LMFDB - Embedded newform 280.2.bv.b.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(117,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 3, 10]))

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

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

chi := DirichletCharacter("280.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bv (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:	$2.23581125660$
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			157.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	280.157
Dual form			280.2.bv.b.173.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 1.36603i) q^{2} +(0.500000 + 1.86603i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-2.36603 + 1.36603i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.633975 + 0.366025i) q^{9} +O(q^{10})$	\(q+(0.366025 + 1.36603i) q^{2} +(0.500000 + 1.86603i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-2.36603 + 1.36603i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.633975 + 0.366025i) q^{9} +(-1.00000 + 3.00000i) q^{10} +(-0.633975 - 0.366025i) q^{11} +(-2.73205 - 2.73205i) q^{12} +(3.00000 - 3.00000i) q^{13} +(-2.09808 - 3.09808i) q^{14} +(-1.36603 + 4.09808i) q^{15} +(2.00000 - 3.46410i) q^{16} +(1.09808 + 4.09808i) q^{17} +(-0.732051 - 0.732051i) q^{18} +(3.00000 - 1.73205i) q^{19} +(-4.46410 - 0.267949i) q^{20} +(-2.86603 - 4.23205i) q^{21} +(0.267949 - 1.00000i) q^{22} +(-1.50000 - 0.401924i) q^{23} +(2.73205 - 4.73205i) q^{24} +(1.96410 + 4.59808i) q^{25} +(5.19615 + 3.00000i) q^{26} +(3.09808 + 3.09808i) q^{27} +(3.46410 - 4.00000i) q^{28} -4.46410 q^{29} +(-6.09808 - 0.366025i) q^{30} +(-8.83013 - 5.09808i) q^{31} +(5.46410 + 1.46410i) q^{32} +(0.366025 - 1.36603i) q^{33} +(-5.19615 + 3.00000i) q^{34} +(-5.73205 - 1.46410i) q^{35} +(0.732051 - 1.26795i) q^{36} +(6.46410 + 1.73205i) q^{37} +(3.46410 + 3.46410i) q^{38} +(7.09808 + 4.09808i) q^{39} +(-1.26795 - 6.19615i) q^{40} +0.464102i q^{41} +(4.73205 - 5.46410i) q^{42} +(2.36603 + 2.36603i) q^{43} +1.46410 q^{44} +(-1.63397 - 0.0980762i) q^{45} -2.19615i q^{46} +(0.633975 + 0.169873i) q^{47} +(7.46410 + 2.00000i) q^{48} +(5.50000 - 4.33013i) q^{49} +(-5.56218 + 4.36603i) q^{50} +(-7.09808 + 4.09808i) q^{51} +(-2.19615 + 8.19615i) q^{52} +(3.00000 - 0.803848i) q^{53} +(-3.09808 + 5.36603i) q^{54} +(-0.732051 - 1.46410i) q^{55} +(6.73205 + 3.26795i) q^{56} +(4.73205 + 4.73205i) q^{57} +(-1.63397 - 6.09808i) q^{58} +(7.73205 + 4.46410i) q^{59} +(-1.73205 - 8.46410i) q^{60} +(-4.96410 - 8.59808i) q^{61} +(3.73205 - 13.9282i) q^{62} +(1.26795 - 1.46410i) q^{63} +8.00000i q^{64} +(9.29423 - 1.90192i) q^{65} +2.00000 q^{66} +(1.03590 + 3.86603i) q^{67} +(-6.00000 - 6.00000i) q^{68} -3.00000i q^{69} +(-0.0980762 - 8.36603i) q^{70} +15.4641 q^{71} +(2.00000 + 0.535898i) q^{72} +(-8.09808 + 2.16987i) q^{73} +9.46410i q^{74} +(-7.59808 + 5.96410i) q^{75} +(-3.46410 + 6.00000i) q^{76} +(1.90192 + 0.366025i) q^{77} +(-3.00000 + 11.1962i) q^{78} +(-11.1962 + 6.46410i) q^{79} +(8.00000 - 4.00000i) q^{80} +(-5.33013 + 9.23205i) q^{81} +(-0.633975 + 0.169873i) q^{82} +(4.56218 - 4.56218i) q^{83} +(9.19615 + 4.46410i) q^{84} +(-3.00000 + 9.00000i) q^{85} +(-2.36603 + 4.09808i) q^{86} +(-2.23205 - 8.33013i) q^{87} +(0.535898 + 2.00000i) q^{88} +(-8.59808 - 14.8923i) q^{89} +(-0.464102 - 2.26795i) q^{90} +(-4.90192 + 10.0981i) q^{91} +(3.00000 - 0.803848i) q^{92} +(5.09808 - 19.0263i) q^{93} +0.928203i q^{94} +(7.73205 + 0.464102i) q^{95} +10.9282i q^{96} +(6.26795 - 6.26795i) q^{97} +(7.92820 + 5.92820i) q^{98} +0.535898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} + 4 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 + 4 * q^5 - 6 * q^6 - 10 * q^7 - 8 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} + 4 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9} - 4 q^{10} - 6 q^{11} - 4 q^{12} + 12 q^{13} + 2 q^{14} - 2 q^{15} + 8 q^{16} - 6 q^{17} + 4 q^{18} + 12 q^{19} - 4 q^{20} - 8 q^{21} + 8 q^{22} - 6 q^{23} + 4 q^{24} - 6 q^{25} + 2 q^{27} - 4 q^{29} - 14 q^{30} - 18 q^{31} + 8 q^{32} - 2 q^{33} - 16 q^{35} - 4 q^{36} + 12 q^{37} + 18 q^{39} - 12 q^{40} + 12 q^{42} + 6 q^{43} - 8 q^{44} - 10 q^{45} + 6 q^{47} + 16 q^{48} + 22 q^{49} + 2 q^{50} - 18 q^{51} + 12 q^{52} + 12 q^{53} - 2 q^{54} + 4 q^{55} + 20 q^{56} + 12 q^{57} - 10 q^{58} + 24 q^{59} - 6 q^{61} + 8 q^{62} + 12 q^{63} + 6 q^{65} + 8 q^{66} + 18 q^{67} - 24 q^{68} + 10 q^{70} + 48 q^{71} + 8 q^{72} - 22 q^{73} - 20 q^{75} + 18 q^{77} - 12 q^{78} - 24 q^{79} + 32 q^{80} - 4 q^{81} - 6 q^{82} - 6 q^{83} + 16 q^{84} - 12 q^{85} - 6 q^{86} - 2 q^{87} + 16 q^{88} - 24 q^{89} + 12 q^{90} - 30 q^{91} + 12 q^{92} + 10 q^{93} + 24 q^{95} + 32 q^{97} + 4 q^{98} + 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 + 4 * q^5 - 6 * q^6 - 10 * q^7 - 8 * q^8 - 6 * q^9 - 4 * q^10 - 6 * q^11 - 4 * q^12 + 12 * q^13 + 2 * q^14 - 2 * q^15 + 8 * q^16 - 6 * q^17 + 4 * q^18 + 12 * q^19 - 4 * q^20 - 8 * q^21 + 8 * q^22 - 6 * q^23 + 4 * q^24 - 6 * q^25 + 2 * q^27 - 4 * q^29 - 14 * q^30 - 18 * q^31 + 8 * q^32 - 2 * q^33 - 16 * q^35 - 4 * q^36 + 12 * q^37 + 18 * q^39 - 12 * q^40 + 12 * q^42 + 6 * q^43 - 8 * q^44 - 10 * q^45 + 6 * q^47 + 16 * q^48 + 22 * q^49 + 2 * q^50 - 18 * q^51 + 12 * q^52 + 12 * q^53 - 2 * q^54 + 4 * q^55 + 20 * q^56 + 12 * q^57 - 10 * q^58 + 24 * q^59 - 6 * q^61 + 8 * q^62 + 12 * q^63 + 6 * q^65 + 8 * q^66 + 18 * q^67 - 24 * q^68 + 10 * q^70 + 48 * q^71 + 8 * q^72 - 22 * q^73 - 20 * q^75 + 18 * q^77 - 12 * q^78 - 24 * q^79 + 32 * q^80 - 4 * q^81 - 6 * q^82 - 6 * q^83 + 16 * q^84 - 12 * q^85 - 6 * q^86 - 2 * q^87 + 16 * q^88 - 24 * q^89 + 12 * q^90 - 30 * q^91 + 12 * q^92 + 10 * q^93 + 24 * q^95 + 32 * q^97 + 4 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$3$	0.500000	+	1.86603i	0.288675	+	1.07735i	0.946112	+	0.323840i	$0.104974\pi$
$3$	0.500000	+	1.86603i	0.288675	+	1.07735i	−0.657437	+	0.753510i	$0.728359\pi$
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$6$	−2.36603	+	1.36603i	−0.965926	+	0.557678i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	−0.633975	+	0.366025i	−0.211325	+	0.122008i
$10$	−1.00000	+	3.00000i	−0.316228	+	0.948683i
$11$	−0.633975	−	0.366025i	−0.191151	−	0.110361i	0.401371	−	0.915916i	$-0.368534\pi$
$11$	−0.633975	−	0.366025i	−0.191151	−	0.110361i	−0.592521	+	0.805555i	$0.701867\pi$
$12$	−2.73205	−	2.73205i	−0.788675	−	0.788675i
$13$	3.00000	−	3.00000i	0.832050	−	0.832050i	−0.155747	−	0.987797i	$-0.549778\pi$
$13$	3.00000	−	3.00000i	0.832050	−	0.832050i	0.987797	+	0.155747i	$0.0497784\pi$
$14$	−2.09808	−	3.09808i	−0.560734	−	0.827996i
$15$	−1.36603	+	4.09808i	−0.352706	+	1.05812i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	1.09808	+	4.09808i	0.266323	+	0.993929i	0.961436	+	0.275029i	$0.0886875\pi$
$17$	1.09808	+	4.09808i	0.266323	+	0.993929i	−0.695113	+	0.718900i	$0.744646\pi$
$18$	−0.732051	−	0.732051i	−0.172546	−	0.172546i
$19$	3.00000	−	1.73205i	0.688247	−	0.397360i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.00000	−	1.73205i	0.688247	−	0.397360i	0.802955	+	0.596040i	$0.203260\pi$
$20$	−4.46410	−	0.267949i	−0.998203	−	0.0599153i
$21$	−2.86603	−	4.23205i	−0.625418	−	0.923509i
$22$	0.267949	−	1.00000i	0.0571270	−	0.213201i
$23$	−1.50000	−	0.401924i	−0.312772	−	0.0838069i	0.0990186	−	0.995086i	$-0.468430\pi$
$23$	−1.50000	−	0.401924i	−0.312772	−	0.0838069i	−0.411790	+	0.911279i	$0.635096\pi$
$24$	2.73205	−	4.73205i	0.557678	−	0.965926i
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$	5.19615	+	3.00000i	1.01905	+	0.588348i
$27$	3.09808	+	3.09808i	0.596225	+	0.596225i
$28$	3.46410	−	4.00000i	0.654654	−	0.755929i
$29$	−4.46410			−0.828963			−0.414481	−	0.910058i	$-0.636037\pi$
$29$	−4.46410			−0.828963			−0.414481	+	0.910058i	$0.636037\pi$
$30$	−6.09808	−	0.366025i	−1.11335	−	0.0668268i
$31$	−8.83013	−	5.09808i	−1.58594	−	0.915642i	−0.993967	−	0.109682i	$-0.965017\pi$
$31$	−8.83013	−	5.09808i	−1.58594	−	0.915642i	−0.591971	−	0.805959i	$-0.701650\pi$
$32$	5.46410	+	1.46410i	0.965926	+	0.258819i
$33$	0.366025	−	1.36603i	0.0637168	−	0.237795i
$34$	−5.19615	+	3.00000i	−0.891133	+	0.514496i
$35$	−5.73205	−	1.46410i	−0.968893	−	0.247478i
$36$	0.732051	−	1.26795i	0.122008	−	0.211325i
$37$	6.46410	+	1.73205i	1.06269	+	0.284747i	0.747487	−	0.664276i	$-0.231260\pi$
$37$	6.46410	+	1.73205i	1.06269	+	0.284747i	0.315205	+	0.949024i	$0.397927\pi$
$38$	3.46410	+	3.46410i	0.561951	+	0.561951i
$39$	7.09808	+	4.09808i	1.13660	+	0.656217i
$40$	−1.26795	−	6.19615i	−0.200480	−	0.979698i
$41$			0.464102i			0.0724805i	0.999343	+	0.0362402i	$0.0115382\pi$
$41$			0.464102i			0.0724805i	−0.999343	+	0.0362402i	$0.988462\pi$
$42$	4.73205	−	5.46410i	0.730171	−	0.843129i
$43$	2.36603	+	2.36603i	0.360815	+	0.360815i	0.864113	−	0.503298i	$-0.167880\pi$
$43$	2.36603	+	2.36603i	0.360815	+	0.360815i	−0.503298	+	0.864113i	$0.667880\pi$
