4.03590	+	15.0622i	−0.198834	+	0.742060i
$413$	13.0981	+	37.8109i	0.644514	+	1.86055i
$414$	20.1962			0.992587
$415$	−5.25833	−	25.6962i	−0.258121	−	1.26137i
$416$			40.0526i			1.96374i
$417$	−10.9019	−	18.8827i	−0.533870	−	0.924689i
$418$	−7.46410	+	7.46410i	−0.365081	+	0.365081i
$419$	1.16987	−	2.02628i	0.0571520	−	0.0989902i	−0.836034	−	0.548678i	$-0.815131\pi$
$419$	1.16987	−	2.02628i	0.0571520	−	0.0989902i	0.893186	+	0.449688i	$0.148465\pi$
$420$	−17.0885	+	4.79423i	−0.833831	+	0.233934i
$421$	−2.40192	−	4.16025i	−0.117063	−	0.202758i	0.801540	−	0.597941i	$-0.204014\pi$
$421$	−2.40192	−	4.16025i	−0.117063	−	0.202758i	−0.918602	+	0.395183i	$0.870681\pi$
$422$	24.3923	+	6.53590i	1.18740	+	0.318163i
$423$	16.0981	+	16.0981i	0.782715	+	0.782715i
$424$	−1.73205	−	1.00000i	−0.0841158	−	0.0485643i
$425$	14.3923	−	35.8564i	0.698129	−	1.73929i
$426$	15.2942	+	4.09808i	0.741008	+	0.198552i
$427$	−5.85641	−	5.07180i	−0.283411	−	0.245441i
$428$	−19.7942	+	5.30385i	−0.956790	+	0.256371i
$429$	17.6603	+	4.73205i	0.852645	+	0.228466i
$430$	6.46410	+	12.9282i	0.311727	+	0.623453i
$431$	−10.2942	+	17.8301i	−0.495856	+	0.858847i	−0.999989	−	0.00477901i	$-0.998479\pi$
$431$	−10.2942	+	17.8301i	−0.495856	+	0.858847i	0.504133	+	0.863626i	$0.331812\pi$
$432$	−11.5981	+	20.0885i	−0.558013	+	0.966506i
$433$	0.124356	−	0.124356i	0.00597615	−	0.00597615i	−0.704112	−	0.710089i	$-0.748655\pi$
$433$	0.124356	−	0.124356i	0.00597615	−	0.00597615i	0.710089	+	0.704112i	$0.248655\pi$
$434$	−4.19615	−	6.19615i	−0.201422	−	0.297425i
$435$	−13.6077	+	6.80385i	−0.652439	+	0.326220i
$436$	−10.8564			−0.519928
$437$	2.46410	−	9.19615i	0.117874	−	0.439912i
$438$			12.0000i			0.573382i
$439$	−17.9282	+	31.0526i	−0.855666	+	1.48206i	0.0203589	+	0.999793i	$0.493519\pi$
$439$	−17.9282	+	31.0526i	−0.855666	+	1.48206i	−0.876025	+	0.482265i	$0.839814\pi$
$440$	−0.732051	+	2.19615i	−0.0348992	+	0.104697i
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$	−55.7128	+	55.7128i	−2.64999	+	2.64999i
$443$	−11.7942	+	3.16025i	−0.560361	+	0.150148i	−0.527872	−	0.849324i	$-0.677010\pi$
$443$	−11.7942	+	3.16025i	−0.560361	+	0.150148i	−0.0324887	+	0.999472i	$0.510343\pi$
$444$	−0.509619	+	1.90192i	−0.0241854	+	0.0902613i
$445$	−18.3923	+	27.8564i	−0.871879	+	1.32052i
$446$		−	14.6603i		−	0.694183i
$447$	−23.1962	−	13.3923i	−1.09714	−	0.633434i
$448$	−2.86603	+	14.8923i	−0.135407	+	0.703595i
$449$			7.33975i			0.346384i	0.984888	+	0.173192i	$0.0554081\pi$
$449$			7.33975i			0.346384i	−0.984888	+	0.173192i	$0.944592\pi$
$450$	−4.09808	−	28.6865i	−0.193185	−	1.35230i
$451$	−5.19615	−	3.00000i	−0.244677	−	0.141264i
$452$	12.0000	−	12.0000i	0.564433	−	0.564433i
$453$	15.2942	−	26.4904i	0.718586	−	1.24463i
$454$	18.5622	−	32.1506i	0.871166	−	1.50890i
$455$	26.8564	−	15.9282i	1.25905	−	0.746726i
$456$	1.73205	+	1.73205i	0.0811107	+	0.0811107i
$457$	−8.43782	−	31.4904i	−0.394705	−	1.47306i	−0.822283	−	0.569079i	$-0.807300\pi$
$457$	−8.43782	−	31.4904i	−0.394705	−	1.47306i	0.427578	−	0.903979i	$-0.359367\pi$
$458$	2.66987	+	9.96410i	0.124755	+	0.465592i
$459$	−38.7846	+	10.3923i	−1.81031	+	0.485071i
$460$	2.70577	+	13.2224i	0.126157	+	0.616499i
$461$	20.7679	−	11.9904i	0.967260	−	0.558448i	0.0688601	−	0.997626i	$-0.478064\pi$
$461$	20.7679	−	11.9904i	0.967260	−	0.558448i	0.898400	+	0.439179i	$0.144730\pi$
$462$	15.9282	+	7.73205i	0.741047	+	0.359728i
$463$	−14.3301	+	3.83975i	−0.665977	+	0.178448i	−0.575942	−	0.817490i	$-0.695365\pi$
$463$	−14.3301	+	3.83975i	−0.665977	+	0.178448i	−0.0900353	+	0.995939i	$0.528698\pi$
$464$			17.5359i			0.814084i
$465$	5.07180	−	2.53590i	0.235199	−	0.117599i
$466$	24.9282			1.15478
$467$	−0.669873	+	2.50000i	−0.0309980	+	0.115686i	−0.979691	−	0.200511i	$-0.935740\pi$
$467$	−0.669873	+	2.50000i	−0.0309980	+	0.115686i	0.948693	+	0.316198i	$0.102406\pi$
$468$	−7.09808	+	26.4904i	−0.328109	+	1.22452i
$469$	−15.0263	−	7.29423i	−0.693849	−	0.336816i
$470$	−18.0622	+	27.3564i	−0.833146	+	1.26186i
$471$	−12.4641	−	12.4641i	−0.574315	−	0.574315i
$472$	−2.02628	+	7.56218i	−0.0932671	+	0.348077i
$473$	1.73205	−	6.46410i	0.0796398	−	0.297220i
$474$	−10.7321	−	10.7321i	−0.492939	−	0.492939i
$475$	−13.5622	−	1.63397i	−0.622275	−	0.0749719i
$476$	−29.3205	+	19.8564i	−1.34390	+	0.910117i
$477$	−8.19615	−	8.19615i	−0.375276	−	0.375276i
$478$	1.00000	−	3.73205i	0.0457389	−	0.170700i
$479$	17.2679			0.788993			0.394496	−	0.918897i	$-0.370919\pi$
$479$	17.2679			0.788993			0.394496	+	0.918897i	$0.370919\pi$
$480$	−27.8827	−	9.29423i	−1.27266	−	0.424222i
$481$		−	3.46410i		−	0.157949i
$482$	41.9186	−	11.2321i	1.90934	−	0.511606i
$483$	−15.9282	+	1.14359i	−0.724758	+	0.0520353i
$484$	10.5000	−	6.06218i	0.477273	−	0.275554i
$485$	33.0263	−	6.75833i	1.49965	−	0.306880i
$486$	−21.2942	+	21.2942i	−0.965926	+	0.965926i
$487$	7.97372	+	29.7583i	0.361324	+	1.34848i	0.872337	+	0.488906i	$0.162604\pi$
$487$	7.97372	+	29.7583i	0.361324	+	1.34848i	−0.511013	+	0.859573i	$0.670730\pi$
$488$	−0.392305	−	1.46410i	−0.0177588	−	0.0662768i
$489$	−11.7846	−	11.7846i	−0.532918	−	0.532918i
$490$	28.4545	−	10.2321i	1.28544	−	0.462237i
$491$	8.29423	−	14.3660i	0.374313	−	0.648330i	−0.615911	−	0.787816i	$-0.711212\pi$
$491$	8.29423	−	14.3660i	0.374313	−	0.648330i	0.990224	+	0.139486i	$0.0445451\pi$
$492$	4.50000	−	7.79423i	0.202876	−	0.351391i
$493$	−21.4641	+	21.4641i	−0.966695	+	0.966695i
$494$	24.1244	+	13.9282i	1.08541	+	0.626659i