$44$	1.46410			0.220722
$45$	−1.63397	−	0.0980762i	−0.243579	−	0.0146203i
$46$		−	2.19615i		−	0.323805i
$47$	0.633975	+	0.169873i	0.0924747	+	0.0247785i	0.304760	−	0.952429i	$-0.401424\pi$
$47$	0.633975	+	0.169873i	0.0924747	+	0.0247785i	−0.212285	+	0.977208i	$0.568091\pi$
$48$	7.46410	+	2.00000i	1.07735	+	0.288675i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−5.56218	+	4.36603i	−0.786611	+	0.617449i
$51$	−7.09808	+	4.09808i	−0.993929	+	0.573845i
$52$	−2.19615	+	8.19615i	−0.304552	+	1.13660i
$53$	3.00000	−	0.803848i	0.412082	−	0.110417i	−0.0468214	−	0.998903i	$-0.514909\pi$
$53$	3.00000	−	0.803848i	0.412082	−	0.110417i	0.458903	+	0.888486i	$0.348243\pi$
$54$	−3.09808	+	5.36603i	−0.421595	+	0.730224i
$55$	−0.732051	−	1.46410i	−0.0987097	−	0.197419i
$56$	6.73205	+	3.26795i	0.899608	+	0.436698i
$57$	4.73205	+	4.73205i	0.626775	+	0.626775i
$58$	−1.63397	−	6.09808i	−0.214551	−	0.800717i
$59$	7.73205	+	4.46410i	1.00663	+	0.581177i	0.910202	−	0.414164i	$-0.135926\pi$
$59$	7.73205	+	4.46410i	1.00663	+	0.581177i	0.0964249	+	0.995340i	$0.469259\pi$
$60$	−1.73205	−	8.46410i	−0.223607	−	1.09271i
$61$	−4.96410	−	8.59808i	−0.635588	−	1.10087i	−0.986390	−	0.164421i	$-0.947424\pi$
$61$	−4.96410	−	8.59808i	−0.635588	−	1.10087i	0.350802	−	0.936450i	$-0.385909\pi$
$62$	3.73205	−	13.9282i	0.473971	−	1.76888i
$63$	1.26795	−	1.46410i	0.159747	−	0.184459i
$64$			8.00000i			1.00000i
$65$	9.29423	−	1.90192i	1.15281	−	0.235905i
$66$	2.00000			0.246183
$67$	1.03590	+	3.86603i	0.126555	+	0.472310i	0.999890	−	0.0148095i	$-0.00471420\pi$
$67$	1.03590	+	3.86603i	0.126555	+	0.472310i	−0.873335	+	0.487120i	$0.838048\pi$
$68$	−6.00000	−	6.00000i	−0.727607	−	0.727607i
$69$		−	3.00000i		−	0.361158i
$70$	−0.0980762	−	8.36603i	−0.0117223	−	0.999931i
$71$	15.4641			1.83525			0.917626	−	0.397446i	$-0.130103\pi$
$71$	15.4641			1.83525			0.917626	+	0.397446i	$0.130103\pi$
$72$	2.00000	+	0.535898i	0.235702	+	0.0631562i
$73$	−8.09808	+	2.16987i	−0.947808	+	0.253964i	−0.699432	−	0.714699i	$-0.746564\pi$
$73$	−8.09808	+	2.16987i	−0.947808	+	0.253964i	−0.248376	+	0.968664i	$0.579897\pi$
$74$			9.46410i			1.10018i
$75$	−7.59808	+	5.96410i	−0.877350	+	0.688675i
$76$	−3.46410	+	6.00000i	−0.397360	+	0.688247i
$77$	1.90192	+	0.366025i	0.216744	+	0.0417125i
$78$	−3.00000	+	11.1962i	−0.339683	+	1.26771i
$79$	−11.1962	+	6.46410i	−1.25967	+	0.727268i	−0.973009	−	0.230765i	$-0.925877\pi$
$79$	−11.1962	+	6.46410i	−1.25967	+	0.727268i	−0.286656	+	0.958034i	$0.592544\pi$
$80$	8.00000	−	4.00000i	0.894427	−	0.447214i
$81$	−5.33013	+	9.23205i	−0.592236	+	1.02578i
$82$	−0.633975	+	0.169873i	−0.0700108	+	0.0187593i
$83$	4.56218	−	4.56218i	0.500764	−	0.500764i	−0.410911	−	0.911675i	$-0.634789\pi$
$83$	4.56218	−	4.56218i	0.500764	−	0.500764i	0.911675	+	0.410911i	$0.134789\pi$
$84$	9.19615	+	4.46410i	1.00338	+	0.487073i
$85$	−3.00000	+	9.00000i	−0.325396	+	0.976187i
$86$	−2.36603	+	4.09808i	−0.255135	+	0.441907i
$87$	−2.23205	−	8.33013i	−0.239301	−	0.893083i
$88$	0.535898	+	2.00000i	0.0571270	+	0.213201i
$89$	−8.59808	−	14.8923i	−0.911394	−	1.57858i	−0.812096	−	0.583523i	$-0.801674\pi$
$89$	−8.59808	−	14.8923i	−0.911394	−	1.57858i	−0.0992979	−	0.995058i	$-0.531660\pi$
$90$	−0.464102	−	2.26795i	−0.0489206	−	0.239063i
$91$	−4.90192	+	10.0981i	−0.513861	+	1.05857i
$92$	3.00000	−	0.803848i	0.312772	−	0.0838069i
$93$	5.09808	−	19.0263i	0.528646	−	1.97293i
$94$			0.928203i			0.0957369i
$95$	7.73205	+	0.464102i	0.793292	+	0.0476158i
$96$			10.9282i			1.11536i
$97$	6.26795	−	6.26795i	0.636414	−	0.636414i	−0.313255	−	0.949669i	$-0.601420\pi$
$97$	6.26795	−	6.26795i	0.636414	−	0.636414i	0.949669	+	0.313255i	$0.101420\pi$
$98$	7.92820	+	5.92820i	0.800869	+	0.598839i
$99$	0.535898			0.0538598
$100$	−8.00000	−	6.00000i	−0.800000	−	0.600000i
$101$	5.06218	−	8.76795i	0.503706	−	0.872444i	−0.496285	−	0.868159i	$-0.665303\pi$
$101$	5.06218	−	8.76795i	0.503706	−	0.872444i	0.999991	−	0.00428406i	$-0.00136366\pi$
$102$	−8.19615	−	8.19615i	−0.811540	−	0.811540i
$103$	3.33013	−	12.4282i	0.328127	−	1.22459i	−0.583003	−	0.812470i	$-0.698123\pi$
$103$	3.33013	−	12.4282i	0.328127	−	1.22459i	0.911131	−	0.412118i	$-0.135211\pi$
$104$	−12.0000			−1.17670
$105$	−0.133975	−	11.4282i	−0.0130746	−	1.11528i
$106$	2.19615	+	3.80385i	0.213309	+	0.369462i
$107$	−5.33013	−	1.42820i	−0.515283	−	0.138070i	−0.00819905	−	0.999966i	$-0.502610\pi$
$107$	−5.33013	−	1.42820i	−0.515283	−	0.138070i	−0.507084	+	0.861897i	$0.669277\pi$
$108$	−8.46410	−	2.26795i	−0.814459	−	0.218234i
$109$	2.13397	−	3.69615i	0.204398	−	0.354027i	−0.745543	−	0.666458i	$-0.767810\pi$
$109$	2.13397	−	3.69615i	0.204398	−	0.354027i	0.949941	+	0.312430i	$0.101143\pi$
$110$	1.73205	−	1.53590i	0.165145	−	0.146442i
$111$			12.9282i			1.22709i
$112$	−2.00000	+	10.3923i	−0.188982	+	0.981981i
$113$	2.53590	−	2.53590i	0.238557	−	0.238557i	−0.577695	−	0.816253i	$-0.696048\pi$
$113$	2.53590	−	2.53590i	0.238557	−	0.238557i	0.816253	+	0.577695i	$0.196048\pi$
$114$	−4.73205	+	8.19615i	−0.443197	+	0.767640i
$115$	−2.30385	−	2.59808i	−0.214835	−	0.242272i
$116$	7.73205	−	4.46410i	0.717903	−	0.414481i
$117$	−0.803848	+	3.00000i	−0.0743157	+	0.277350i
$118$	−3.26795	+	12.1962i	−0.300839	+	1.12275i
$119$	−6.29423	−	9.29423i	−0.576991	−	0.852001i
$120$	10.9282	−	5.46410i	0.997604	−	0.498802i
$121$	−5.23205	−	9.06218i	−0.475641	−	0.823834i
$122$	9.92820	−	9.92820i	0.898857	−	0.898857i
$123$	−0.866025	+	0.232051i	−0.0780869	+	0.0209233i
$124$	20.3923			1.83128
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$	2.46410	+	1.19615i	0.219520	+	0.106562i
$127$	−11.0000	−	11.0000i	−0.976092	−	0.976092i	0.0236286	−	0.999721i	$-0.492478\pi$
$127$	−11.0000	−	11.0000i	−0.976092	−	0.976092i	−0.999721	+	0.0236286i	$0.992478\pi$
$128$	−10.9282	+	2.92820i	−0.965926	+	0.258819i
$129$	−3.23205	+	5.59808i	−0.284566	+	0.492883i
$130$	6.00000	+	12.0000i	0.526235	+	1.05247i
$131$	−3.73205	−	6.46410i	−0.326071	−	0.564771i	0.655658	−	0.755058i	$-0.272391\pi$
$131$	−3.73205	−	6.46410i	−0.326071	−	0.564771i	−0.981728	+	0.190287i	$0.939058\pi$
$132$	0.732051	+	2.73205i	0.0637168	+	0.237795i
$133$	−6.00000	+	6.92820i	−0.520266	+	0.600751i
$134$	−4.90192	+	2.83013i	−0.423462	+	0.244486i
$135$	1.96410	+	9.59808i	0.169043	+	0.826071i
$136$	6.00000	−	10.3923i	0.514496	−	0.891133i
$137$	−8.19615	+	2.19615i	−0.700245	+	0.187630i	−0.591340	−	0.806422i	$-0.701401\pi$
$137$	−8.19615	+	2.19615i	−0.700245	+	0.187630i	−0.108904	+	0.994052i	$0.534734\pi$
$138$	4.09808	−	1.09808i	0.348851	−	0.0934745i
$139$		−	1.26795i		−	0.107546i	−0.998553	−	0.0537730i	$-0.982875\pi$
$139$		−	1.26795i		−	0.107546i	0.998553	−	0.0537730i	$-0.0171247\pi$
$140$	11.3923	−	3.19615i	0.962825	−	0.270124i
$141$			1.26795i			0.106781i
$142$	5.66025	+	21.1244i	0.474998	+	1.77272i
$143$	−3.00000	+	0.803848i	−0.250873	+	0.0672211i
$144$			2.92820i			0.244017i
$145$	−8.33013	−	5.50000i	−0.691779	−	0.456750i
$146$	−5.92820	−	10.2679i	−0.490622	−	0.849782i
$147$	10.8301	+	8.09808i	0.893254	+	0.667918i
$148$	−12.9282	+	3.46410i	−1.06269	+	0.284747i
$149$	11.3301	+	19.6244i	0.928200	+	1.60769i	0.786332	+	0.617804i	$0.211978\pi$
$149$	11.3301	+	19.6244i	0.928200	+	1.60769i	0.141868	+	0.989886i	$0.454689\pi$
$150$	−10.9282	−	8.19615i	−0.892284	−	0.669213i
$151$	−6.90192	+	11.9545i	−0.561671	+	0.972842i	0.435680	+	0.900101i	$0.356508\pi$
$151$	−6.90192	+	11.9545i	−0.561671	+	0.972842i	−0.997351	+	0.0727405i	$0.976826\pi$
$152$	−9.46410	−	2.53590i	−0.767640	−	0.205689i
$153$	−2.19615	−	2.19615i	−0.177548	−	0.177548i
$154$	0.196152	+	2.73205i	0.0158064	+	0.220155i
$155$	−10.1962	−	20.3923i	−0.818975	−	1.63795i
$156$	−16.3923			−1.31243
$157$	−17.0263	+	4.56218i	−1.35885	+	0.364101i	−0.863392	−	0.504533i	$-0.831665\pi$
$157$	−17.0263	+	4.56218i	−1.35885	+	0.364101i	−0.495453	+	0.868635i	$0.664998\pi$
$158$	−12.9282	−	12.9282i	−1.02851	−	1.02851i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$	8.39230	+	9.46410i	0.663470	+	0.748203i
$161$	4.09808	−	0.294229i	0.322974	−	0.0231885i
$162$	−14.5622	−	3.90192i	−1.14411	−	0.306564i
$163$	0.973721	−	3.63397i	0.0762677	−	0.284635i	−0.917250	−	0.398312i	$-0.869596\pi$
$163$	0.973721	−	3.63397i	0.0762677	−	0.284635i	0.993518	+	0.113677i	$0.0362629\pi$
$164$	−0.464102	−	0.803848i	−0.0362402	−	0.0627700i
$165$	2.36603	−	2.09808i	0.184195	−	0.163335i
$166$	7.90192	+	4.56218i	0.613308	+	0.354094i
$167$	3.29423	−	3.29423i	0.254915	−	0.254915i	−0.568067	−	0.822982i	$-0.692309\pi$
$167$	3.29423	−	3.29423i	0.254915	−	0.254915i	0.822982	+	0.568067i	$0.192309\pi$
$168$	−2.73205	+	14.1962i	−0.210782	+	1.09526i
$169$		−	5.00000i		−	0.384615i
$170$	−13.3923	−	0.803848i	−1.02714	−	0.0616523i
$171$	−1.26795	+	2.19615i	−0.0969625	+	0.167944i
$172$	−6.46410	−	1.73205i	−0.492883	−	0.132068i
$173$	−0.464102	−	0.124356i	−0.0352850	−	0.00945459i	0.241133	−	0.970492i	$-0.422481\pi$
$173$	−0.464102	−	0.124356i	−0.0352850	−	0.00945459i	−0.276418	+	0.961037i	$0.589148\pi$
$174$	10.5622	−	6.09808i	0.800717	−	0.462294i
$175$	−8.89230	−	9.79423i	−0.672195	−	0.740374i
$176$	−2.53590	+	1.46410i	−0.191151	+	0.110361i
$177$	−4.46410	+	16.6603i	−0.335542	+	1.25226i
$178$	17.1962	−	17.1962i	1.28891	−	1.28891i
$179$	7.02628	−	12.1699i	0.525169	−	0.909619i	−0.474402	−	0.880309i	$-0.657336\pi$
$179$	7.02628	−	12.1699i	0.525169	−	0.909619i	0.999570	−	0.0293105i	$-0.00933115\pi$
$180$	2.92820	−	1.46410i	0.218255	−	0.109128i
$181$	−22.5167			−1.67365			−0.836825	−	0.547470i	$-0.815591\pi$
$181$	−22.5167			−1.67365			−0.836825	+	0.547470i	$0.815591\pi$
$182$	−15.5885	−	3.00000i	−1.15549	−	0.222375i
$183$	13.5622	−	13.5622i	1.00255	−	1.00255i
$184$	2.19615	+	3.80385i	0.161903	+	0.280423i
$185$	9.92820	+	11.1962i	0.729936	+	0.823157i
$186$	27.8564			2.04253
$187$	0.803848	−	3.00000i	0.0587832	−	0.219382i
$188$	−1.26795	+	0.339746i	−0.0924747	+	0.0247785i
$189$	−10.4282	−	5.06218i	−0.758540	−	0.368219i
$190$	2.19615	+	10.7321i	0.159326	+	0.778585i
$191$	−1.56218	−	2.70577i	−0.113035	−	0.195783i	0.803957	−	0.594687i	$-0.202724\pi$
$191$	−1.56218	−	2.70577i	−0.113035	−	0.195783i	−0.916993	+	0.398904i	$0.869391\pi$
$192$	−14.9282	+	4.00000i	−1.07735	+	0.288675i
$193$	3.09808	+	11.5622i	0.223004	+	0.832264i	0.983194	+	0.182563i	$0.0584393\pi$
$193$	3.09808	+	11.5622i	0.223004	+	0.832264i	−0.760190	+	0.649701i	$0.774894\pi$
$194$	10.8564	+	6.26795i	0.779445	+	0.450013i
$195$	8.19615	+	16.3923i	0.586939	+	1.17388i
$196$	−5.19615	+	13.0000i	−0.371154	+	0.928571i
$197$	−5.53590	+	5.53590i	−0.394416	+	0.394416i	−0.876258	−	0.481842i	$-0.839968\pi$
$197$	−5.53590	+	5.53590i	−0.394416	+	0.394416i	0.481842	+	0.876258i	$0.339968\pi$
$198$	0.196152	+	0.732051i	0.0139399	+	0.0520246i
$199$	−1.73205	+	3.00000i	−0.122782	+	0.212664i	−0.920864	−	0.389885i	$-0.872515\pi$
$199$	−1.73205	+	3.00000i	−0.122782	+	0.212664i	0.798082	+	0.602549i	$0.205848\pi$
$200$	5.26795	−	13.1244i	0.372500	−	0.928032i
$201$	−6.69615	+	3.86603i	−0.472310	+	0.272688i
$202$	13.8301	+	3.70577i	0.973084	+	0.260737i
$203$	11.1603	−	3.86603i	0.783296	−	0.271342i
$204$	8.19615	−	14.1962i	0.573845	−	0.993929i
$205$	−0.571797	+	0.866025i	−0.0399360	+	0.0604858i
$206$	18.1962			1.26779
$207$	1.09808	−	0.294229i	0.0763216	−	0.0204503i
$208$	−4.39230	−	16.3923i	−0.304552	−	1.13660i
$209$	−2.53590			−0.175412
$210$	15.5622	−	4.36603i	1.07389	−	0.301284i
$211$		−	20.5359i		−	1.41375i	−0.707339	−	0.706875i	$-0.750104\pi$
$211$		−	20.5359i		−	1.41375i	0.707339	−	0.706875i	$-0.249896\pi$
$212$	−4.39230	+	4.39230i	−0.301665	+	0.301665i
$213$	7.73205	+	28.8564i	0.529791	+	1.97721i
$214$		−	7.80385i		−	0.533460i
$215$	1.50000	+	7.33013i	0.102299	+	0.499911i
$216$		−	12.3923i		−	0.843190i
$217$	26.4904	+	5.09808i	1.79828	+	0.346080i
$218$	5.83013	+	1.56218i	0.394866	+	0.105804i
$219$	−8.09808	−	14.0263i	−0.547217	−	0.947808i
$220$	2.73205	+	1.80385i	0.184195	+	0.121615i
$221$	15.5885	+	9.00000i	1.04859	+	0.605406i
$222$	−17.6603	+	4.73205i	−1.18528	+	0.317594i
$223$	7.92820	+	7.92820i	0.530912	+	0.530912i	0.920844	−	0.389932i	$-0.127501\pi$
$223$	7.92820	+	7.92820i	0.530912	+	0.530912i	−0.389932	+	0.920844i	$0.627501\pi$
$224$	−14.9282	+	1.07180i	−0.997433	+	0.0716124i
$225$	−2.92820	−	2.19615i	−0.195214	−	0.146410i
$226$	4.39230	+	2.53590i	0.292172	+	0.168685i
$227$	−12.8301	+	3.43782i	−0.851565	+	0.228176i	−0.658100	−	0.752931i	$-0.728639\pi$
$227$	−12.8301	+	3.43782i	−0.851565	+	0.228176i	−0.193466	+	0.981107i	$0.561973\pi$
$228$	−12.9282	−	3.46410i	−0.856191	−	0.229416i
$229$	13.3923	−	7.73205i	0.884988	−	0.510948i	0.0126885	−	0.999919i	$-0.495961\pi$
$229$	13.3923	−	7.73205i	0.884988	−	0.510948i	0.872300	+	0.488971i	$0.162628\pi$
$230$	2.70577	−	4.09808i	0.178413	−	0.270219i
$231$	0.267949	+	3.73205i	0.0176298	+	0.245551i
$232$	8.92820	+	8.92820i	0.586165	+	0.586165i
$233$	7.09808	+	1.90192i	0.465010	+	0.124599i	0.483714	−	0.875226i	$-0.339287\pi$
$233$	7.09808	+	1.90192i	0.465010	+	0.124599i	−0.0187040	+	0.999825i	$0.505954\pi$
$234$	−4.39230			−0.287134
$235$	0.973721	+	1.09808i	0.0635185	+	0.0716306i
$236$	−17.8564			−1.16235
$237$	−17.6603	−	17.6603i	−1.14716	−	1.14716i
$238$	10.3923	−	12.0000i	0.673633	−	0.777844i
$239$			4.73205i			0.306091i	0.988219	+	0.153045i	$0.0489081\pi$
$239$			4.73205i			0.306091i	−0.988219	+	0.153045i	$0.951092\pi$
$240$	11.4641	+	12.9282i	0.740005	+	0.834512i
$241$	−17.6603	−	10.1962i	−1.13760	−	0.656792i	−0.191763	−	0.981441i	$-0.561420\pi$
$241$	−17.6603	−	10.1962i	−1.13760	−	0.656792i	−0.945834	+	0.324649i	$0.894754\pi$
$242$	10.4641	−	10.4641i	0.672658	−	0.672658i
$243$	−7.19615	−	1.92820i	−0.461633	−	0.123694i
$244$	17.1962	+	9.92820i	1.10087	+	0.635588i
$245$	15.5981	−	1.30385i	0.996525	−	0.0832998i
$246$	−0.633975	−	1.09808i	−0.0404207	−	0.0700108i
$247$	3.80385	−	14.1962i	0.242033	−	0.903280i
$248$	7.46410	+	27.8564i	0.473971	+	1.76888i
$249$	10.7942	+	6.23205i	0.684056	+	0.394940i
$250$	−15.7583	+	1.29423i	−0.996644	+	0.0818542i
$251$	19.6603			1.24094			0.620472	−	0.784229i	$-0.286941\pi$
$251$	19.6603			1.24094			0.620472	+	0.784229i	$0.286941\pi$
$252$	−0.732051	+	3.80385i	−0.0461149	+	0.239620i
$253$	0.803848	+	0.803848i	0.0505375	+	0.0505375i
$254$	11.0000	−	19.0526i	0.690201	−	1.19546i
$255$	−18.2942	−	1.09808i	−1.14563	−	0.0687642i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	25.8564	+	6.92820i	1.61288	+	0.432169i	0.948899	−	0.315581i	$-0.102199\pi$
$257$	25.8564	+	6.92820i	1.61288	+	0.432169i	0.663980	+	0.747751i	$0.268866\pi$
$258$	−8.83013	−	2.36603i	−0.549740	−	0.147302i
$259$	−17.6603	+	1.26795i	−1.09735	+	0.0787865i
$260$	−14.1962	+	12.5885i	−0.880408	+	0.780703i
$261$	2.83013	−	1.63397i	0.175180	−	0.101140i
$262$	7.46410	−	7.46410i	0.461134	−	0.461134i
$263$	−0.107695	−	0.401924i	−0.00664077	−	0.0247837i	0.962526	−	0.271190i	$-0.0874170\pi$
$263$	−0.107695	−	0.401924i	−0.00664077	−	0.0247837i	−0.969167	+	0.246406i	$0.920750\pi$
$264$	−3.46410	+	2.00000i	−0.213201	+	0.123091i
$265$	6.58846	+	2.19615i	0.404726	+	0.134909i
$266$	−11.6603	−	5.66025i	−0.714936	−	0.347052i
$267$	23.4904	−	23.4904i	1.43759	−	1.43759i
$268$	−5.66025	−	5.66025i	−0.345755	−	0.345755i
$269$	−3.06218	−	1.76795i	−0.186704	−	0.107794i	0.403734	−	0.914876i	$-0.367712\pi$
$269$	−3.06218	−	1.76795i	−0.186704	−	0.107794i	−0.590439	+	0.807082i	$0.701045\pi$
$270$	−12.3923	+	6.19615i	−0.754172	+	0.377086i
$271$	10.3923	−	6.00000i	0.631288	−	0.364474i	−0.149963	−	0.988692i	$-0.547915\pi$
$271$	10.3923	−	6.00000i	0.631288	−	0.364474i	0.781251	+	0.624218i	$0.214582\pi$
$272$	16.3923	+	4.39230i	0.993929	+	0.266323i
$273$	−21.2942	−	4.09808i	−1.28879	−	0.248027i
$274$	−6.00000	−	10.3923i	−0.362473	−	0.627822i
$275$	0.437822	−	3.63397i	0.0264017	−	0.219137i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	5.02628	+	18.7583i	0.302000	+	1.12708i	0.935497	+	0.353334i	$0.114952\pi$
$277$	5.02628	+	18.7583i	0.302000	+	1.12708i	−0.633497	+	0.773745i	$0.718381\pi$
$278$	1.73205	−	0.464102i	0.103882	−	0.0278350i
$279$	7.46410			0.446864
$280$	8.53590	+	14.3923i	0.510117	+	0.860105i
$281$	−24.2487			−1.44656			−0.723278	−	0.690557i	$-0.757366\pi$
$281$	−24.2487			−1.44656			−0.723278	+	0.690557i	$0.757366\pi$
$282$	−1.73205	+	0.464102i	−0.103142	+	0.0276368i
$283$	3.63397	+	13.5622i	0.216017	+	0.806188i	0.985806	+	0.167889i	$0.0536950\pi$
$283$	3.63397	+	13.5622i	0.216017	+	0.806188i	−0.769789	+	0.638299i	$0.779638\pi$
$284$	−26.7846	+	15.4641i	−1.58937	+	0.917626i
$285$	3.00000	+	14.6603i	0.177705	+	0.868399i
$286$	−2.19615	−	3.80385i	−0.129861	−	0.224926i
$287$	−0.401924	−	1.16025i	−0.0237248	−	0.0684876i
$288$	−4.00000	+	1.07180i	−0.235702	+	0.0631562i
$289$	−0.866025	+	0.500000i	−0.0509427	+	0.0294118i
$290$	4.46410	−	13.3923i	0.262141	−	0.786423i
$291$	14.8301	+	8.56218i	0.869357	+	0.501924i
$292$	11.8564	−	11.8564i	0.693844	−	0.693844i
$293$	−4.19615	+	4.19615i	−0.245142	+	0.245142i	−0.818973	−	0.573832i	$-0.805456\pi$
$293$	−4.19615	+	4.19615i	−0.245142	+	0.245142i	0.573832	+	0.818973i	$0.305456\pi$
$294$	−7.09808	+	17.7583i	−0.413968	+	1.03569i
$295$	8.92820	+	17.8564i	0.519820	+	1.03964i
$296$	−9.46410	−	16.3923i	−0.550090	−	0.952783i
$297$	−0.830127	−	3.09808i	−0.0481689	−	0.179769i
$298$	−22.6603	+	22.6603i	−1.31267	+	1.31267i
$299$	−5.70577	+	3.29423i	−0.329973	+	0.190510i
$300$	7.19615	−	17.9282i	0.415470	−	1.03509i
$301$	−7.96410	−	3.86603i	−0.459043	−	0.222834i
$302$	−18.8564	−	5.05256i	−1.08506	−	0.290742i
$303$	18.8923	+	5.06218i	1.08533	+	0.290815i
$304$		−	13.8564i		−	0.794719i
$305$	1.33013	−	22.1603i	0.0761629	−	1.26889i
$306$	2.19615	−	3.80385i	0.125546	−	0.217451i
$307$	0.758330	+	0.758330i	0.0432802	+	0.0432802i	0.728416	−	0.685135i	$-0.240257\pi$
$307$	0.758330	+	0.758330i	0.0432802	+	0.0432802i	−0.685135	+	0.728416i	$0.740257\pi$