$495$	−7.39230	+	11.1962i	−0.332259	+	0.503230i
$496$		−	6.53590i		−	0.293471i
$497$	−12.2942	−	2.36603i	−0.551472	−	0.106131i
$498$	−33.9904	−	19.6244i	−1.52315	−	0.879388i
$499$		−	17.6077i		−	0.788229i	−0.919061	−	0.394114i	$-0.871051\pi$
$499$		−	17.6077i		−	0.788229i	0.919061	−	0.394114i	$-0.128949\pi$
$500$	18.2321	−	6.52628i	0.815362	−	0.291864i
$501$	1.56218	−	5.83013i	0.0697930	−	0.260471i
$502$	6.83013	−	1.83013i	0.304843	−	0.0816826i
$503$	−4.36603	+	4.36603i	−0.194671	+	0.194671i	−0.797711	−	0.603040i	$-0.793956\pi$
$503$	−4.36603	+	4.36603i	−0.194671	+	0.194671i	0.603040	+	0.797711i	$0.293956\pi$
$504$	1.79423	−	3.69615i	0.0799213	−	0.164640i
$505$	−7.46410	+	3.73205i	−0.332148	+	0.166074i
$506$	6.73205	−	11.6603i	0.299276	−	0.518362i
$507$		−	25.7321i		−	1.14280i
$508$	−6.10770	+	22.7942i	−0.270985	+	1.01133i
$509$	32.9090			1.45866			0.729332	−	0.684160i	$-0.239831\pi$
$509$	32.9090			1.45866			0.729332	+	0.684160i	$0.239831\pi$
$510$	−25.8564	−	51.7128i	−1.14494	−	2.28988i
$511$	−0.679492	−	9.46410i	−0.0300590	−	0.418667i
$512$	−20.6865	+	20.6865i	−0.914224	+	0.914224i
$513$	7.09808	+	12.2942i	0.313388	+	0.542803i
$514$	0.267949	−	0.464102i	0.0118187	−	0.0204706i
$515$	19.0981	+	6.36603i	0.841562	+	0.280521i
$516$	9.69615	+	2.59808i	0.426849	+	0.114374i
$517$	14.6603	−	3.92820i	0.644757	−	0.172762i
$518$	0.633975	−	3.29423i	0.0278552	−	0.144740i
$519$	−37.8564	−	10.1436i	−1.66171	−	0.445254i
$520$	6.09808	+	0.366025i	0.267418	+	0.0160513i
$521$	−6.35641	−	3.66987i	−0.278479	−	0.160780i	0.354256	−	0.935149i	$-0.384734\pi$
$521$	−6.35641	−	3.66987i	−0.278479	−	0.160780i	−0.632735	+	0.774369i	$0.718068\pi$
$522$	−5.89230	+	21.9904i	−0.257899	+	0.962493i
$523$	23.2583	+	6.23205i	1.01702	+	0.272509i	0.728558	−	0.684984i	$-0.240191\pi$
$523$	23.2583	+	6.23205i	1.01702	+	0.272509i	0.288458	+	0.957493i	$0.406858\pi$
$524$	−4.39230	−	7.60770i	−0.191879	−	0.332344i
$525$	4.85641	+	22.3923i	0.211951	+	0.977280i
$526$	5.33013	−	9.23205i	0.232405	−	0.402537i
$527$	8.00000	−	8.00000i	0.348485	−	0.348485i
$528$	7.73205	+	13.3923i	0.336494	+	0.582825i
$529$		−	10.8564i		−	0.472018i
$530$	9.19615	−	13.9282i	0.399455	−	0.605002i
$531$	−22.6865	+	39.2942i	−0.984512	+	1.70522i
$532$	9.46410	+	8.19615i	0.410321	+	0.355348i
$533$	−4.09808	+	15.2942i	−0.177507	+	0.662467i
$534$	12.9282	+	48.2487i	0.559458	+	2.08793i
$535$	5.30385	+	25.9186i	0.229305	+	1.12056i
$536$	−1.63397	−	2.83013i	−0.0705770	−	0.122243i
$537$	1.90192	−	1.09808i	0.0820741	−	0.0473855i
$538$	52.9808	+	14.1962i	2.28416	+	0.612040i
$539$	−13.0000	−	5.19615i	−0.559950	−	0.223814i
$540$	−16.7942	−	11.0885i	−0.722709	−	0.477171i
$541$	3.46410	+	6.00000i	0.148933	+	0.257960i	0.930834	−	0.365444i	$-0.119083\pi$
$541$	3.46410	+	6.00000i	0.148933	+	0.257960i	−0.781900	+	0.623404i	$0.785749\pi$
$542$	44.5167	+	44.5167i	1.91215	+	1.91215i
$543$	30.1865	+	17.4282i	1.29543	+	0.747916i
$544$	−58.6410			−2.51421
$545$	−0.839746	+	13.9904i	−0.0359708	+	0.599282i
$546$	8.83013	−	45.8827i	0.377895	−	1.96360i
$547$	38.8205	+	10.4019i	1.65985	+	0.444754i	0.962345	−	0.271831i	$-0.0876291\pi$
$547$	38.8205	+	10.4019i	1.65985	+	0.444754i	0.697500	+	0.716585i	$0.254296\pi$
$548$	−0.633975	+	2.36603i	−0.0270821	+	0.101072i
$549$		−	8.78461i		−	0.374918i
$550$	−17.9282	−	7.19615i	−0.764461	−	0.306845i
$551$	9.29423	+	5.36603i	0.395947	+	0.228600i
$552$	−2.70577	−	1.56218i	−0.115165	−	0.0664907i
$553$	9.07180	+	7.85641i	0.385772	+	0.334088i
$554$	19.3923	+	11.1962i	0.823900	+	0.475679i
$555$	2.41154	+	0.803848i	0.102364	+	0.0341214i
$556$		−	21.8038i		−	0.924689i
$557$	−11.0718	−	41.3205i	−0.469127	−	1.75081i	−0.642831	−	0.766008i	$-0.722240\pi$
$557$	−11.0718	−	41.3205i	−0.469127	−	1.75081i	0.173704	−	0.984798i	$-0.444426\pi$
$558$	2.19615	−	8.19615i	0.0929705	−	0.346971i
$559$	−17.6603			−0.746949
$560$	25.5885	+	6.53590i	1.08131	+	0.276192i
$561$	−6.92820	+	25.8564i	−0.292509	+	1.09166i
$562$	−30.4186	+	30.4186i	−1.28313	+	1.28313i
$563$	−4.09808	−	1.09808i	−0.172713	−	0.0462784i	0.171426	−	0.985197i	$-0.445163\pi$
$563$	−4.09808	−	1.09808i	−0.172713	−	0.0462784i	−0.344139	+	0.938919i	$0.611829\pi$
$564$	5.89230	+	21.9904i	0.248111	+	0.925962i
$565$	−14.5359	−	16.3923i	−0.611530	−	0.689629i
$566$		−	26.3205i		−	1.10633i
$567$	15.5885	−	18.0000i	0.654654	−	0.755929i
$568$	−1.73205	−	1.73205i	−0.0726752	−	0.0726752i
$569$	−9.46410	−	5.46410i	−0.396756	−	0.229067i	0.288327	−	0.957532i	$-0.406901\pi$
$569$	−9.46410	−	5.46410i	−0.396756	−	0.229067i	−0.685083	+	0.728465i	$0.740234\pi$
$570$	−15.2942	+	13.5622i	−0.640605	+	0.568057i
$571$	−3.09808	−	5.36603i	−0.129650	−	0.224561i	0.793891	−	0.608060i	$-0.208052\pi$
$571$	−3.09808	−	5.36603i	−0.129650	−	0.224561i	−0.923541	+	0.383499i	$0.874719\pi$
$572$	12.9282	+	12.9282i	0.540555	+	0.540555i
$573$	8.49038	+	14.7058i	0.354691	+	0.614342i
$574$	−6.69615	+	13.7942i	−0.279492	+	0.575760i
$575$	17.2487	−	2.46410i	0.719321	−	0.102760i
$576$	−14.8923	+	8.59808i	−0.620513	+	0.358253i
$577$	32.8564	−	8.80385i	1.36783	−	0.366509i	0.501144	−	0.865364i	$-0.332913\pi$
$577$	32.8564	−	8.80385i	1.36783	−	0.366509i	0.866686	+	0.498855i	$0.166246\pi$
$578$	−58.3468	−	58.3468i	−2.42691	−	2.42691i
$579$	0.339746	+	0.339746i	0.0141194	+	0.0141194i
$580$	−15.1865	−	0.911543i	−0.630586	−	0.0378498i
$581$	27.9186	+	13.5526i	1.15826	+	0.562255i
$582$	25.2224	−	43.6865i	1.04550	−	1.81087i
$583$	−7.46410	+	2.00000i	−0.309132	+	0.0828315i