$308$	−3.66025	+	1.26795i	−0.208562	+	0.0722481i
$309$	24.8564			1.41403
$310$	24.1244	−	21.3923i	1.37017	−	1.21500i
$311$	21.5885	+	12.4641i	1.22417	+	0.706774i	0.965804	−	0.259273i	$-0.0834829\pi$
$311$	21.5885	+	12.4641i	1.22417	+	0.706774i	0.258365	+	0.966047i	$0.416816\pi$
$312$	−6.00000	−	22.3923i	−0.339683	−	1.26771i
$313$	−4.32051	+	16.1244i	−0.244210	+	0.911402i	0.729570	+	0.683907i	$0.239720\pi$
$313$	−4.32051	+	16.1244i	−0.244210	+	0.911402i	−0.973779	+	0.227496i	$0.926946\pi$
$314$	−12.4641	−	21.5885i	−0.703390	−	1.21831i
$315$	4.16987	−	1.16987i	0.234946	−	0.0659149i
$316$	12.9282	−	22.3923i	0.727268	−	1.25967i
$317$	−4.36603	−	1.16987i	−0.245220	−	0.0657066i	0.134115	−	0.990966i	$-0.457181\pi$
$317$	−4.36603	−	1.16987i	−0.245220	−	0.0657066i	−0.379336	+	0.925259i	$0.623847\pi$
$318$	−6.00000	+	6.00000i	−0.336463	+	0.336463i
$319$	2.83013	+	1.63397i	0.158457	+	0.0914850i
$320$	−9.85641	+	14.9282i	−0.550990	+	0.834512i
$321$		−	10.6603i		−	0.594997i
$322$	1.90192	+	5.49038i	0.105990	+	0.305967i
$323$	10.3923	+	10.3923i	0.578243	+	0.578243i
$324$		−	21.3205i		−	1.18447i
$325$	19.6865	+	7.90192i	1.09201	+	0.438320i
$326$	5.32051			0.294676
$327$	7.96410	+	2.13397i	0.440416	+	0.118009i
$328$	0.928203	−	0.928203i	0.0512514	−	0.0512514i
$329$	−1.73205	+	0.124356i	−0.0954911	+	0.00685595i
$330$	3.73205	+	2.46410i	0.205443	+	0.135644i
$331$	−6.29423	+	3.63397i	−0.345962	+	0.199741i	−0.662905	−	0.748703i	$-0.730677\pi$
$331$	−6.29423	+	3.63397i	−0.345962	+	0.199741i	0.316943	+	0.948444i	$0.397344\pi$
$332$	−3.33975	+	12.4641i	−0.183292	+	0.684056i
$333$	−4.73205	+	1.26795i	−0.259315	+	0.0694832i
$334$	5.70577	+	3.29423i	0.312206	+	0.180252i
$335$	−2.83013	+	8.49038i	−0.154626	+	0.463879i
$336$	−20.3923	+	1.46410i	−1.11249	+	0.0798733i
$337$	−19.6603	−	19.6603i	−1.07096	−	1.07096i	−0.997282	−	0.0736804i	$-0.976526\pi$
$337$	−19.6603	−	19.6603i	−1.07096	−	1.07096i	−0.0736804	−	0.997282i	$-0.523474\pi$
$338$	6.83013	−	1.83013i	0.371510	−	0.0995458i
$339$	6.00000	+	3.46410i	0.325875	+	0.188144i
$340$	−3.80385	−	18.5885i	−0.206293	−	1.00810i
$341$	3.73205	+	6.46410i	0.202102	+	0.350051i
$342$	−3.46410	−	0.928203i	−0.187317	−	0.0501915i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		−	9.46410i		−	0.510270i
$345$	3.69615	−	5.59808i	0.198994	−	0.301390i
$346$		−	0.679492i		−	0.0365297i
$347$	−9.35641	−	34.9186i	−0.502278	−	1.87453i	−0.484697	−	0.874682i	$-0.661070\pi$
$347$	−9.35641	−	34.9186i	−0.502278	−	1.87453i	−0.0175817	−	0.999845i	$-0.505597\pi$
$348$	12.1962	+	12.1962i	0.653782	+	0.653782i
$349$		−	19.9808i		−	1.06955i	−0.844996	−	0.534773i	$-0.820397\pi$
$349$		−	19.9808i		−	1.06955i	0.844996	−	0.534773i	$-0.179603\pi$
$350$	10.1244	−	15.7321i	0.541170	−	0.840913i
$351$	18.5885			0.992178
$352$	−2.92820	−	2.92820i	−0.156074	−	0.156074i
$353$	−25.3923	+	6.80385i	−1.35150	+	0.362132i	−0.860687	−	0.509135i	$-0.829965\pi$
$353$	−25.3923	+	6.80385i	−1.35150	+	0.362132i	−0.490809	+	0.871267i	$0.663299\pi$
$354$	−24.3923			−1.29644
$355$	28.8564	+	19.0526i	1.53154	+	1.01120i
$356$	29.7846	+	17.1962i	1.57858	+	0.911394i
$357$	14.1962	−	16.3923i	0.751340	−	0.867573i
$358$	19.1962	+	5.14359i	1.01455	+	0.271847i
$359$	4.09808	−	2.36603i	0.216288	−	0.124874i	−0.387942	−	0.921684i	$-0.626814\pi$
$359$	4.09808	−	2.36603i	0.216288	−	0.124874i	0.604230	+	0.796810i	$0.293481\pi$
$360$	3.07180	+	3.46410i	0.161898	+	0.182574i
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$	−8.24167	−	30.7583i	−0.433173	−	1.61662i
$363$	14.2942	−	14.2942i	0.750252	−	0.750252i
$364$	−1.60770	−	22.3923i	−0.0842661	−	1.17368i
$365$	−17.7846	−	5.92820i	−0.930889	−	0.310296i
$366$	23.4904	+	13.5622i	1.22786	+	0.708906i
$367$	2.16025	+	8.06218i	0.112764	+	0.420842i	0.999110	−	0.0421820i	$-0.0134309\pi$
$367$	2.16025	+	8.06218i	0.112764	+	0.420842i	−0.886346	+	0.463024i	$0.846764\pi$
$368$	−4.39230	+	4.39230i	−0.228965	+	0.228965i
$369$	−0.169873	−	0.294229i	−0.00884323	−	0.0153169i
$370$	−11.6603	+	17.6603i	−0.606188	+	0.918113i
$371$	−6.80385	+	4.60770i	−0.353238	+	0.239220i
$372$	10.1962	+	38.0526i	0.528646	+	1.97293i
$373$	2.53590	−	9.46410i	0.131304	−	0.490033i	−0.868682	−	0.495370i	$-0.835032\pi$
$373$	2.53590	−	9.46410i	0.131304	−	0.490033i	0.999986	+	0.00533769i	$0.00169905\pi$
$374$	4.39230			0.227121
$375$	−21.5263	+	1.76795i	−1.11161	+	0.0912965i
$376$	−0.928203	−	1.60770i	−0.0478684	−	0.0829105i
$377$	−13.3923	+	13.3923i	−0.689739	+	0.689739i
$378$	3.09808	−	16.0981i	0.159348	−	0.827996i
$379$	−30.2487			−1.55377			−0.776886	−	0.629641i	$-0.783202\pi$
$379$	−30.2487			−1.55377			−0.776886	+	0.629641i	$0.783202\pi$
$380$	−13.8564	+	6.92820i	−0.710819	+	0.355409i
$381$	15.0263	−	26.0263i	0.769820	−	1.33337i
$382$	3.12436	−	3.12436i	0.159856	−	0.159856i
$383$	−1.96410	+	7.33013i	−0.100361	+	0.374552i	−0.997778	−	0.0666319i	$-0.978775\pi$
$383$	−1.96410	+	7.33013i	−0.100361	+	0.374552i	0.897417	+	0.441184i	$0.145441\pi$
$384$	−10.9282	−	18.9282i	−0.557678	−	0.965926i
$385$	3.09808	+	3.02628i	0.157893	+	0.154233i
$386$	−14.6603	+	8.46410i	−0.746187	+	0.430811i
$387$	−2.36603	−	0.633975i	−0.120272	−	0.0322267i
$388$	−4.58846	+	17.1244i	−0.232944	+	0.869357i
$389$	−7.53590	+	13.0526i	−0.382085	+	0.661791i	−0.991360	−	0.131168i	$-0.958127\pi$
$389$	−7.53590	+	13.0526i	−0.382085	+	0.661791i	0.609275	+	0.792959i	$0.291461\pi$
$390$	−19.3923	+	17.1962i	−0.981968	+	0.870761i
$391$		−	6.58846i		−	0.333193i
$392$	−19.6603	−	2.33975i	−0.992993	−	0.118175i
$393$	10.1962	−	10.1962i	0.514328	−	0.514328i
$394$	−9.58846	−	5.53590i	−0.483059	−	0.278895i
$395$	−28.8564	−	1.73205i	−1.45192	−	0.0871489i
$396$	−0.928203	+	0.535898i	−0.0466440	+	0.0269299i
$397$	−5.83013	+	21.7583i	−0.292606	+	1.09202i	0.650495	+	0.759511i	$0.274562\pi$
$397$	−5.83013	+	21.7583i	−0.292606	+	1.09202i	−0.943100	+	0.332508i	$0.892105\pi$
$398$	−4.73205	−	1.26795i	−0.237196	−	0.0635566i
$399$	−15.9282	−	7.73205i	−0.797408	−	0.387087i
$400$	19.8564	+	2.39230i	0.992820	+	0.119615i
$401$	15.3564	+	26.5981i	0.766862	+	1.32824i	0.939256	+	0.343216i	$0.111516\pi$
$401$	15.3564	+	26.5981i	0.766862	+	1.32824i	−0.172394	+	0.985028i	$0.555150\pi$
$402$	−7.73205	−	7.73205i	−0.385640	−	0.385640i
$403$	−41.7846	+	11.1962i	−2.08144	+	0.557720i
$404$			20.2487i			1.00741i
$405$	−21.3205	+	10.6603i	−1.05942	+	0.529712i
$406$	9.36603	+	13.8301i	0.464828	+	0.686378i
$407$	−3.46410	−	3.46410i	−0.171709	−	0.171709i
$408$	22.3923	+	6.00000i	1.10858	+	0.297044i
$409$	5.69615	−	9.86603i	0.281657	−	0.487844i	−0.690136	−	0.723679i	$-0.742449\pi$
$409$	5.69615	−	9.86603i	0.281657	−	0.487844i	0.971793	+	0.235836i	$0.0757828\pi$
$410$	−1.39230	−	0.464102i	−0.0687610	−	0.0229203i
$411$	−8.19615	−	14.1962i	−0.404286	−	0.700245i
$412$	6.66025	+	24.8564i	0.328127	+	1.22459i
$413$	−23.1962	−	4.46410i	−1.14141	−	0.219664i
$414$	0.803848	+	1.39230i	0.0395070	+	0.0684280i
$415$	14.1340	−	2.89230i	0.693810	−	0.141978i
$416$	20.7846	−	12.0000i	1.01905	−	0.588348i
$417$	2.36603	−	0.633975i	0.115865	−	0.0310459i
$418$	−0.928203	−	3.46410i	−0.0453999	−	0.169435i
$419$		−	2.39230i		−	0.116872i	−0.998291	−	0.0584359i	$-0.981389\pi$
$419$		−	2.39230i		−	0.116872i	0.998291	−	0.0584359i	$-0.0186113\pi$
$420$	11.6603	+	19.6603i	0.568962	+	0.959322i
$421$			30.1244i			1.46817i	0.679057	+	0.734086i	$0.262389\pi$
$421$			30.1244i			1.46817i	−0.679057	+	0.734086i	$0.737611\pi$
$422$	28.0526	−	7.51666i	1.36558	−	0.365905i
$423$	−0.464102	+	0.124356i	−0.0225654	+	0.00604638i
$424$	−7.60770	−	4.39230i	−0.369462	−	0.213309i
$425$	−16.6865	+	13.0981i	−0.809416	+	0.635350i
$426$	−36.5885	+	21.1244i	−1.77272	+	1.02348i
$427$	19.8564	+	17.1962i	0.960919	+	0.832180i
$428$	10.6603	−	2.85641i	0.515283	−	0.138070i
$429$	−3.00000	−	5.19615i	−0.144841	−	0.250873i
$430$	−9.46410	+	4.73205i	−0.456400	+	0.228200i
$431$	6.63397	−	11.4904i	0.319547	−	0.553472i	−0.660846	−	0.750521i	$-0.729802\pi$
$431$	6.63397	−	11.4904i	0.319547	−	0.553472i	0.980394	+	0.197049i	$0.0631358\pi$
$432$	16.9282	−	4.53590i	0.814459	−	0.218234i
$433$	−11.4641	−	11.4641i	−0.550930	−	0.550930i	0.375780	−	0.926709i	$-0.377375\pi$
$433$	−11.4641	−	11.4641i	−0.550930	−	0.550930i	−0.926709	+	0.375780i	$0.877375\pi$
$434$	2.73205	+	38.0526i	0.131143	+	1.82658i
$435$	6.09808	−	18.2942i	0.292380	−	0.877141i
$436$			8.53590i			0.408795i
$437$	−5.19615	+	1.39230i	−0.248566	+	0.0666030i
$438$	16.1962	−	16.1962i	0.773882	−	0.773882i
$439$	−2.66025	−	4.60770i	−0.126967	−	0.219913i	0.795533	−	0.605910i	$-0.207191\pi$
$439$	−2.66025	−	4.60770i	−0.126967	−	0.219913i	−0.922500	+	0.385997i	$0.873858\pi$
$440$	−1.46410	+	4.39230i	−0.0697983	+	0.209395i
$441$	−1.90192	+	4.75833i	−0.0905678	+	0.226587i
$442$	−6.58846	+	24.5885i	−0.313381	+	1.16955i
$443$	−8.93782	+	33.3564i	−0.424649	+	1.58481i	0.340040	+	0.940411i	$0.389559\pi$
$443$	−8.93782	+	33.3564i	−0.424649	+	1.58481i	−0.764689	+	0.644400i	$0.777107\pi$