$584$	0.928203	−	1.60770i	0.0384093	−	0.0665269i
$585$	33.5885	+	11.1962i	1.38871	+	0.462904i
$586$	−11.6603	+	6.73205i	−0.481681	+	0.278098i
$587$	−7.00962	+	26.1603i	−0.289318	+	1.07975i	0.656308	+	0.754493i	$0.272117\pi$
$587$	−7.00962	+	26.1603i	−0.289318	+	1.07975i	−0.945626	+	0.325256i	$0.894549\pi$
$588$	7.79423	−	19.5000i	0.321429	−	0.804166i
$589$	−3.46410	−	2.00000i	−0.142736	−	0.0824086i
$590$	−61.9808	−	20.6603i	−2.55171	−	0.850569i
$591$	2.53590	+	9.46410i	0.104313	+	0.389301i
$592$	2.07180	−	2.07180i	0.0851503	−	0.0851503i
$593$	28.9545	+	7.75833i	1.18902	+	0.318596i	0.798498	−	0.601998i	$-0.205628\pi$
$593$	28.9545	+	7.75833i	1.18902	+	0.318596i	0.390520	+	0.920594i	$0.372295\pi$
$594$	5.19615	+	19.3923i	0.213201	+	0.795676i
$595$	23.3205	+	39.3205i	0.956048	+	1.61198i
$596$	−13.3923	−	23.1962i	−0.548570	−	0.950151i
$597$	−3.80385	−	6.58846i	−0.155681	−	0.269648i
$598$	−34.3205	−	9.19615i	−1.40347	−	0.376059i
$599$	−15.7128	+	9.07180i	−0.642008	+	0.370664i	−0.785388	−	0.619004i	$-0.787536\pi$
$599$	−15.7128	+	9.07180i	−0.642008	+	0.370664i	0.143380	+	0.989668i	$0.454203\pi$
$600$	−1.66987	+	4.16025i	−0.0681723	+	0.169842i
$601$	29.3205	−	16.9282i	1.19601	−	0.690516i	0.236346	−	0.971669i	$-0.424050\pi$
$601$	29.3205	−	16.9282i	1.19601	−	0.690516i	0.959663	+	0.281153i	$0.0907169\pi$
$602$	−16.7942	−	3.23205i	−0.684482	−	0.131729i
$603$	−4.90192	−	18.2942i	−0.199622	−	0.744999i
$604$	26.4904	−	15.2942i	1.07788	−	0.622313i
$605$	−7.00000	−	14.0000i	−0.284590	−	0.569181i
$606$	−3.23205	+	12.0622i	−0.131293	+	0.489992i
$607$	−2.70577	−	2.70577i	−0.109824	−	0.109824i	0.650059	−	0.759883i	$-0.274744\pi$
$607$	−2.70577	−	2.70577i	−0.109824	−	0.109824i	−0.759883	+	0.650059i	$0.774744\pi$
$608$	5.36603	+	20.0263i	0.217621	+	0.812173i
$609$	3.40192	−	17.6769i	0.137853	−	0.716305i
$610$	12.3923	−	2.53590i	0.501750	−	0.102676i
$611$	−20.0263	−	34.6865i	−0.810177	−	1.40327i
$612$	−38.7846	−	10.3923i	−1.56777	−	0.420084i
$613$	−22.7583	+	6.09808i	−0.919200	+	0.246299i	−0.687244	−	0.726427i	$-0.741179\pi$
$613$	−22.7583	+	6.09808i	−0.919200	+	0.246299i	−0.231957	+	0.972726i	$0.574513\pi$
$614$	7.33013	−	12.6962i	0.295820	−	0.512375i
$615$	−9.69615	−	6.40192i	−0.390987	−	0.258150i
$616$	−1.53590	−	2.26795i	−0.0618831	−	0.0913783i
$617$	−3.32051	−	12.3923i	−0.133679	−	0.498895i	0.866321	−	0.499487i	$-0.166478\pi$
$617$	−3.32051	−	12.3923i	−0.133679	−	0.498895i	−1.00000		0.000591902i	$0.999812\pi$
$618$	26.0885	−	15.0622i	1.04943	−	0.605890i
$619$	40.7846			1.63927			0.819636	−	0.572885i	$-0.194176\pi$
$619$	40.7846			1.63927			0.819636	+	0.572885i	$0.194176\pi$
$620$	5.66025	+	0.339746i	0.227321	+	0.0136445i
$621$	−12.8038	−	12.8038i	−0.513801	−	0.513801i
$622$	9.73205	+	9.73205i	0.390220	+	0.390220i
$623$	−12.9282	−	37.3205i	−0.517958	−	1.49521i
$624$	28.8564	−	28.8564i	1.15518	−	1.15518i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−3.80385	+	2.19615i	−0.152032	+	0.0877759i
$627$	9.46410			0.377960
$628$	−4.56218	−	17.0263i	−0.182051	−	0.679423i
$629$	5.07180			0.202226
$630$	29.8923	+	16.7942i	1.19094	+	0.669098i
$631$	15.8564			0.631234			0.315617	−	0.948887i	$-0.397789\pi$
$631$	15.8564			0.631234			0.315617	+	0.948887i	$0.397789\pi$
$632$	0.607695	+	2.26795i	0.0241728	+	0.0902142i
$633$	−11.3205	−	19.6077i	−0.449950	−	0.779336i
$634$	20.0263	−	11.5622i	0.795345	−	0.459193i
$635$	28.9019	+	9.63397i	1.14694	+	0.382313i
$636$	−3.00000	−	11.1962i	−0.118958	−	0.443956i
$637$	−4.36603	+	36.6865i	−0.172988	+	1.45357i
$638$	10.7321	+	10.7321i	0.424886	+	0.424886i
$639$	−7.09808	−	12.2942i	−0.280796	−	0.486352i
$640$	6.08846	+	6.86603i	0.240667	+	0.271403i
$641$	38.3923			1.51640			0.758202	−	0.652019i	$-0.226078\pi$
$641$	38.3923			1.51640			0.758202	+	0.652019i	$0.226078\pi$
$642$	34.2846	+	19.7942i	1.35311	+	0.781216i
$643$	−9.82051	−	36.6506i	−0.387283	−	1.44536i	−0.834536	−	0.550953i	$-0.814264\pi$
$643$	−9.82051	−	36.6506i	−0.387283	−	1.44536i	0.447253	−	0.894407i	$-0.352402\pi$
$644$	−14.3660	−	6.97372i	−0.566101	−	0.274803i
$645$	4.09808	−	12.2942i	0.161362	−	0.484085i
$646$	−20.3923	+	35.3205i	−0.802325	+	1.38967i
$647$	−27.6244	+	7.40192i	−1.08603	+	0.291000i	−0.757062	−	0.653343i	$-0.773366\pi$
$647$	−27.6244	+	7.40192i	−1.08603	+	0.291000i	−0.328963	+	0.944343i	$0.606699\pi$
$648$	4.50000	−	1.20577i	0.176777	−	0.0473672i
$649$	15.1244	+	26.1962i	0.593683	+	1.02829i
$650$	−6.09808	+	50.6147i	−0.239186	+	1.98527i
$651$	−1.26795	+	6.58846i	−0.0496948	+	0.258222i
$652$	−4.31347	−	16.0981i	−0.168928	−	0.630449i
$653$	11.2679	+	11.2679i	0.440949	+	0.440949i	0.892331	−	0.451382i	$-0.149069\pi$
$653$	11.2679	+	11.2679i	0.440949	+	0.440949i	−0.451382	+	0.892331i	$0.649069\pi$
$654$	14.8301	+	14.8301i	0.579904	+	0.579904i
$655$	−10.1436	+	5.07180i	−0.396343	+	0.198171i
$656$	−11.5981	+	6.69615i	−0.452829	+	0.261441i
$657$	7.60770	−	7.60770i	0.296804	−	0.296804i
$658$	−12.6962	−	36.6506i	−0.494948	−	1.42879i
$659$	−34.3468	+	19.8301i	−1.33796	+	0.772472i	−0.986505	−	0.163732i	$-0.947647\pi$
$659$	−34.3468	+	19.8301i	−1.33796	+	0.772472i	−0.351456	+	0.936204i	$0.614313\pi$
$660$	−12.0000	+	6.00000i	−0.467099	+	0.233550i
$661$	20.2583	−	11.6962i	0.787958	−	0.454928i	−0.0512854	−	0.998684i	$-0.516332\pi$
$661$	20.2583	−	11.6962i	0.787958	−	0.454928i	0.839243	+	0.543756i	$0.182998\pi$
$662$	−11.1962	−	3.00000i	−0.435151	−	0.116598i
$663$	70.6410			2.74347
$664$	3.03590	+	5.25833i	0.117816	+	0.204063i
$665$	11.2942	−	11.5622i	0.437971	−	0.448362i
$666$	3.29423	−	1.90192i	0.127649	−	0.0736980i
$667$	−13.2224	−	3.54294i	−0.511975	−	0.137183i
$668$	4.26795	−	4.26795i	0.165132	−	0.165132i
$669$	−9.29423	+	9.29423i	−0.359336	+	0.359336i
$670$	24.3923	−	12.1962i	0.942357	−	0.471178i
$671$	−5.07180	−	2.92820i	−0.195795	−	0.113042i
$672$	28.7942	−	19.5000i	1.11076	−	0.752229i
$673$	3.63397	−	13.5622i	0.140079	−	0.522784i	−0.859846	−	0.510554i	$-0.829440\pi$
$673$	3.63397	−	13.5622i	0.140079	−	0.522784i	0.999925	−	0.0122297i	$-0.00389293\pi$
$674$	12.7583	−	7.36603i	0.491433	−	0.283729i
$675$	−15.5885	+	20.7846i	−0.600000	+	0.800000i
$676$	12.8660	−	22.2846i	0.494847	−	0.857100i
$677$	−47.1506	+	12.6340i	−1.81215	+	0.485563i	−0.995764	−	0.0919487i	$-0.970690\pi$
$677$	−47.1506	+	12.6340i	−1.81215	+	0.485563i	−0.816382	+	0.577512i	$0.804024\pi$
$678$	−32.7846			−1.25909
$679$	−17.4186	+	35.8827i	−0.668464	+	1.37705i
$680$	−0.535898	+	8.92820i	−0.0205508	+	0.342381i
$681$	−32.1506	+	8.61474i	−1.23202	+	0.330117i
$682$	−4.00000	−	4.00000i	−0.153168	−	0.153168i
$683$	11.5000	−	3.08142i	0.440035	−	0.117907i	−0.0319978	−	0.999488i	$-0.510187\pi$
$683$	11.5000	−	3.08142i	0.440035	−	0.117907i	0.472033	+	0.881581i	$0.343520\pi$
$684$			14.1962i			0.542803i
$685$	3.00000	+	1.00000i	0.114624	+	0.0382080i
$686$	−10.8660	+	34.0885i	−0.414867	+	1.30150i
$687$	4.62436	−	8.00962i	0.176430	−	0.305586i
$688$	−10.5622	−	10.5622i	−0.402679	−	0.402679i
$689$	10.1962	+	17.6603i	0.388442	+	0.672802i
$690$	14.3660	−	21.7583i	0.546905	−	0.828325i
$691$	10.8564	+	6.26795i	0.412997	+	0.238444i	0.692077	−	0.721824i	$-0.256696\pi$
$691$	10.8564	+	6.26795i	0.412997	+	0.238444i	−0.279080	+	0.960268i	$0.590029\pi$
$692$	−27.7128	−	27.7128i	−1.05348	−	1.05348i
$693$	−5.19615	−	15.0000i	−0.197386	−	0.569803i
$694$			18.1244i			0.687991i
$695$	−28.0981	−	1.68653i	−1.06582	−	0.0639739i
$696$	2.49038	−	2.49038i	0.0943977	−	0.0943977i
$697$	−22.3923	−	6.00000i	−0.848169	−	0.227266i
$698$	−13.6603	+	13.6603i	−0.517048	+	0.517048i
$699$	−15.8038	−	15.8038i	−0.597756	−	0.597756i
$700$	−6.99038	+	21.8205i	−0.264212	+	0.824738i
$701$	−27.0526			−1.02176			−0.510881	−	0.859652i	$-0.670681\pi$
$701$	−27.0526			−1.02176			−0.510881	+	0.859652i	$0.670681\pi$
$702$	45.8827	−	26.4904i	1.73173	−	0.999815i
$703$	−0.464102	−	1.73205i	−0.0175039	−	0.0653255i
$704$			11.4641i			0.432070i
$705$	28.7942	−	5.89230i	1.08445	−	0.221917i
$706$	−29.4904	−	17.0263i	−1.10989	−	0.640792i
$707$	1.86603	−	9.69615i	0.0701791	−	0.364661i
$708$	−39.2942	+	22.6865i	−1.47677	+	0.852612i
$709$	−24.8038	−	14.3205i	−0.931528	−	0.537818i	−0.0442335	−	0.999021i	$-0.514085\pi$
$709$	−24.8038	−	14.3205i	−0.931528	−	0.537818i	−0.887295	+	0.461203i	$0.847418\pi$
$710$	15.2942	−	13.5622i	0.573982	−	0.508979i
$711$			13.6077i			0.510328i
$712$	2.00000	−	7.46410i	0.0749532	−	0.279729i
$713$	4.92820	+	1.32051i	0.184563	+	0.0494534i
$714$	67.1769	+	12.9282i	2.51403	+	0.483826i
$715$	17.6603	−	15.6603i	0.660456	−	0.585660i
$716$	2.19615			0.0820741
$717$	−3.00000	+	1.73205i	−0.112037	+	0.0646846i
$718$	14.9282	+	14.9282i	0.557116	+	0.557116i
$719$	−4.53590	−	7.85641i	−0.169160	−	0.292995i	0.768964	−	0.639292i	$-0.220772\pi$
$719$	−4.53590	−	7.85641i	−0.169160	−	0.292995i	−0.938125	+	0.346297i	$0.887439\pi$
$720$	13.3923	+	26.7846i	0.499102	+	0.998203i
$721$	−19.7224	+	13.3564i	−0.734502	+	0.497419i
$722$	−21.5263	−	5.76795i	−0.801125	−	0.214661i
$723$	−33.6962	−	19.4545i	−1.25317	−	0.723520i
$724$	17.4282	+	30.1865i	0.647714	+	1.12187i
$725$	−2.34936	+	19.5000i	−0.0872532	+	0.724212i
$726$	−22.6244	−	6.06218i	−0.839669	−	0.224989i
$727$	−4.22243	+	15.7583i	−0.156601	+	0.584444i	0.842362	+	0.538913i	$0.181165\pi$
$727$	−4.22243	+	15.7583i	−0.156601	+	0.584444i	−0.998963	+	0.0455314i	$0.985502\pi$
$728$	−4.73205	+	5.46410i	−0.175381	+	0.202513i
$729$	27.0000			1.00000
$730$	12.9282	+	8.53590i	0.478494	+	0.315928i
$731$		−	25.8564i		−	0.956334i
$732$	4.39230	−	7.60770i	0.162344	−	0.281189i
$733$	−30.3205	+	30.3205i	−1.11991	+	1.11991i	−0.128160	+	0.991754i	$0.540907\pi$
$733$	−30.3205	+	30.3205i	−1.11991	+	1.11991i	−0.991754	+	0.128160i	$0.959093\pi$
$734$	−5.33013	+	9.23205i	−0.196739	+	0.340761i
$735$	−24.5263	−	11.5526i	−0.904665	−	0.426123i
$736$	−13.2224	−	22.9019i	−0.487385	−	0.844176i
$737$	−12.1962	−	3.26795i	−0.449251	−	0.120376i
$738$	−16.7942	+	4.50000i	−0.618204	+	0.165647i
$739$	35.3205	+	20.3923i	1.29929	+	0.750143i	0.980281	−	0.197610i	$-0.0633179\pi$
$739$	35.3205	+	20.3923i	1.29929	+	0.750143i	0.319005	+	0.947753i	$0.396651\pi$
$740$	1.68653	+	1.90192i	0.0619982	+	0.0699161i
$741$	−6.46410	−	24.1244i	−0.237465	−	0.886230i
$742$	6.46410	+	18.6603i	0.237305	+	0.685039i
$743$	−18.3564	+	4.91858i	−0.673431	+	0.180445i	−0.579300	−	0.815114i	$-0.696674\pi$
$743$	−18.3564	+	4.91858i	−0.673431	+	0.180445i	−0.0941313	+	0.995560i	$0.530007\pi$
$744$	−0.928203	+	0.928203i	−0.0340296	+	0.0340296i
$745$	−30.9282	+	15.4641i	−1.13312	+	0.566561i
$746$	−7.56218	+	13.0981i	−0.276871	+	0.479555i
$747$	9.10770	+	33.9904i	0.333233	+	1.24364i
$748$	−18.9282	+	18.9282i	−0.692084	+	0.692084i
$749$	−28.1603	−	13.6699i	−1.02895	−	0.499486i
$750$	−33.8205	−	15.9904i	−1.23495	−	0.583886i
$751$	49.1244			1.79257			0.896287	−	0.443475i	$-0.146255\pi$
$751$	49.1244			1.79257			0.896287	+	0.443475i	$0.146255\pi$