$444$	−12.9282	−	22.3923i	−0.613545	−	1.06269i
$445$	2.30385	−	38.3827i	0.109213	−	1.81951i
$446$	−7.92820	+	13.7321i	−0.375411	+	0.650231i
$447$	−30.9545	+	30.9545i	−1.46410	+	1.46410i
$448$	−6.92820	−	20.0000i	−0.327327	−	0.944911i
$449$			23.1962i			1.09469i	0.836906	+	0.547347i	$0.184362\pi$
$449$			23.1962i			1.09469i	−0.836906	+	0.547347i	$0.815638\pi$
$450$	1.92820	−	4.80385i	0.0908964	−	0.226456i
$451$	0.169873	−	0.294229i	0.00799901	−	0.0138547i
$452$	−1.85641	+	6.92820i	−0.0873180	+	0.325875i
$453$	−25.7583	−	6.90192i	−1.21023	−	0.324281i
$454$	−9.39230	−	16.2679i	−0.440803	−	0.763493i
$455$	−21.5885	+	12.8038i	−1.01208	+	0.600254i
$456$		−	18.9282i		−	0.886394i
$457$	−3.73205	+	13.9282i	−0.174578	+	0.651534i	0.822045	+	0.569422i	$0.192833\pi$
$457$	−3.73205	+	13.9282i	−0.174578	+	0.651534i	−0.996623	+	0.0821116i	$0.973834\pi$
$458$	15.4641	+	15.4641i	0.722590	+	0.722590i
$459$	−9.29423	+	16.0981i	−0.433817	+	0.751394i
$460$	6.58846	+	2.19615i	0.307188	+	0.102396i
$461$	12.1436			0.565584			0.282792	−	0.959181i	$-0.408739\pi$
$461$	12.1436			0.565584			0.282792	+	0.959181i	$0.408739\pi$
$462$	−5.00000	+	1.73205i	−0.232621	+	0.0805823i
$463$	0.830127	−	0.830127i	0.0385793	−	0.0385793i	−0.687554	−	0.726133i	$-0.741316\pi$
$463$	0.830127	−	0.830127i	0.0385793	−	0.0385793i	0.726133	+	0.687554i	$0.241316\pi$
$464$	−8.92820	+	15.4641i	−0.414481	+	0.717903i
$465$	32.9545	−	29.2224i	1.52823	−	1.35516i
$466$			10.3923i			0.481414i
$467$	1.66987	−	6.23205i	0.0772725	−	0.288385i	−0.916466	−	0.400111i	$-0.868971\pi$
$467$	1.66987	−	6.23205i	0.0772725	−	0.288385i	0.993739	+	0.111727i	$0.0356381\pi$
$468$	−1.60770	−	6.00000i	−0.0743157	−	0.277350i
$469$	−5.93782	−	8.76795i	−0.274183	−	0.404866i
$470$	−1.14359	+	1.73205i	−0.0527500	+	0.0798935i
$471$	−17.0263	−	29.4904i	−0.784530	−	1.35885i
$472$	−6.53590	−	24.3923i	−0.300839	−	1.12275i
$473$	−0.633975	−	2.36603i	−0.0291502	−	0.108790i
$474$	17.6603	−	30.5885i	0.811162	−	1.40497i
$475$	13.8564	+	10.3923i	0.635776	+	0.476832i
$476$	20.1962	+	9.80385i	0.925689	+	0.449359i
$477$	−1.60770	+	1.60770i	−0.0736113	+	0.0736113i
$478$	−6.46410	+	1.73205i	−0.295661	+	0.0792222i
$479$	1.90192	−	3.29423i	0.0869011	−	0.150517i	−0.819299	−	0.573367i	$-0.805637\pi$
$479$	1.90192	−	3.29423i	0.0869011	−	0.150517i	0.906200	+	0.422850i	$0.138970\pi$
$480$	−13.4641	+	20.3923i	−0.614549	+	0.930777i
$481$	24.5885	−	14.1962i	1.12114	−	0.647289i
$482$	7.46410	−	27.8564i	0.339981	−	1.26882i
$483$	2.59808	+	7.50000i	0.118217	+	0.341262i
$484$	18.1244	+	10.4641i	0.823834	+	0.475641i
$485$	19.4186	−	3.97372i	0.881752	−	0.180437i
$486$		−	10.5359i		−	0.477918i
$487$	−19.0263	+	5.09808i	−0.862163	+	0.231016i	−0.662696	−	0.748889i	$-0.730588\pi$
$487$	−19.0263	+	5.09808i	−0.862163	+	0.231016i	−0.199467	+	0.979905i	$0.563921\pi$
$488$	−7.26795	+	27.1244i	−0.329005	+	1.22786i
$489$	7.26795			0.328668
$490$	7.49038	+	20.8301i	0.338381	+	0.941009i
$491$			12.1962i			0.550405i	0.961386	+	0.275202i	$0.0887448\pi$
$491$			12.1962i			0.550405i	−0.961386	+	0.275202i	$0.911255\pi$
$492$	1.26795	−	1.26795i	0.0571636	−	0.0571636i
$493$	−4.90192	−	18.2942i	−0.220772	−	0.823931i
$494$	20.7846			0.935144
$495$	1.00000	+	0.660254i	0.0449467	+	0.0296762i
$496$	−35.3205	+	20.3923i	−1.58594	+	0.915642i
$497$	−38.6603	+	13.3923i	−1.73415	+	0.600727i
$498$	−4.56218	+	17.0263i	−0.204436	+	0.762966i
$499$	6.75833	+	11.7058i	0.302544	+	0.524022i	0.976712	−	0.214556i	$-0.0688306\pi$
$499$	6.75833	+	11.7058i	0.302544	+	0.524022i	−0.674167	+	0.738579i	$0.735497\pi$
$500$	−7.53590	−	21.0526i	−0.337016	−	0.941499i
$501$	7.79423	+	4.50000i	0.348220	+	0.201045i
$502$	7.19615	+	26.8564i	0.321180	+	1.19866i
$503$	−22.6865	−	22.6865i	−1.01154	−	1.01154i	−0.999933	−	0.0116099i	$-0.996304\pi$
$503$	−22.6865	−	22.6865i	−1.01154	−	1.01154i	−0.0116099	−	0.999933i	$-0.503696\pi$
$504$	−5.46410	+	0.392305i	−0.243390	+	0.0174746i
$505$	20.2487	−	10.1244i	0.901056	−	0.450528i
$506$	−0.803848	+	1.39230i	−0.0357354	+	0.0618955i
$507$	9.33013	−	2.50000i	0.414365	−	0.111029i
$508$	30.0526	+	8.05256i	1.33337	+	0.357275i
$509$	9.57180	−	5.52628i	0.424262	−	0.244948i	−0.272637	−	0.962117i	$-0.587896\pi$
$509$	9.57180	−	5.52628i	0.424262	−	0.244948i	0.696899	+	0.717169i	$0.254562\pi$
$510$	−5.19615	−	25.3923i	−0.230089	−	1.12439i
$511$	18.3660	−	12.4378i	0.812465	−	0.550217i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	14.6603	+	3.92820i	0.647266	+	0.173434i
$514$			37.8564i			1.66977i
$515$	21.5263	−	19.0885i	0.948561	−	0.841138i
$516$		−	12.9282i		−	0.569132i
$517$	−0.339746	−	0.339746i	−0.0149420	−	0.0149420i
$518$	−8.19615	−	23.6603i	−0.360118	−	1.03957i
$519$		−	0.928203i		−	0.0407436i
$520$	−22.3923	−	14.7846i	−0.981968	−	0.648348i
$521$	7.39230	+	4.26795i	0.323863	+	0.186982i	0.653113	−	0.757260i	$-0.273463\pi$
$521$	7.39230	+	4.26795i	0.323863	+	0.186982i	−0.329250	+	0.944243i	$0.606796\pi$
$522$	3.26795	+	3.26795i	0.143034	+	0.143034i
$523$	24.2942	+	6.50962i	1.06231	+	0.284646i	0.747331	−	0.664452i	$-0.231335\pi$
$523$	24.2942	+	6.50962i	1.06231	+	0.284646i	0.314982	+	0.949098i	$0.398002\pi$
$524$	12.9282	+	7.46410i	0.564771	+	0.326071i
$525$	13.8301	−	21.4904i	0.603596	−	0.937917i
$526$	0.509619	−	0.294229i	0.0222204	−	0.0128290i
$527$	11.1962	−	41.7846i	0.487712	−	1.82017i
$528$	−4.00000	−	4.00000i	−0.174078	−	0.174078i
$529$	−17.8301	−	10.2942i	−0.775223	−	0.447575i
$530$	−0.588457	+	9.80385i	−0.0255610	+	0.425852i
$531$	−6.53590			−0.283634
$532$	3.46410	−	18.0000i	0.150188	−	0.780399i
$533$	1.39230	+	1.39230i	0.0603074	+	0.0603074i
$534$	40.6865	+	23.4904i	1.76068	+	1.01653i
$535$	−8.18653	−	9.23205i	−0.353935	−	0.399136i
$536$	5.66025	−	9.80385i	0.244486	−	0.423462i
$537$	26.2224	+	7.02628i	1.13158	+	0.303206i
$538$	1.29423	−	4.83013i	0.0557982	−	0.208242i
$539$	−5.07180	+	0.732051i	−0.218458	+	0.0315317i
$540$	−13.0000	−	14.6603i	−0.559431	−	0.630877i
$541$	−1.79423	+	1.03590i	−0.0771399	+	0.0445368i	−0.538074	−	0.842898i	$-0.680848\pi$
$541$	−1.79423	+	1.03590i	−0.0771399	+	0.0445368i	0.460934	+	0.887434i	$0.347515\pi$
$542$	12.0000	+	12.0000i	0.515444	+	0.515444i
$543$	−11.2583	−	42.0167i	−0.483141	−	1.80311i
$544$			24.0000i			1.02899i
$545$	8.53590	−	4.26795i	0.365638	−	0.182819i
$546$	−2.19615	−	30.5885i	−0.0939866	−	1.30907i
$547$	−14.4904	+	14.4904i	−0.619564	+	0.619564i	−0.945420	−	0.325856i	$-0.894348\pi$
$547$	−14.4904	+	14.4904i	−0.619564	+	0.619564i	0.325856	+	0.945420i	$0.394348\pi$
$548$	12.0000	−	12.0000i	0.512615	−	0.512615i
$549$	6.29423	+	3.63397i	0.268631	+	0.155094i
$550$	5.12436	−	0.732051i	0.218503	−	0.0312148i
$551$	−13.3923	+	7.73205i	−0.570531	+	0.329396i
$552$	−6.00000	+	6.00000i	−0.255377	+	0.255377i
$553$	22.3923	−	25.8564i	0.952218	−	1.09953i
$554$	−23.7846	+	13.7321i	−1.01051	+	0.583419i
$555$	−15.9282	+	24.1244i	−0.676115	+	1.02402i
$556$	1.26795	+	2.19615i	0.0537730	+	0.0931376i
$557$	8.24167	+	30.7583i	0.349211	+	1.30327i	0.887615	+	0.460586i	$0.152361\pi$
$557$	8.24167	+	30.7583i	0.349211	+	1.30327i	−0.538404	+	0.842687i	$0.680973\pi$
$558$	2.73205	+	10.1962i	0.115657	+	0.431638i
$559$	14.1962			0.600433
$560$	−16.5359	+	16.9282i	−0.698769	+	0.715347i
$561$	6.00000			0.253320
$562$	−8.87564	−	33.1244i	−0.374396	−	1.39727i
$563$	−7.06218	−	26.3564i	−0.297635	−	1.11079i	−0.939102	−	0.343639i	$-0.888340\pi$
$563$	−7.06218	−	26.3564i	−0.297635	−	1.11079i	0.641466	−	0.767151i	$-0.278326\pi$
$564$	−1.26795	−	2.19615i	−0.0533903	−	0.0924747i
$565$	7.85641	−	1.60770i	0.330522	−	0.0676362i
$566$	−17.1962	+	9.92820i	−0.722808	+	0.417314i
$567$	5.33013	−	27.6962i	0.223844	−	1.16313i
$568$	−30.9282	−	30.9282i	−1.29772	−	1.29772i
$569$	18.8038	−	10.8564i	0.788298	−	0.455124i	−0.0510648	−	0.998695i	$-0.516262\pi$
$569$	18.8038	−	10.8564i	0.788298	−	0.455124i	0.839363	+	0.543571i	$0.182928\pi$
$570$	−18.9282	+	9.46410i	−0.792815	+	0.396408i
$571$	14.7846	+	8.53590i	0.618717	+	0.357216i	0.776369	−	0.630278i	$-0.217059\pi$
$571$	14.7846	+	8.53590i	0.618717	+	0.357216i	−0.157653	+	0.987495i	$0.550393\pi$
$572$	4.39230	−	4.39230i	0.183651	−	0.183651i
$573$	4.26795	−	4.26795i	0.178296	−	0.178296i
$574$	1.43782	−	0.973721i	0.0600135	−	0.0406423i
$575$	−1.09808	−	7.68653i	−0.0457929	−	0.320551i
$576$	−2.92820	−	5.07180i	−0.122008	−	0.211325i
$577$	−4.41858	−	16.4904i	−0.183948	−	0.686504i	−0.994853	−	0.101326i	$-0.967691\pi$
$577$	−4.41858	−	16.4904i	−0.183948	−	0.686504i	0.810905	−	0.585178i	$-0.198975\pi$
$578$	−1.00000	−	1.00000i	−0.0415945	−	0.0415945i
$579$	−20.0263	+	11.5622i	−0.832264	+	0.480508i
$580$	19.9282	+	1.19615i	0.827474	+	0.0496675i
$581$	−7.45448	+	15.3564i	−0.309264	+	0.637091i
$582$	−6.26795	+	23.3923i	−0.259815	+	0.969642i
$583$	−2.19615	−	0.588457i	−0.0909553	−	0.0243714i
$584$	20.5359	+	11.8564i	0.849782	+	0.490622i
$585$	−5.19615	+	4.60770i	−0.214834	+	0.190505i
$586$	−7.26795	−	4.19615i	−0.300236	−	0.173341i
$587$	−9.00000	−	9.00000i	−0.371470	−	0.371470i	0.496543	−	0.868012i	$-0.334603\pi$
$587$	−9.00000	−	9.00000i	−0.371470	−	0.371470i	−0.868012	+	0.496543i	$0.834603\pi$
$588$	−26.8564	−	3.19615i	−1.10754	−	0.131807i
$589$	−35.3205			−1.45536
$590$	−21.1244	+	18.7321i	−0.869676	+	0.771186i
$591$	−13.0981	−	7.56218i	−0.538783	−	0.311066i
$592$	18.9282	−	18.9282i	0.777944	−	0.777944i
$593$	−3.80385	+	14.1962i	−0.156205	+	0.582966i	0.842794	+	0.538237i	$0.180909\pi$
$593$	−3.80385	+	14.1962i	−0.156205	+	0.582966i	−0.998999	+	0.0447296i	$0.985757\pi$
$594$	3.92820	−	2.26795i	0.161176	−	0.0930551i
$595$	−0.294229	−	25.0981i	−0.0120622	−	1.02892i
$596$	−39.2487	−	22.6603i	−1.60769	−	0.928200i
$597$	−6.46410	−	1.73205i	−0.264558	−	0.0708881i
$598$	−6.58846	−	6.58846i	−0.269422	−	0.269422i
$599$	21.0000	+	12.1244i	0.858037	+	0.495388i	0.863354	−	0.504598i	$-0.168359\pi$
$599$	21.0000	+	12.1244i	0.858037	+	0.495388i	−0.00531761	+	0.999986i	$0.501693\pi$
$600$	27.1244	+	3.26795i	1.10735	+	0.133413i
$601$		−	28.3923i		−	1.15815i	−0.815276	−	0.579073i	$-0.803415\pi$
$601$		−	28.3923i		−	1.15815i	0.815276	−	0.579073i	$-0.196585\pi$
$602$	2.36603	−	12.2942i	0.0964320	−	0.501075i
$603$	−2.07180	−	2.07180i	−0.0843701	−	0.0843701i
$604$		−	27.6077i		−	1.12334i
$605$	1.40192	−	23.3564i	0.0569963	−	0.949573i
$606$			27.6603i			1.12362i
$607$	−22.9904	−	6.16025i	−0.933151	−	0.250037i	−0.239953	−	0.970784i	$-0.577132\pi$
$607$	−22.9904	−	6.16025i	−0.933151	−	0.250037i	−0.693198	+	0.720747i	$0.743799\pi$
$608$	18.9282	−	5.07180i	0.767640	−	0.205689i
$609$	12.7942	+	18.8923i	0.518448	+	0.765555i
$610$	30.7583	−	6.29423i	1.24537	−	0.254846i
$611$	2.41154	−	1.39230i	0.0975606	−	0.0563266i
$612$	6.00000	+	1.60770i	0.242536	+	0.0649872i
$613$	5.36603	−	1.43782i	0.216732	−	0.0580731i	−0.148819	−	0.988864i	$-0.547547\pi$
$613$	5.36603	−	1.43782i	0.216732	−	0.0580731i	0.365551	+	0.930791i	$0.380881\pi$
$614$	−0.758330	+	1.31347i	−0.0306037	+	0.0530072i
$615$	−1.90192	−	0.633975i	−0.0766930	−	0.0255643i
$616$	−3.07180	−	4.53590i	−0.123766	−	0.182757i
$617$	−0.928203	−	0.928203i	−0.0373681	−	0.0373681i	0.688176	−	0.725544i	$-0.258412\pi$
$617$	−0.928203	−	0.928203i	−0.0373681	−	0.0373681i	−0.725544	+	0.688176i	$0.758412\pi$
$618$	9.09808	+	33.9545i	0.365978	+	1.36585i
$619$	15.2942	+	8.83013i	0.614727	+	0.354913i	0.774813	−	0.632190i	$-0.217844\pi$
$619$	15.2942	+	8.83013i	0.614727	+	0.354913i	−0.160086	+	0.987103i	$0.551177\pi$
$620$	38.0526	+	25.1244i	1.52823	+	1.00902i
$621$	−3.40192	−	5.89230i	−0.136514	−	0.236450i
$622$	−9.12436	+	34.0526i	−0.365853	+	1.36538i
$623$	34.3923	+	29.7846i	1.37790	+	1.19330i
$624$	28.3923	−	16.3923i	1.13660	−	0.656217i
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	−23.6077			−0.943553
$627$	−1.26795	−	4.73205i	−0.0506370	−	0.188980i
$628$	24.9282	−	24.9282i	0.994744	−	0.994744i
$629$			28.3923i			1.13208i
$630$	3.12436	+	5.26795i	0.124477	+	0.209880i
$631$	−7.26795			−0.289332			−0.144666	−	0.989481i	$-0.546211\pi$
$631$	−7.26795			−0.289332			−0.144666	+	0.989481i	$0.546211\pi$
$632$	35.3205	+	9.46410i	1.40497	+	0.376462i
$633$	38.3205	−	10.2679i	1.52310	−	0.408114i
$634$		−	6.39230i		−	0.253871i
$635$	−6.97372	−	34.0788i	−0.276744	−	1.35238i
$636$	−10.3923	−	6.00000i	−0.412082	−	0.237915i
$637$	3.50962	−	29.4904i	0.139056	−	1.16845i
$638$	−1.19615	+	4.46410i	−0.0473561	+	0.176735i
$639$	−9.80385	+	5.66025i	−0.387834	+	0.223916i
$640$	−24.0000	−	8.00000i	−0.948683	−	0.316228i
$641$	16.3301	−	28.2846i	0.645001	−	1.11717i	−0.339300	−	0.940678i	$-0.610190\pi$
$641$	16.3301	−	28.2846i	0.645001	−	1.11717i	0.984301	−	0.176497i	$-0.0564765\pi$
$642$	14.5622	−	3.90192i	0.574723	−	0.153997i
$643$	−9.00000	+	9.00000i	−0.354925	+	0.354925i	−0.861938	−	0.507013i	$-0.830750\pi$
$643$	−9.00000	+	9.00000i	−0.354925	+	0.354925i	0.507013	+	0.861938i	$0.330750\pi$
$644$	−6.80385	+	4.60770i	−0.268109	+	0.181569i
$645$	−12.9282	+	6.46410i	−0.509048	+	0.254524i
$646$	−10.3923	+	18.0000i	−0.408880	+	0.708201i
$647$	7.03590	+	26.2583i	0.276610	+	1.03232i	0.954755	+	0.297394i	$0.0961174\pi$
$647$	7.03590	+	26.2583i	0.276610	+	1.03232i	−0.678145	+	0.734928i	$0.737216\pi$
$648$	29.1244	−	7.80385i	1.14411	−	0.306564i
$649$	−3.26795	−	5.66025i	−0.128278	−	0.222184i
$650$	−3.58846	+	29.7846i	−0.140751	+	1.16825i
$651$	3.73205	+	51.9808i	0.146271	+	2.03729i
$652$	1.94744	+	7.26795i	0.0762677	+	0.284635i
$653$	8.41858	−	31.4186i	0.329445	−	1.22950i	−0.580323	−	0.814386i	$-0.697074\pi$
$653$	8.41858	−	31.4186i	0.329445	−	1.22950i	0.909768	−	0.415118i	$-0.136260\pi$
$654$			11.6603i			0.455952i
$655$	1.00000	−	16.6603i	0.0390732	−	0.650970i
$656$	1.60770	+	0.928203i	0.0627700	+	0.0362402i
$657$	4.33975	−	4.33975i	0.169310	−	0.169310i
$658$	−0.803848	−	2.32051i	−0.0313372	−	0.0904628i
$659$	39.3205			1.53171			0.765855	−	0.643014i	$-0.222316\pi$
$659$	39.3205			1.53171			0.765855	+	0.643014i	$0.222316\pi$
$660$	−2.00000	+	6.00000i	−0.0778499	+	0.233550i
$661$	19.9641	−	34.5788i	0.776514	−	1.34496i	−0.157426	−	0.987531i	$-0.550320\pi$
$661$	19.9641	−	34.5788i	0.776514	−	1.34496i	0.933940	−	0.357430i	$-0.116347\pi$
$662$	−7.26795	−	7.26795i	−0.282477	−	0.282477i
$663$	−9.00000	+	33.5885i	−0.349531	+	1.30447i
$664$	−18.2487			−0.708187
$665$	−19.7321	+	5.53590i	−0.765176	+	0.214673i
$666$	−3.46410	−	6.00000i	−0.134231	−	0.232495i
$667$	6.69615	+	1.79423i	0.259276	+	0.0694728i
$668$	−2.41154	+	9.00000i	−0.0933054	+	0.348220i
$669$	−10.8301	+	18.7583i	−0.418717	+	0.725239i
$670$	−12.6340	−	0.758330i	−0.488093	−	0.0292969i
$671$			7.26795i			0.280576i
$672$	−9.46410	−	27.3205i	−0.365086	−	1.05391i
$673$	−10.1962	+	10.1962i	−0.393033	+	0.393033i	−0.875767	−	0.482734i	$-0.839644\pi$
$673$	−10.1962	+	10.1962i	−0.393033	+	0.393033i	0.482734	+	0.875767i	$0.339644\pi$
$674$	19.6603	−	34.0526i	0.757285	−	1.31166i
$675$	−8.16025	+	20.3301i	−0.314088	+	0.782507i
$676$	5.00000	+	8.66025i	0.192308	+	0.333087i
$677$	−1.22243	+	4.56218i	−0.0469819	+	0.175339i	−0.985430	−	0.170081i	$-0.945597\pi$
$677$	−1.22243	+	4.56218i	−0.0469819	+	0.175339i	0.938448	+	0.345420i	$0.112264\pi$
$678$	−2.53590	+	9.46410i	−0.0973906	+	0.363467i
$679$	−10.2417	+	21.0981i	−0.393039	+	0.809670i
$680$	24.0000	−	12.0000i	0.920358	−	0.460179i
$681$	−12.8301	−	22.2224i	−0.491652	−	0.851565i
$682$	−7.46410	+	7.46410i	−0.285815	+	0.285815i
$683$	−29.3564	+	7.86603i	−1.12329	+	0.300985i	−0.772215	−	0.635362i	$-0.780851\pi$
$683$	−29.3564	+	7.86603i	−1.12329	+	0.300985i	−0.351077	+	0.936347i	$0.614184\pi$
$684$		−	5.07180i		−	0.193925i
$685$	−18.0000	−	6.00000i	−0.687745	−	0.229248i
$686$	−24.9545	−	7.95448i	−0.952767	−	0.303704i
$687$	21.1244	+	21.1244i	0.805944	+	0.805944i
$688$	12.9282	−	3.46410i	0.492883	−	0.132068i
$689$	6.58846	−	11.4115i	0.251000	−	0.434745i
$690$	9.00000	+	3.00000i	0.342624	+	0.114208i
$691$	−21.7583	−	37.6865i	−0.827726	−	1.43366i	−0.899818	−	0.436265i	$-0.856301\pi$
$691$	−21.7583	−	37.6865i	−0.827726	−	1.43366i	0.0720922	−	0.997398i	$-0.477032\pi$
$692$	0.928203	−	0.248711i	0.0352850	−	0.00945459i
$693$	−1.33975	+	0.464102i	−0.0508927	+	0.0176298i
$694$	44.2750	−	25.5622i	1.68066	−	0.970327i
$695$	1.56218	−	2.36603i	0.0592568	−	0.0897485i
$696$	−12.1962	+	21.1244i	−0.462294	+	0.800717i
$697$	−1.90192	+	0.509619i	−0.0720405	+	0.0193032i
$698$	27.2942	−	7.31347i	1.03310	−	0.276819i
$699$			14.1962i			0.536948i
$700$	25.1962	+	8.07180i	0.952325	+	0.305085i
$701$			33.9808i			1.28344i	0.766941	+	0.641718i	$0.221778\pi$
$701$			33.9808i			1.28344i	−0.766941	+	0.641718i	$0.778222\pi$
$702$	6.80385	+	25.3923i	0.256795	+	0.958371i
$703$	22.3923	−	6.00000i	0.844542	−	0.226294i
$704$	2.92820	−	5.07180i	0.110361	−	0.191151i
$705$	−1.56218	+	2.36603i	−0.0588350	+	0.0891097i
$706$	−18.5885	−	32.1962i	−0.699586	−	1.21172i
$707$	−5.06218	+	26.3038i	−0.190383	+	0.989258i
$708$	−8.92820	−	33.3205i	−0.335542	−	1.25226i
$709$	7.96410	+	13.7942i	0.299098	+	0.518053i	0.975930	−	0.218085i	$-0.0699809\pi$
$709$	7.96410	+	13.7942i	0.299098	+	0.518053i	−0.676832	+	0.736138i	$0.736648\pi$
$710$	−15.4641	+	46.3923i	−0.580357	+	1.74107i
$711$	4.73205	−	8.19615i	0.177466	−	0.307380i
$712$	−12.5885	+	46.9808i	−0.471772	+	1.76068i
$713$	11.1962	+	11.1962i	0.419299	+	0.419299i
$714$	27.5885	+	13.3923i	1.03247	+	0.501194i
$715$	−6.58846	−	2.19615i	−0.246394	−	0.0821314i
$716$			28.1051i			1.05034i
$717$	−8.83013	+	2.36603i	−0.329767	+	0.0883608i
$718$	4.73205	+	4.73205i	0.176599	+	0.176599i
$719$	−5.36603	−	9.29423i	−0.200119	−	0.346616i	0.748448	−	0.663194i	$-0.230800\pi$
$719$	−5.36603	−	9.29423i	−0.200119	−	0.346616i	−0.948567	+	0.316578i	$0.897466\pi$
$720$	−3.60770	+	5.46410i	−0.134451	+	0.203635i
$721$	2.43782	+	33.9545i	0.0907892	+	1.26453i
$722$	−9.56218	−	2.56218i	−0.355867	−	0.0953544i
$723$	10.1962	−	38.0526i	0.379199	−	1.41519i