$752$	8.76795	−	32.7224i	0.319734	−	1.19326i
$753$	−5.49038	−	3.16987i	−0.200081	−	0.115517i
$754$	20.0263	−	34.6865i	0.729314	−	1.26321i
$755$	−17.6603	−	35.3205i	−0.642722	−	1.28544i
$756$	22.5000	−	7.79423i	0.818317	−	0.283473i
$757$	6.39230	−	6.39230i	0.232332	−	0.232332i	−0.581333	−	0.813666i	$-0.697469\pi$
$757$	6.39230	−	6.39230i	0.232332	−	0.232332i	0.813666	+	0.581333i	$0.197469\pi$
$758$	32.6865	−	8.75833i	1.18723	−	0.318117i
$759$	−11.6603	+	3.12436i	−0.423240	+	0.113407i
$760$	3.09808	−	0.633975i	0.112379	−	0.0229967i
$761$			1.19615i			0.0433605i	0.999765	+	0.0216802i	$0.00690158\pi$
$761$			1.19615i			0.0433605i	−0.999765	+	0.0216802i	$0.993098\pi$
$762$	39.4808	−	22.7942i	1.43024	−	0.825748i
$763$	−12.5359	−	10.8564i	−0.453830	−	0.393028i
$764$			16.9808i			0.614342i
$765$	−16.3923	+	49.1769i	−0.592665	+	1.77800i
$766$	−18.3564	−	10.5981i	−0.663244	−	0.382924i
$767$	56.4449	−	56.4449i	2.03811	−	2.03811i
$768$	33.5885			1.21202
$769$	7.40192	−	12.8205i	0.266920	−	0.462319i	−0.701145	−	0.713019i	$-0.747327\pi$
$769$	7.40192	−	12.8205i	0.266920	−	0.462319i	0.968065	+	0.250700i	$0.0806607\pi$
$770$	19.6603	−	11.6603i	0.708506	−	0.420206i
$771$	−0.464102	+	0.124356i	−0.0167142	+	0.00447856i
$772$	0.124356	+	0.464102i	0.00447566	+	0.0167034i
$773$	−11.9019	−	44.4186i	−0.428082	−	1.59763i	−0.757098	−	0.653301i	$-0.773384\pi$
$773$	−11.9019	−	44.4186i	−0.428082	−	1.59763i	0.329016	−	0.944324i	$-0.393283\pi$
$774$	−9.69615	−	16.7942i	−0.348521	−	0.603656i
$775$	0.875644	−	7.26795i	0.0314541	−	0.261072i
$776$	−6.75833	+	3.90192i	−0.242610	+	0.140071i
$777$	−2.49038	+	1.68653i	−0.0893419	+	0.0605041i
$778$	16.8923	−	4.52628i	0.605618	−	0.162275i
$779$			8.19615i			0.293658i
$780$	23.4904	+	26.4904i	0.841091	+	0.948508i
$781$	−9.46410			−0.338652
$782$	13.4641	−	50.2487i	0.481475	−	1.79689i
$783$	17.6769	−	10.2058i	0.631721	−	0.364725i
$784$	−24.5526	+	19.3301i	−0.876877	+	0.690362i
$785$	−22.2942	+	4.56218i	−0.795715	+	0.162831i
$786$	−4.39230	+	16.3923i	−0.156668	+	0.584694i
$787$	13.8468	−	51.6769i	0.493585	−	1.84208i	−0.0442321	−	0.999021i	$-0.514084\pi$
$787$	13.8468	−	51.6769i	0.493585	−	1.84208i	0.537817	−	0.843062i	$-0.319249\pi$
$788$	−2.53590	+	9.46410i	−0.0903376	+	0.337145i
$789$	−9.23205	+	2.47372i	−0.328670	+	0.0880668i
$790$	−19.1962	+	3.92820i	−0.682968	+	0.139759i
$791$	25.8564	−	1.85641i	0.919348	−	0.0660062i
$792$	0.803848	−	3.00000i	0.0285635	−	0.106600i
$793$	−4.00000	+	14.9282i	−0.142044	+	0.530116i
$794$	−58.6410			−2.08109
$795$	−14.6603	+	3.00000i	−0.519946	+	0.106399i
$796$		−	7.60770i		−	0.269648i
$797$	−44.3468	+	11.8827i	−1.57084	+	0.420906i	−0.936076	−	0.351797i	$-0.885571\pi$
$797$	−44.3468	+	11.8827i	−1.57084	+	0.420906i	−0.634767	+	0.772703i	$0.718904\pi$
$798$	−1.73205	−	24.1244i	−0.0613139	−	0.853993i
$799$	50.7846	−	29.3205i	1.79663	−	1.03729i
$800$	−29.8468	+	23.4282i	−1.05524	+	0.828312i
$801$	22.3923	−	38.7846i	0.791193	−	1.37039i
$802$	4.69615	+	17.5263i	0.165827	+	0.618874i
$803$	−1.85641	−	6.92820i	−0.0655112	−	0.244491i
$804$	4.90192	−	18.2942i	0.172878	−	0.645188i
$805$	−10.0981	+	17.9737i	−0.355910	+	0.633490i
$806$	−7.46410	+	12.9282i	−0.262912	+	0.455377i
$807$	−24.5885	−	42.5885i	−0.865555	−	1.49918i
$808$	1.36603	−	1.36603i	0.0480566	−	0.0480566i
$809$	8.38269	+	4.83975i	0.294720	+	0.170156i	0.640068	−	0.768318i	$-0.278906\pi$
$809$	8.38269	+	4.83975i	0.294720	+	0.170156i	−0.345349	+	0.938474i	$0.612239\pi$
$810$	7.79423	+	38.0885i	0.273861	+	1.33829i
$811$		−	24.5885i		−	0.863418i	−0.902013	−	0.431709i	$-0.857911\pi$
$811$		−	24.5885i		−	0.863418i	0.902013	−	0.431709i	$-0.142089\pi$
$812$	11.7846	−	13.6077i	0.413559	−	0.477536i
$813$		−	56.4449i		−	1.97961i
$814$		−	2.53590i		−	0.0888832i
$815$	−21.0788	+	4.31347i	−0.738360	+	0.151094i
$816$	42.2487	+	42.2487i	1.47900	+	1.47900i
$817$	−8.83013	+	2.36603i	−0.308927	+	0.0827768i
$818$	−30.4904	+	30.4904i	−1.06607	+	1.06607i
$819$	−34.6865	+	23.4904i	−1.21205	+	0.820820i
$820$	−5.19615	−	10.3923i	−0.181458	−	0.362915i
$821$	−5.20577	+	9.01666i	−0.181683	+	0.314684i	−0.942454	−	0.334337i	$-0.891488\pi$
$821$	−5.20577	+	9.01666i	−0.181683	+	0.314684i	0.760771	+	0.649020i	$0.224821\pi$
$822$	4.09808	−	2.36603i	0.142937	−	0.0825246i
$823$	7.16025	−	26.7224i	0.249591	−	0.931485i	−0.721429	−	0.692488i	$-0.756515\pi$
$823$	7.16025	−	26.7224i	0.249591	−	0.931485i	0.971020	−	0.238997i	$-0.0768188\pi$
$824$	−4.66025			−0.162348
$825$	6.80385	+	15.9282i	0.236880	+	0.554549i
$826$	64.0070	−	43.3468i	2.22709	−	1.50823i
$827$	22.8301	−	22.8301i	0.793881	−	0.793881i	−0.188241	−	0.982123i	$-0.560279\pi$
$827$	22.8301	−	22.8301i	0.793881	−	0.793881i	0.982123	+	0.188241i	$0.0602788\pi$
$828$	−4.68653	−	17.4904i	−0.162868	−	0.607833i
$829$	4.83975	−	8.38269i	0.168091	−	0.291143i	−0.769657	−	0.638457i	$-0.779573\pi$
$829$	4.83975	−	8.38269i	0.168091	−	0.291143i	0.937749	+	0.347314i	$0.112906\pi$
$830$	−45.3205	+	22.6603i	−1.57310	+	0.786549i
$831$	−5.19615	−	19.3923i	−0.180253	−	0.672712i
$832$	29.2224	−	7.83013i	1.01311	−	0.271461i
$833$	−53.7128	−	6.39230i	−1.86104	−	0.221480i
$834$	−29.7846	+	29.7846i	−1.03136	+	1.03136i
$835$	−5.16987	−	5.83013i	−0.178911	−	0.201760i
$836$	8.19615	+	4.73205i	0.283470	+	0.163661i
$837$	−6.58846	+	3.80385i	−0.227730	+	0.131480i
$838$	−4.36603	−	1.16987i	−0.150822	−	0.0404126i
$839$	27.6147	+	47.8301i	0.953367	+	1.65128i	0.738063	+	0.674732i	$0.235741\pi$
$839$	27.6147	+	47.8301i	0.953367	+	1.65128i	0.215304	+	0.976547i	$0.430926\pi$
$840$	−2.70577	−	4.56218i	−0.0933580	−	0.157410i
$841$	−6.78461	+	11.7513i	−0.233952	+	0.405217i
$842$	−6.56218	+	6.56218i	−0.226148	+	0.226148i
$843$	38.5692			1.32839
$844$		−	22.6410i		−	0.779336i
$845$	−27.7224	−	18.3038i	−0.953681	−	0.629671i
$846$	21.9904	−	38.0885i	0.756045	−	1.30951i
$847$	18.1865	+	3.50000i	0.624897	+	0.120261i
$848$	−4.46410	+	16.6603i	−0.153298	+	0.572115i
$849$	−16.6865	+	16.6865i	−0.572680	+	0.572680i
$850$	−74.1051	−	8.92820i	−2.54178	−	0.306235i
$851$	1.14359	+	1.98076i	0.0392019	+	0.0678997i
$852$		−	14.1962i		−	0.486352i
$853$	0.464102	+	0.124356i	0.0158905	+	0.00425786i	0.266756	−	0.963764i	$-0.414048\pi$
$853$	0.464102	+	0.124356i	0.0158905	+	0.00425786i	−0.250865	+	0.968022i	$0.580715\pi$
$854$	−6.53590	+	13.4641i	−0.223654	+	0.460732i
$855$	18.2942	+	1.09808i	0.625649	+	0.0375534i
$856$	−3.06218	−	5.30385i	−0.104663	−	0.181282i
$857$	−4.92820	−	4.92820i	−0.168344	−	0.168344i	0.617907	−	0.786251i	$-0.287981\pi$
$857$	−4.92820	−	4.92820i	−0.168344	−	0.168344i	−0.786251	+	0.617907i	$0.787981\pi$
$858$		−	35.3205i		−	1.20582i
$859$	−10.3397			−0.352788			−0.176394	−	0.984320i	$-0.556443\pi$
$859$	−10.3397			−0.352788			−0.176394	+	0.984320i	$0.556443\pi$
$860$	9.69615	−	8.59808i	0.330636	−	0.293192i
$861$	12.9904	−	4.50000i	0.442711	−	0.153360i
$862$	38.4186	+	10.2942i	1.30854	+	0.350623i
$863$	10.0788	−	37.6147i	0.343088	−	1.28042i	−0.551743	−	0.834014i	$-0.686037\pi$
$863$	10.0788	−	37.6147i	0.343088	−	1.28042i	0.894830	−	0.446406i	$-0.147296\pi$
$864$	38.0885	+	10.2058i	1.29580	+	0.347207i
$865$	−37.8564	+	33.5692i	−1.28716	+	1.14139i
$866$	−0.294229	−	0.169873i	−0.00999830	−	0.00577252i
$867$			73.9808i			2.51252i
$868$	−4.39230	+	5.07180i	−0.149085	+	0.172148i
$869$	7.85641	+	4.53590i	0.266510	+	0.153870i
$870$	19.5000	+	21.9904i	0.661112	+	0.745544i
$871$			33.3205i			1.12902i
$872$	−0.839746	−	3.13397i	−0.0284374	−	0.106130i
$873$	−43.6865	+	11.7058i	−1.47857	+	0.396180i
$874$	−18.3923			−0.622129
$875$	27.5788	+	10.6962i	0.932335	+	0.361596i
$876$	10.3923	−	2.78461i	0.351123	−	0.0940832i
$877$	−9.19615	+	9.19615i	−0.310532	+	0.310532i	−0.845116	−	0.534584i	$-0.820468\pi$
$877$	−9.19615	+	9.19615i	−0.310532	+	0.310532i	0.534584	+	0.845116i	$0.320468\pi$
$878$	66.9090	+	17.9282i	2.25807	+	0.605048i
$879$	11.6603	+	3.12436i	0.393291	+	0.105382i
$880$	19.9282	+	1.19615i	0.671780	+	0.0403223i
$881$			51.0333i			1.71936i	0.510836	+	0.859678i	$0.329336\pi$
$881$			51.0333i			1.71936i	−0.510836	+	0.859678i	$0.670664\pi$
$882$	−37.2846	+	15.9904i	−1.25544	+	0.538424i
$883$	19.4378	+	19.4378i	0.654135	+	0.654135i	0.953986	−	0.299851i	$-0.0969370\pi$
$883$	19.4378	+	19.4378i	0.654135	+	0.654135i	−0.299851	+	0.953986i	$0.596937\pi$
$884$	61.1769	+	35.3205i	2.05760	+	1.18796i
$885$	26.1962	+	52.3923i	0.880574	+	1.76115i
$886$	11.7942	+	20.4282i	0.396235	+	0.686299i
$887$	6.49038	+	6.49038i	0.217926	+	0.217926i	0.807624	−	0.589698i	$-0.200753\pi$
$887$	6.49038	+	6.49038i	0.217926	+	0.217926i	−0.589698	+	0.807624i	$0.700753\pi$
$888$	−0.588457			−0.0197473
$889$	−29.8468	+	20.2128i	−1.00103	+	0.677916i
$890$	61.1769	+	20.3923i	2.05065	+	0.683552i
$891$	9.00000	−	15.5885i	0.301511	−	0.522233i
$892$	−12.6962	+	3.40192i	−0.425099	+	0.113905i
$893$	−14.6603	−	14.6603i	−0.490587	−	0.490587i
$894$	−13.3923	+	49.9808i	−0.447906	+	1.67161i
$895$	0.169873	−	2.83013i	0.00567823	−	0.0946007i
$896$	−10.8301	+	0.777568i	−0.361809	+	0.0259767i
$897$	15.9282	+	27.5885i	0.531827	+	0.921152i
$898$	13.6962	−	3.66987i	0.457047	−	0.122465i
$899$	−2.87564	+	4.98076i	−0.0959081	+	0.166118i
$900$	−23.8923	+	10.2058i	−0.796410	+	0.340192i
$901$	−25.8564	+	14.9282i	−0.861402	+	0.497331i
$902$	−3.00000	+	11.1962i	−0.0998891	+	0.372791i
$903$	8.59808	+	12.6962i	0.286126	+	0.422501i
$904$	4.39230	+	2.53590i	0.146086	+	0.0843427i
$905$	40.2487	−	20.1244i	1.33791	−	0.668956i
$906$	−57.0788	−	15.2942i	−1.89632	−	0.508117i
$907$	9.36603	−	9.36603i	0.310994	−	0.310994i	−0.534301	−	0.845294i	$-0.679425\pi$
$907$	9.36603	−	9.36603i	0.310994	−	0.310994i	0.845294	+	0.534301i	$0.179425\pi$
$908$	−32.1506	−	8.61474i	−1.06696	−	0.285890i
$909$	9.69615	−	5.59808i	0.321601	−	0.185676i
$910$	−43.1506	−	42.1506i	−1.43043	−	1.39728i
$911$	−0.633975	−	1.09808i	−0.0210045	−	0.0363809i	0.855332	−	0.518080i	$-0.173353\pi$
$911$	−0.633975	−	1.09808i	−0.0210045	−	0.0363809i	−0.876337	+	0.481699i	$0.840020\pi$
$912$	10.5622	−	18.2942i	0.349749	−	0.605782i
$913$	22.6603	+	6.07180i	0.749945	+	0.200947i
$914$	−54.5429	+	31.4904i	−1.80412	+	1.04161i
$915$	−9.46410	−	6.24871i	−0.312874	−	0.206576i
$916$	8.00962	−	4.62436i	0.264645	−	0.152793i
$917$	2.53590	−	13.1769i	0.0837427	−	0.435140i
$918$	38.7846	+	67.1769i	1.28008	+	2.21717i
$919$	−16.0981	+	9.29423i	−0.531027	+	0.306588i	−0.741434	−	0.671025i	$-0.765854\pi$
$919$	−16.0981	+	9.29423i	−0.531027	+	0.306588i	0.210408	+	0.977614i	$0.432521\pi$
$920$	−3.60770	+	1.80385i	−0.118942	+	0.0594711i
$921$	−12.6962	+	3.40192i	−0.418352	+	0.112097i
$922$	−32.7583	−	32.7583i	−1.07884	−	1.07884i
$923$	6.46410	+	24.1244i	0.212768	+	0.794063i
$924$	3.00000	−	15.5885i	0.0986928	−	0.512823i
$925$	2.58142	−	2.02628i	0.0848764	−	0.0666237i
$926$	14.3301	+	24.8205i	0.470917	+	0.815653i
$927$	−26.0885	−	6.99038i	−0.856857	−	0.229594i
$928$	28.7942	−	7.71539i	0.945217	−	0.253270i