$724$	39.0000	−	22.5167i	1.44942	−	0.836825i
$725$	−8.76795	−	20.5263i	−0.325633	−	0.762327i
$726$	24.7583	+	14.2942i	0.918868	+	0.530509i
$727$	−17.2942	+	17.2942i	−0.641407	+	0.641407i	−0.950901	−	0.309494i	$-0.899840\pi$
$727$	−17.2942	+	17.2942i	−0.641407	+	0.641407i	0.309494	+	0.950901i	$0.399840\pi$
$728$	30.0000	−	10.3923i	1.11187	−	0.385164i
$729$			17.5885i			0.651424i
$730$	1.58846	−	26.4641i	0.0587914	−	0.979480i
$731$	−7.09808	+	12.2942i	−0.262532	+	0.454718i
$732$	−9.92820	+	37.0526i	−0.366957	+	1.36950i
$733$	−21.2942	−	5.70577i	−0.786520	−	0.210747i	−0.156863	−	0.987620i	$-0.550138\pi$
$733$	−21.2942	−	5.70577i	−0.786520	−	0.210747i	−0.629657	+	0.776873i	$0.716805\pi$
$734$	−10.2224	+	5.90192i	−0.377317	+	0.217844i
$735$	10.2321	+	28.4545i	0.377415	+	1.04956i
$736$	−7.60770	−	4.39230i	−0.280423	−	0.161903i
$737$	0.758330	−	2.83013i	0.0279335	−	0.104249i
$738$	0.339746	−	0.339746i	0.0125062	−	0.0125062i
$739$	5.83013	−	10.0981i	0.214465	−	0.371464i	−0.738642	−	0.674098i	$-0.764533\pi$
$739$	5.83013	−	10.0981i	0.214465	−	0.371464i	0.953107	+	0.302634i	$0.0978660\pi$
$740$	−28.3923	−	9.46410i	−1.04372	−	0.347907i
$741$	28.3923			1.04302
$742$	−8.78461	−	7.60770i	−0.322493	−	0.279287i
$743$	−33.4186	+	33.4186i	−1.22601	+	1.22601i	−0.260548	+	0.965461i	$0.583903\pi$
$743$	−33.4186	+	33.4186i	−1.22601	+	1.22601i	−0.965461	+	0.260548i	$0.916097\pi$
$744$	−48.2487	+	27.8564i	−1.76888	+	1.02127i
$745$	−3.03590	+	50.5788i	−0.111227	+	1.85307i
$746$	13.8564			0.507319
$747$	−1.22243	+	4.56218i	−0.0447264	+	0.166921i
$748$	1.60770	+	6.00000i	0.0587832	+	0.219382i
$749$	14.5622	−	1.04552i	0.532090	−	0.0382024i
$750$	−10.2942	−	28.7583i	−0.375892	−	1.05011i
$751$	5.19615	+	9.00000i	0.189610	+	0.328415i	0.945120	−	0.326722i	$-0.105944\pi$
$751$	5.19615	+	9.00000i	0.189610	+	0.328415i	−0.755510	+	0.655137i	$0.772611\pi$
$752$	1.85641	−	1.85641i	0.0676962	−	0.0676962i
$753$	9.83013	+	36.6865i	0.358230	+	1.33693i
$754$	−23.1962	−	13.3923i	−0.844754	−	0.487719i
$755$	−27.6077	+	13.8038i	−1.00475	+	0.502373i
$756$	23.1244	−	1.66025i	0.841025	−	0.0603829i
$757$	37.0526	−	37.0526i	1.34670	−	1.34670i	0.457476	−	0.889222i	$-0.348753\pi$
$757$	37.0526	−	37.0526i	1.34670	−	1.34670i	0.889222	−	0.457476i	$-0.151247\pi$
$758$	−11.0718	−	41.3205i	−0.402146	−	1.50083i
$759$	−1.09808	+	1.90192i	−0.0398576	+	0.0690355i
$760$	−14.5359	−	16.3923i	−0.527272	−	0.594611i
$761$	−30.8038	+	17.7846i	−1.11664	+	0.644692i	−0.940541	−	0.339681i	$-0.889681\pi$
$761$	−30.8038	+	17.7846i	−1.11664	+	0.644692i	−0.176098	+	0.984373i	$0.556348\pi$
$762$	41.0526	+	11.0000i	1.48718	+	0.398488i
$763$	−2.13397	+	11.0885i	−0.0772551	+	0.401429i
$764$	5.41154	+	3.12436i	0.195783	+	0.113035i
$765$	−1.39230	−	6.80385i	−0.0503389	−	0.245994i
$766$	−10.7321			−0.387765
$767$	36.5885	−	9.80385i	1.32113	−	0.353996i
$768$	21.8564	−	21.8564i	0.788675	−	0.788675i
$769$	22.6410			0.816456			0.408228	−	0.912880i	$-0.366147\pi$
$769$	22.6410			0.816456			0.408228	+	0.912880i	$0.366147\pi$
$770$	−3.00000	+	5.33975i	−0.108112	+	0.192431i
$771$			51.7128i			1.86239i
$772$	−16.9282	−	16.9282i	−0.609259	−	0.609259i
$773$	3.50962	+	13.0981i	0.126232	+	0.471105i	0.999881	−	0.0154528i	$-0.00491896\pi$
$773$	3.50962	+	13.0981i	0.126232	+	0.471105i	−0.873648	+	0.486558i	$0.838252\pi$
$774$		−	3.46410i		−	0.124515i
$775$	6.09808	−	50.6147i	0.219049	−	1.81814i
$776$	−25.0718			−0.900025
$777$	−11.1962	−	32.3205i	−0.401660	−	1.15949i
$778$	−20.5885	−	5.51666i	−0.738132	−	0.197782i
$779$	0.803848	+	1.39230i	0.0288008	+	0.0498845i
$780$	−30.5885	−	20.1962i	−1.09524	−	0.723138i
$781$	−9.80385	−	5.66025i	−0.350809	−	0.202540i
$782$	9.00000	−	2.41154i	0.321839	−	0.0862366i
$783$	−13.8301	−	13.8301i	−0.494248	−	0.494248i
$784$	−4.00000	−	27.7128i	−0.142857	−	0.989743i
$785$	−37.3923	−	12.4641i	−1.33459	−	0.444863i
$786$	17.6603	+	10.1962i	0.629920	+	0.363685i
$787$	−10.1603	+	2.72243i	−0.362174	+	0.0970442i	−0.435317	−	0.900277i	$-0.643364\pi$
$787$	−10.1603	+	2.72243i	−0.362174	+	0.0970442i	0.0731430	+	0.997321i	$0.476697\pi$
$788$	4.05256	−	15.1244i	0.144366	−	0.538783i
$789$	0.696152	−	0.401924i	0.0247837	−	0.0143089i
$790$	−8.19615	−	40.0526i	−0.291606	−	1.42501i
$791$	−4.14359	+	8.53590i	−0.147329	+	0.303502i
$792$	−1.07180	−	1.07180i	−0.0380846	−	0.0380846i
$793$	−40.6865	−	10.9019i	−1.44482	−	0.387139i
$794$	−31.8564			−1.13054
$795$	−0.803848	+	13.3923i	−0.0285095	+	0.474976i
$796$		−	6.92820i		−	0.245564i
$797$	0.928203	+	0.928203i	0.0328786	+	0.0328786i	0.723355	−	0.690476i	$-0.242599\pi$
$797$	0.928203	+	0.928203i	0.0328786	+	0.0328786i	−0.690476	+	0.723355i	$0.742599\pi$
$798$	4.73205	−	24.5885i	0.167513	−	0.870422i
$799$			2.78461i			0.0985124i
$800$	4.00000	+	28.0000i	0.141421	+	0.989949i
$801$	10.9019	+	6.29423i	0.385201	+	0.222396i
$802$	−30.7128	+	30.7128i	−1.08451	+	1.08451i
$803$	5.92820	+	1.58846i	0.209202	+	0.0560554i
$804$	7.73205	−	13.3923i	0.272688	−	0.472310i
$805$	8.00962	+	4.50000i	0.282302	+	0.158604i
$806$	−30.5885	−	52.9808i	−1.07743	−	1.86617i
$807$	1.76795	−	6.59808i	0.0622348	−	0.232263i
$808$	−27.6603	+	7.41154i	−0.973084	+	0.260737i
$809$	−40.5788	−	23.4282i	−1.42668	−	0.823692i	−0.429819	−	0.902915i	$-0.641423\pi$
$809$	−40.5788	−	23.4282i	−1.42668	−	0.823692i	−0.996857	+	0.0792233i	$0.974756\pi$
$810$	−22.3660	−	25.2224i	−0.785862	−	0.886226i
$811$	30.3397			1.06537			0.532686	−	0.846313i	$-0.321183\pi$
$811$	30.3397			1.06537			0.532686	+	0.846313i	$0.321183\pi$
$812$	−15.4641	+	17.8564i	−0.542684	+	0.626637i
$813$	16.3923	+	16.3923i	0.574903	+	0.574903i
$814$	3.46410	−	6.00000i	0.121417	−	0.210300i
$815$	6.29423	−	5.58142i	0.220477	−	0.195508i
$816$			32.7846i			1.14769i
$817$	11.1962	+	3.00000i	0.391704	+	0.104957i
$818$	15.5622	+	4.16987i	0.544119	+	0.145796i
$819$	−0.588457	−	8.19615i	−0.0205624	−	0.286397i
$820$	0.124356	−	2.07180i	0.00434269	−	0.0723503i
$821$	−9.92820	+	5.73205i	−0.346497	+	0.200050i	−0.663141	−	0.748494i	$-0.730777\pi$
$821$	−9.92820	+	5.73205i	−0.346497	+	0.200050i	0.316645	+	0.948544i	$0.397444\pi$
$822$	16.3923	−	16.3923i	0.571747	−	0.571747i
$823$	3.66987	+	13.6962i	0.127924	+	0.477418i	0.999927	−	0.0120822i	$-0.00384597\pi$
$823$	3.66987	+	13.6962i	0.127924	+	0.477418i	−0.872003	+	0.489500i	$0.837179\pi$
$824$	−31.5167	+	18.1962i	−1.09793	+	0.633893i
$825$	7.00000	−	1.00000i	0.243709	−	0.0348155i
$826$	−2.39230	−	33.3205i	−0.0832389	−	1.15937i
$827$	17.1506	−	17.1506i	0.596386	−	0.596386i	−0.342963	−	0.939349i	$-0.611431\pi$
$827$	17.1506	−	17.1506i	0.596386	−	0.596386i	0.939349	+	0.342963i	$0.111431\pi$
$828$	−1.60770	+	1.60770i	−0.0558713	+	0.0558713i
$829$	−8.19615	−	4.73205i	−0.284664	−	0.164351i	0.350869	−	0.936425i	$-0.385886\pi$
$829$	−8.19615	−	4.73205i	−0.284664	−	0.164351i	−0.635533	+	0.772074i	$0.719220\pi$
$830$	9.12436	+	18.2487i	0.316711	+	0.633422i
$831$	−32.4904	+	18.7583i	−1.12708	+	0.650719i
$832$	24.0000	+	24.0000i	0.832050	+	0.832050i
$833$	23.7846	+	17.7846i	0.824088	+	0.616200i
$834$	1.73205	+	3.00000i	0.0599760	+	0.103882i
$835$	10.2058	−	2.08846i	0.353185	−	0.0722740i
$836$	4.39230	−	2.53590i	0.151911	−	0.0877059i
$837$	−11.5622	−	43.1506i	−0.399647	−	1.49150i
$838$	3.26795	−	0.875644i	0.112889	−	0.0302486i
$839$	14.1962			0.490106			0.245053	−	0.969510i	$-0.421195\pi$
$839$	14.1962			0.490106			0.245053	+	0.969510i	$0.421195\pi$
$840$	−22.5885	+	23.1244i	−0.779376	+	0.797866i
$841$	−9.07180			−0.312821
$842$	−41.1506	+	11.0263i	−1.41814	+	0.379991i
$843$	−12.1244	−	45.2487i	−0.417585	−	1.55845i
$844$	20.5359	+	35.5692i	0.706875	+	1.22434i
$845$	6.16025	−	9.33013i	0.211919	−	0.320966i
$846$	−0.339746	−	0.588457i	−0.0116807	−	0.0202316i
$847$	20.9282	+	18.1244i	0.719102	+	0.622760i
$848$	3.21539	−	12.0000i	0.110417	−	0.412082i
$849$	−23.4904	+	13.5622i	−0.806188	+	0.465453i
$850$	−24.0000	−	18.0000i	−0.823193	−	0.617395i
$851$	−9.00000	−	5.19615i	−0.308516	−	0.178122i
$852$	−42.2487	−	42.2487i	−1.44742	−	1.44742i
$853$	29.3205	−	29.3205i	1.00392	−	1.00392i	0.00392277	−	0.999992i	$-0.498751\pi$
$853$	29.3205	−	29.3205i	1.00392	−	1.00392i	0.999992	−	0.00392277i	$-0.00124866\pi$
$854$	−16.2224	+	33.4186i	−0.555120	+	1.14356i
$855$	−5.07180	+	2.53590i	−0.173452	+	0.0867259i
$856$	7.80385	+	13.5167i	0.266730	+	0.461990i
$857$	4.22243	+	15.7583i	0.144236	+	0.538294i	0.999788	+	0.0205786i	$0.00655083\pi$
$857$	4.22243	+	15.7583i	0.144236	+	0.538294i	−0.855553	+	0.517716i	$0.826782\pi$
$858$	6.00000	−	6.00000i	0.204837	−	0.204837i
$859$	14.1962	−	8.19615i	0.484366	−	0.279649i	−0.237868	−	0.971298i	$-0.576449\pi$
$859$	14.1962	−	8.19615i	0.484366	−	0.279649i	0.722234	+	0.691648i	$0.243115\pi$
$860$	−9.92820	−	11.1962i	−0.338549	−	0.381786i
$861$	1.96410	−	1.33013i	0.0669364	−	0.0453306i
$862$	18.1244	+	4.85641i	0.617318	+	0.165410i
$863$	−23.2583	−	6.23205i	−0.791723	−	0.212141i	−0.159776	−	0.987153i	$-0.551077\pi$