$929$	15.8923	−	27.5263i	0.521410	−	0.903108i	−0.478280	−	0.878207i	$-0.658740\pi$
$929$	15.8923	−	27.5263i	0.521410	−	0.903108i	0.999690	−	0.0249007i	$-0.00792696\pi$
$930$	−7.26795	−	8.19615i	−0.238325	−	0.268762i
$931$	2.73205	+	18.9282i	0.0895393	+	0.620347i
$932$	−5.78461	−	21.5885i	−0.189481	−	0.707153i
$933$		−	12.3397i		−	0.403985i
$934$	5.00000			0.163605
$935$	22.9282	+	25.8564i	0.749832	+	0.845595i
$936$	−8.19615			−0.267900
$937$	−5.53590	−	5.53590i	−0.180850	−	0.180850i	0.610876	−	0.791726i	$-0.290817\pi$
$937$	−5.53590	−	5.53590i	−0.180850	−	0.180850i	−0.791726	+	0.610876i	$0.790817\pi$
$938$	−6.09808	+	31.6865i	−0.199109	+	1.03460i
$939$	3.80385	+	1.01924i	0.124134	+	0.0332616i
$940$	27.8827	+	9.29423i	0.909433	+	0.303144i
$941$	−6.10770	+	3.52628i	−0.199105	+	0.114953i	−0.596238	−	0.802808i	$-0.703339\pi$
$941$	−6.10770	+	3.52628i	−0.199105	+	0.114953i	0.397133	+	0.917761i	$0.370005\pi$
$942$	−17.0263	+	29.4904i	−0.554746	+	0.960849i
$943$	−2.70577	−	10.0981i	−0.0881120	−	0.328839i
$944$	67.5167			2.19748
$945$	−8.30385	−	29.5981i	−0.270124	−	0.962825i
$946$	−12.9282			−0.420332
$947$	1.83013	+	6.83013i	0.0594711	+	0.221949i	0.989265	−	0.146131i	$-0.0466820\pi$
$947$	1.83013	+	6.83013i	0.0594711	+	0.221949i	−0.929794	+	0.368080i	$0.880015\pi$
$948$	−6.80385	+	11.7846i	−0.220979	+	0.382746i
$949$	−16.3923	+	9.46410i	−0.532117	+	0.307218i
$950$	3.73205	+	26.1244i	0.121084	+	0.847586i
$951$	−20.0263	−	5.36603i	−0.649397	−	0.174005i
$952$	−8.00000	−	6.92820i	−0.259281	−	0.224544i
$953$	22.0526	+	22.0526i	0.714352	+	0.714352i	0.967443	−	0.253090i	$-0.0814470\pi$
$953$	22.0526	+	22.0526i	0.714352	+	0.714352i	−0.253090	+	0.967443i	$0.581447\pi$
$954$	−11.1962	+	19.3923i	−0.362489	+	0.627849i
$955$	21.8827	+	1.31347i	0.708107	+	0.0425028i
$956$	−3.46410			−0.112037
$957$		−	13.6077i		−	0.439874i
$958$	−8.63397	−	32.2224i	−0.278951	−	1.04106i
$959$	−3.09808	+	2.09808i	−0.100042	+	0.0677504i
$960$	−1.33013	+	22.1603i	−0.0429297	+	0.715219i
$961$	−14.4282	+	24.9904i	−0.465426	+	0.806141i
$962$	−6.46410	+	1.73205i	−0.208411	+	0.0558436i
$963$	−9.18653	−	34.2846i	−0.296032	−	1.10481i
$964$	−19.4545	−	33.6962i	−0.626587	−	1.08528i
$965$	0.607695	−	0.124356i	0.0195624	−	0.00400315i
$966$	10.0981	+	29.1506i	0.324900	+	0.937906i
$967$	13.6865	+	51.0788i	0.440129	+	1.64258i	0.728485	+	0.685061i	$0.240225\pi$
$967$	13.6865	+	51.0788i	0.440129	+	1.64258i	−0.288356	+	0.957523i	$0.593109\pi$
$968$	2.56218	+	2.56218i	0.0823515	+	0.0823515i
$969$	35.3205	−	9.46410i	1.13466	−	0.304031i
$970$	−29.1244	−	58.2487i	−0.935127	−	1.87025i
$971$	−13.2224	+	7.63397i	−0.424328	+	0.244986i	−0.696927	−	0.717142i	$-0.745450\pi$
$971$	−13.2224	+	7.63397i	−0.424328	+	0.244986i	0.272599	+	0.962128i	$0.412117\pi$
$972$	23.3827	+	13.5000i	0.750000	+	0.433013i
$973$	21.8038	−	25.1769i	0.698999	−	0.807135i
$974$	51.5429	−	29.7583i	1.65154	−	0.953518i
$975$	35.9545	−	28.2224i	1.15146	−	0.903841i
$976$	−11.3205	+	6.53590i	−0.362361	+	0.209209i
$977$	38.5167	+	10.3205i	1.23226	+	0.330182i	0.815458	−	0.578816i	$-0.196485\pi$
$977$	38.5167	+	10.3205i	1.23226	+	0.330182i	0.416799	+	0.908999i	$0.363152\pi$
$978$	−16.0981	+	27.8827i	−0.514760	+	0.891590i
$979$	−14.9282	−	25.8564i	−0.477107	−	0.826374i
$980$	−15.4641	−	22.2679i	−0.493983	−	0.711324i
$981$		−	18.8038i		−	0.600361i
$982$	−30.9545	−	8.29423i	−0.987797	−	0.264679i
$983$	−20.9737	+	20.9737i	−0.668958	+	0.668958i	−0.957475	−	0.288517i	$-0.906838\pi$
$983$	−20.9737	+	20.9737i	−0.668958	+	0.668958i	0.288517	+	0.957475i	$0.406838\pi$
$984$	2.59808	+	0.696152i	0.0828236	+	0.0221925i
$985$	12.0000	+	4.00000i	0.382352	+	0.127451i
$986$	50.7846	+	29.3205i	1.61731	+	0.933755i
$987$	−15.1865	+	31.2846i	−0.483393	+	0.995800i
$988$	6.46410	−	24.1244i	0.205650	−	0.767498i
$989$	10.0981	−	5.83013i	0.321100	−	0.185387i
$990$	24.5885	+	8.19615i	0.781472	+	0.260491i
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	−0.795474	−	0.605988i	$-0.792778\pi$
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	0.922538	+	0.385906i	$0.126111\pi$
$992$	−10.7321	+	2.87564i	−0.340743	+	0.0913018i
$993$	5.19615	+	9.00000i	0.164895	+	0.285606i
$994$	1.73205	+	24.1244i	0.0549373	+	0.765178i
$995$	−9.80385	−	0.588457i	−0.310803	−	0.0186553i
$996$	−9.10770	+	33.9904i	−0.288588	+	1.07703i
$997$	−35.1962	−	35.1962i	−1.11467	−	1.11467i	−0.992510	−	0.122163i	$-0.961017\pi$
$997$	−35.1962	−	35.1962i	−1.11467	−	1.11467i	−0.122163	−	0.992510i	$-0.538983\pi$
$998$	−32.8564	+	8.80385i	−1.04005	+	0.278681i
$999$	−3.29423	−	0.882686i	−0.104225	−	0.0279269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.cg.b.283.1	yes	4
3.2	odd	2		945.2.cj.c.388.1		4
5.2	odd	4		315.2.cg.d.157.1	yes	4
7.5	odd	6		315.2.bs.a.103.1	yes	4
9.2	odd	6		945.2.bv.c.73.1		4
9.7	even	3		315.2.bs.d.178.1	yes	4
15.2	even	4		945.2.cj.b.577.1		4
21.5	even	6		945.2.bv.b.523.1		4
35.12	even	12		315.2.bs.d.292.1	yes	4
45.2	even	12		945.2.bv.b.262.1		4
45.7	odd	12		315.2.bs.a.52.1	✓	4
63.47	even	6		945.2.cj.b.208.1		4
63.61	odd	6		315.2.cg.d.313.1	yes	4
105.47	odd	12		945.2.bv.c.712.1		4
315.47	odd	12		945.2.cj.c.397.1		4
315.187	even	12	inner	315.2.cg.b.187.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.a.52.1	✓	4	45.7	odd	12
315.2.bs.a.103.1	yes	4	7.5	odd	6
315.2.bs.d.178.1	yes	4	9.7	even	3
315.2.bs.d.292.1	yes	4	35.12	even	12
315.2.cg.b.187.1	yes	4	315.187	even	12	inner
315.2.cg.b.283.1	yes	4	1.1	even	1	trivial
315.2.cg.d.157.1	yes	4	5.2	odd	4
315.2.cg.d.313.1	yes	4	63.61	odd	6
945.2.bv.b.262.1		4	45.2	even	12
945.2.bv.b.523.1		4	21.5	even	6
945.2.bv.c.73.1		4	9.2	odd	6
945.2.bv.c.712.1		4	105.47	odd	12
945.2.cj.b.208.1		4	63.47	even	6
945.2.cj.b.577.1		4	15.2	even	4
945.2.cj.c.388.1		4	3.2	odd	2
945.2.cj.c.397.1		4	315.47	odd	12

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 1.86603i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(1.00000 + 2.00000i) q^{5} +(3.23205 + 0.866025i) q^{6} +(-2.59808 - 0.500000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 1.86603i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(1.00000 + 2.00000i) q^{5} +(3.23205 + 0.866025i) q^{6} +(-2.59808 - 0.500000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(3.23205 - 2.86603i) q^{10} -2.00000 q^{11} -3.00000i q^{12} +(1.36603 + 5.09808i) q^{13} +(0.366025 + 5.09808i) q^{14} +(-3.86603 - 0.232051i) q^{15} +(-2.23205 + 3.86603i) q^{16} +(-7.46410 + 2.00000i) q^{17} +(-4.09808 + 4.09808i) q^{18} +(1.36603 + 2.36603i) q^{19} +(-3.23205 - 2.13397i) q^{20} +(3.00000 - 3.46410i) q^{21} +(1.00000 + 3.73205i) q^{22} +(-2.46410 - 2.46410i) q^{23} +(0.866025 - 0.232051i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(8.83013 - 5.09808i) q^{26} +5.19615 q^{27} +(4.33013 - 1.50000i) q^{28} +(3.40192 - 1.96410i) q^{29} +(1.50000 + 7.33013i) q^{30} +(-1.26795 + 0.732051i) q^{31} +(7.33013 + 1.96410i) q^{32} +(1.73205 - 3.00000i) q^{33} +(7.46410 + 12.9282i) q^{34} +(-1.59808 - 5.69615i) q^{35} +(4.50000 + 2.59808i) q^{36} +(-0.633975 - 0.169873i) q^{37} +(3.73205 - 3.73205i) q^{38} +(-8.83013 - 2.36603i) q^{39} +(0.366025 - 1.09808i) q^{40} +(2.59808 + 1.50000i) q^{41} +(-7.96410 - 3.86603i) q^{42} +(-0.866025 + 3.23205i) q^{43} +(3.00000 - 1.73205i) q^{44} +(3.69615 - 5.59808i) q^{45} +(-3.36603 + 5.83013i) q^{46} +(-7.33013 + 1.96410i) q^{47} +(-3.86603 - 6.69615i) q^{48} +(6.50000 + 2.59808i) q^{49} +(8.96410 + 3.59808i) q^{50} +(3.46410 - 12.9282i) q^{51} +(-6.46410 - 6.46410i) q^{52} +(3.73205 - 1.00000i) q^{53} +(-2.59808 - 9.69615i) q^{54} +(-2.00000 - 4.00000i) q^{55} +(0.767949 + 1.13397i) q^{56} -4.73205 q^{57} +(-5.36603 - 5.36603i) q^{58} +(-7.56218 - 13.0981i) q^{59} +(6.00000 - 3.00000i) q^{60} +(2.53590 + 1.46410i) q^{61} +(2.00000 + 2.00000i) q^{62} +(2.59808 + 7.50000i) q^{63} -5.73205i q^{64} +(-8.83013 + 7.83013i) q^{65} +(-6.46410 - 1.73205i) q^{66} +(6.09808 + 1.63397i) q^{67} +(9.46410 - 9.46410i) q^{68} +(5.83013 - 1.56218i) q^{69} +(-9.83013 + 5.83013i) q^{70} +4.73205 q^{71} +(-0.401924 + 1.50000i) q^{72} +(0.928203 + 3.46410i) q^{73} +1.26795i q^{74} +(-3.40192 - 7.96410i) q^{75} +(-4.09808 - 2.36603i) q^{76} +(5.19615 + 1.00000i) q^{77} +17.6603i q^{78} +(-3.92820 - 2.26795i) q^{79} +(-9.96410 - 0.598076i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(1.50000 - 5.59808i) q^{82} +(-11.3301 - 3.03590i) q^{83} +(-1.50000 + 7.79423i) q^{84} +(-11.4641 - 12.9282i) q^{85} +6.46410 q^{86} +6.80385i q^{87} +(0.732051 + 0.732051i) q^{88} +(7.46410 + 12.9282i) q^{89} +(-12.2942 - 4.09808i) q^{90} +(-1.00000 - 13.9282i) q^{91} +(5.83013 + 1.56218i) q^{92} -2.53590i q^{93} +(7.33013 + 12.6962i) q^{94} +(-3.36603 + 5.09808i) q^{95} +(-9.29423 + 9.29423i) q^{96} +(3.90192 - 14.5622i) q^{97} +(1.59808 - 13.4282i) q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{4} + 4 q^{5} + 6 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^4 + 4 * q^5 + 6 * q^6 + 2 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} - 6 q^{4} + 4 q^{5} + 6 q^{6} + 2 q^{8} - 6 q^{9} + 6 q^{10} - 8 q^{11} + 2 q^{13} - 2 q^{14} - 12 q^{15} - 2 q^{16} - 16 q^{17} - 6 q^{18} + 2 q^{19} - 6 q^{20} + 12 q^{21} + 4 q^{22} + 4 q^{23} - 12 q^{25} + 18 q^{26} + 24 q^{29} + 6 q^{30} - 12 q^{31} + 12 q^{32} + 16 q^{34} + 4 q^{35} + 18 q^{36} - 6 q^{37} + 8 q^{38} - 18 q^{39} - 2 q^{40} - 18 q^{42} + 12 q^{44} - 6 q^{45} - 10 q^{46} - 12 q^{47} - 12 q^{48} + 26 q^{49} + 22 q^{50} - 12 q^{52} + 8 q^{53} - 8 q^{55} + 10 q^{56} - 12 q^{57} - 18 q^{58} - 6 q^{59} + 24 q^{60} + 24 q^{61} + 8 q^{62} - 18 q^{65} - 12 q^{66} + 14 q^{67} + 24 q^{68} + 6 q^{69} - 22 q^{70} + 12 q^{71} - 12 q^{72} - 24 q^{73} - 24 q^{75} - 6 q^{76} + 12 q^{79} - 26 q^{80} - 18 q^{81} + 6 q^{82} - 28 q^{83} - 6 q^{84} - 32 q^{85} + 12 q^{86} - 4 q^{88} + 16 q^{89} - 18 q^{90} - 4 q^{91} + 6 q^{92} + 12 q^{94} - 10 q^{95} - 6 q^{96} + 26 q^{97} - 4 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^4 + 4 * q^5 + 6 * q^6 + 2 * q^8 - 6 * q^9 + 6 * q^10 - 8 * q^11 + 2 * q^13 - 2 * q^14 - 12 * q^15 - 2 * q^16 - 16 * q^17 - 6 * q^18 + 2 * q^19 - 6 * q^20 + 12 * q^21 + 4 * q^22 + 4 * q^23 - 12 * q^25 + 18 * q^26 + 24 * q^29 + 6 * q^30 - 12 * q^31 + 12 * q^32 + 16 * q^34 + 4 * q^35 + 18 * q^36 - 6 * q^37 + 8 * q^38 - 18 * q^39 - 2 * q^40 - 18 * q^42 + 12 * q^44 - 6 * q^45 - 10 * q^46 - 12 * q^47 - 12 * q^48 + 26 * q^49 + 22 * q^50 - 12 * q^52 + 8 * q^53 - 8 * q^55 + 10 * q^56 - 12 * q^57 - 18 * q^58 - 6 * q^59 + 24 * q^60 + 24 * q^61 + 8 * q^62 - 18 * q^65 - 12 * q^66 + 14 * q^67 + 24 * q^68 + 6 * q^69 - 22 * q^70 + 12 * q^71 - 12 * q^72 - 24 * q^73 - 24 * q^75 - 6 * q^76 + 12 * q^79 - 26 * q^80 - 18 * q^81 + 6 * q^82 - 28 * q^83 - 6 * q^84 - 32 * q^85 + 12 * q^86 - 4 * q^88 + 16 * q^89 - 18 * q^90 - 4 * q^91 + 6 * q^92 + 12 * q^94 - 10 * q^95 - 6 * q^96 + 26 * q^97 - 4 * q^98 + 12 * q^99

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