$863$	−23.2583	−	6.23205i	−0.791723	−	0.212141i	−0.631947	+	0.775012i	$0.717744\pi$
$864$	12.3923	+	21.4641i	0.421595	+	0.730224i
$865$	−0.712813	−	0.803848i	−0.0242364	−	0.0273316i
$866$	11.4641	−	19.8564i	0.389566	−	0.674748i
$867$	−1.36603	−	1.36603i	−0.0463927	−	0.0463927i
$868$	−50.9808	+	17.6603i	−1.73040	+	0.599428i
$869$	9.46410			0.321048
$870$	27.2224	+	1.63397i	0.922927	+	0.0553969i
$871$	14.7058	+	8.49038i	0.498286	+	0.287686i
$872$	−11.6603	+	3.12436i	−0.394866	+	0.105804i
$873$	−1.67949	+	6.26795i	−0.0568422	+	0.212138i
$874$	−3.80385	−	6.58846i	−0.128667	−	0.222858i
$875$	−4.52628	−	29.2321i	−0.153016	−	0.988224i
$876$	28.0526	+	16.1962i	0.947808	+	0.547217i
$877$	19.3923	+	5.19615i	0.654832	+	0.175462i	0.570912	−	0.821011i	$-0.306590\pi$
$877$	19.3923	+	5.19615i	0.654832	+	0.175462i	0.0839192	+	0.996473i	$0.473256\pi$
$878$	5.32051	−	5.32051i	0.179558	−	0.179558i
$879$	−9.92820	−	5.73205i	−0.334870	−	0.193337i
$880$	−6.53590	−	0.392305i	−0.220325	−	0.0132246i
$881$		−	27.2487i		−	0.918032i	−0.888428	−	0.459016i	$-0.848202\pi$
$881$		−	27.2487i		−	0.918032i	0.888428	−	0.459016i	$-0.151798\pi$
$882$	−7.19615	−	0.856406i	−0.242307	−	0.0288367i
$883$	15.2487	+	15.2487i	0.513160	+	0.513160i	0.915493	−	0.402333i	$-0.131801\pi$
$883$	15.2487	+	15.2487i	0.513160	+	0.513160i	−0.402333	+	0.915493i	$0.631801\pi$
$884$	−36.0000			−1.21081
$885$	−28.8564	+	25.5885i	−0.969997	+	0.860147i
$886$	−48.8372			−1.64072
$887$	−3.06218	−	0.820508i	−0.102818	−	0.0275500i	0.207043	−	0.978332i	$-0.433616\pi$
$887$	−3.06218	−	0.820508i	−0.102818	−	0.0275500i	−0.309861	+	0.950782i	$0.600283\pi$
$888$	25.8564	−	25.8564i	0.867684	−	0.867684i
$889$	37.0263	+	17.9737i	1.24182	+	0.602819i
$890$	53.2750	−	10.9019i	1.78578	−	0.365433i
$891$	6.75833	−	3.90192i	0.226413	−	0.130719i
$892$	−21.6603	−	5.80385i	−0.725239	−	0.194327i
$893$	2.19615	−	0.588457i	0.0734914	−	0.0196920i
$894$	−53.6147	−	30.9545i	−1.79315	−	1.03527i
$895$	28.1051	−	14.0526i	0.939450	−	0.469725i
$896$	24.7846	−	16.7846i	0.827996	−	0.560734i
$897$	−9.00000	−	9.00000i	−0.300501	−	0.300501i
$898$	−31.6865	+	8.49038i	−1.05739	+	0.283328i
$899$	39.4186	+	22.7583i	1.31468	+	0.759033i
$900$	7.26795	+	0.875644i	0.242265	+	0.0291881i
$901$	6.58846	+	11.4115i	0.219493	+	0.380174i
$902$	0.464102	+	0.124356i	0.0154529	+	0.00414059i
$903$	3.23205	−	16.7942i	0.107556	−	0.558877i
$904$	−10.1436			−0.337371
$905$	−42.0167	−	27.7417i	−1.39668	−	0.922164i
$906$		−	37.7128i		−	1.25292i
$907$	−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	$0.941311\pi$
$908$	18.7846	−	18.7846i	0.623389	−	0.623389i
$909$			7.41154i			0.245825i
$910$	−25.3923	−	24.8038i	−0.841747	−	0.822240i
$911$	8.19615			0.271551			0.135775	−	0.990740i	$-0.456647\pi$
$911$	8.19615			0.271551			0.135775	+	0.990740i	$0.456647\pi$
$912$	25.8564	−	6.92820i	0.856191	−	0.229416i
$913$	−4.56218	+	1.22243i	−0.150986	+	0.0404566i
$914$	−20.3923			−0.674517
$915$	42.0167	−	8.59808i	1.38903	−	0.284244i
$916$	−15.4641	+	26.7846i	−0.510948	+	0.884988i
$917$	14.9282	+	12.9282i	0.492973	+	0.426927i
$918$	−25.3923	−	6.80385i	−0.838071	−	0.224560i
$919$	−39.0000	+	22.5167i	−1.28649	+	0.742756i	−0.978027	−	0.208480i	$-0.933148\pi$
$919$	−39.0000	+	22.5167i	−1.28649	+	0.742756i	−0.308465	+	0.951236i	$0.599815\pi$
$920$	−0.588457	+	9.80385i	−0.0194009	+	0.323223i
$921$	−1.03590	+	1.79423i	−0.0341340	+	0.0591218i
$922$	4.44486	+	16.5885i	0.146384	+	0.546312i
$923$	46.3923	−	46.3923i	1.52702	−	1.52702i
$924$	−4.19615	−	6.19615i	−0.138043	−	0.203838i
$925$	4.73205	+	33.1244i	0.155589	+	1.08912i
$926$	1.43782	+	0.830127i	0.0472498	+	0.0272797i
$927$	2.43782	+	9.09808i	0.0800686	+	0.298820i
$928$	−24.3923	−	6.53590i	−0.800717	−	0.214551i
$929$	−4.16025	−	7.20577i	−0.136494	−	0.236414i	0.789673	−	0.613527i	$-0.210250\pi$
$929$	−4.16025	−	7.20577i	−0.136494	−	0.236414i	−0.926167	+	0.377114i	$0.876917\pi$
$930$	51.9808	+	34.3205i	1.70452	+	1.12541i
$931$	9.00000	−	22.5167i	0.294963	−	0.737954i
$932$	−14.1962	+	3.80385i	−0.465010	+	0.124599i
$933$	−12.4641	+	46.5167i	−0.408056	+	1.52289i
$934$	9.12436			0.298558
$935$	5.19615	−	4.60770i	0.169932	−	0.150688i
$936$	7.60770	−	4.39230i	0.248665	−	0.143567i
$937$	0.392305	−	0.392305i	0.0128160	−	0.0128160i	−0.700670	−	0.713486i	$-0.747115\pi$
$937$	0.392305	−	0.392305i	0.0128160	−	0.0128160i	0.713486	+	0.700670i	$0.247115\pi$
$938$	9.80385	−	11.3205i	0.320107	−	0.369628i
$939$	−32.2487			−1.05240
$940$	−2.78461	−	0.928203i	−0.0908240	−	0.0302747i
$941$	−9.73205	+	16.8564i	−0.317256	+	0.549503i	−0.979914	−	0.199418i	$-0.936095\pi$
$941$	−9.73205	+	16.8564i	−0.317256	+	0.549503i	0.662659	+	0.748922i	$0.269428\pi$
$942$	34.0526	−	34.0526i	1.10949	−	1.10949i
$943$	0.186533	−	0.696152i	0.00607437	−	0.0226698i
$944$	30.9282	−	17.8564i	1.00663	−	0.581177i
$945$	−13.2224	−	22.2942i	−0.430126	−	0.725231i
$946$	3.00000	−	1.73205i	0.0975384	−	0.0563138i
$947$	−22.3301	−	5.98334i	−0.725632	−	0.194432i	−0.122949	−	0.992413i	$-0.539235\pi$
$947$	−22.3301	−	5.98334i	−0.725632	−	0.194432i	−0.602683	+	0.797981i	$0.705902\pi$
$948$	48.2487	+	12.9282i	1.56705	+	0.419889i
$949$	−17.7846	+	30.8038i	−0.577313	+	0.999935i
$950$	−9.12436	+	22.7321i	−0.296033	+	0.737525i
$951$		−	8.73205i		−	0.283156i
$952$	−6.00000	+	31.1769i	−0.194461	+	1.01045i
$953$	3.46410	−	3.46410i	0.112213	−	0.112213i	−0.648771	−	0.760984i	$-0.724717\pi$
$953$	3.46410	−	3.46410i	0.112213	−	0.112213i	0.760984	+	0.648771i	$0.224717\pi$
$954$	−2.78461	−	1.60770i	−0.0901551	−	0.0520511i
$955$	0.418584	−	6.97372i	0.0135451	−	0.225664i
$956$	−4.73205	−	8.19615i	−0.153045	−	0.265083i
$957$	−1.63397	+	6.09808i	−0.0528189	+	0.197123i
$958$	5.19615	+	1.39230i	0.167880	+	0.0449833i
$959$	18.5885	−	12.5885i	0.600253	−	0.406502i
$960$	−32.7846	−	10.9282i	−1.05812	−	0.352706i
$961$	36.4808	+	63.1865i	1.17680	+	2.03828i
$962$	28.3923	+	28.3923i	0.915405	+	0.915405i
$963$	3.90192	−	1.04552i	0.125738	−	0.0336913i
$964$	40.7846			1.31358
$965$	−8.46410	+	25.3923i	−0.272469	+	0.817407i
$966$	−9.29423	+	6.29423i	−0.299037	+	0.202513i
$967$	−10.5096	−	10.5096i	−0.337967	−	0.337967i	0.517635	−	0.855602i	$-0.326813\pi$
$967$	−10.5096	−	10.5096i	−0.337967	−	0.337967i	−0.855602	+	0.517635i	$0.826813\pi$
$968$	−7.66025	+	28.5885i	−0.246210	+	0.918868i
$969$	−14.1962	+	24.5885i	−0.456046	+	0.789895i
$970$	12.5359	+	25.0718i	0.402503	+	0.805007i
$971$	10.0000	+	17.3205i	0.320915	+	0.555842i	0.980677	−	0.195633i	$-0.0626762\pi$
$971$	10.0000	+	17.3205i	0.320915	+	0.555842i	−0.659762	+	0.751475i	$0.729343\pi$
$972$	14.3923	−	3.85641i	0.461633	−	0.123694i
$973$	1.09808	+	3.16987i	0.0352027	+	0.101621i
$974$	−13.9282	−	24.1244i	−0.446288	−	0.772994i
$975$	−4.90192	+	40.6865i	−0.156987	+	1.30301i
$976$	−39.7128			−1.27118
$977$	20.0263	−	5.36603i	0.640697	−	0.171674i	0.0761781	−	0.997094i	$-0.475728\pi$
$977$	20.0263	−	5.36603i	0.640697	−	0.171674i	0.564519	+	0.825420i	$0.309062\pi$
$978$	2.66025	+	9.92820i	0.0850655	+	0.317469i
$979$			12.5885i			0.402329i
$980$	−25.7128	+	17.8564i	−0.821366	+	0.570402i
$981$			3.12436i			0.0997530i
$982$	−16.6603	+	4.46410i	−0.531650	+	0.142455i
$983$	12.2321	−	3.27757i	0.390142	−	0.104538i	−0.0584153	−	0.998292i	$-0.518605\pi$
$983$	12.2321	−	3.27757i	0.390142	−	0.104538i	0.448557	+	0.893754i	$0.351938\pi$
$984$	2.19615	+	1.26795i	0.0700108	+	0.0404207i
$985$	−17.1506	+	3.50962i	−0.546465	+	0.111826i
$986$	23.1962	−	13.3923i	0.738716	−	0.426498i
$987$	−1.09808	−	3.16987i	−0.0349522	−	0.100898i
$988$	7.60770	+	28.3923i	0.242033	+	0.903280i
$989$	−2.59808	−	4.50000i	−0.0826140	−	0.143092i
$990$	−0.535898	+	1.60770i	−0.0170320	+	0.0510959i
$991$	−17.6865	+	30.6340i	−0.561831	+	0.973120i	0.435506	+	0.900186i	$0.356570\pi$
$991$	−17.6865	+	30.6340i	−0.561831	+	0.973120i	−0.997337	+	0.0729342i	$0.976764\pi$
$992$	−40.7846	−	40.7846i	−1.29491	−	1.29491i
$993$	−9.92820	−	9.92820i	−0.315062	−	0.315062i
$994$	−32.4449	−	47.9090i	−1.02909	−	1.51958i
$995$	−6.92820	+	3.46410i	−0.219639	+	0.109819i
$996$	−24.9282			−0.789880
$997$	11.1962	−	3.00000i	0.354586	−	0.0950110i	−0.0771291	−	0.997021i	$-0.524575\pi$
$997$	11.1962	−	3.00000i	0.354586	−	0.0950110i	0.431715	+	0.902010i	$0.357909\pi$
$998$	−13.5167	+	13.5167i	−0.427862	+	0.427862i
$999$	14.6603	+	25.3923i	0.463830	+	0.803377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bv.b.157.1	yes	4
5.3	odd	4		280.2.bv.c.213.1	yes	4
7.5	odd	6		280.2.bv.d.117.1	yes	4
8.5	even	2		280.2.bv.a.157.1	✓	4
35.33	even	12		280.2.bv.a.173.1	yes	4
40.13	odd	4		280.2.bv.d.213.1	yes	4
56.5	odd	6		280.2.bv.c.117.1	yes	4
280.173	even	12	inner	280.2.bv.b.173.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bv.a.157.1	✓	4	8.5	even	2
280.2.bv.a.173.1	yes	4	35.33	even	12
280.2.bv.b.157.1	yes	4	1.1	even	1	trivial
280.2.bv.b.173.1	yes	4	280.173	even	12	inner
280.2.bv.c.117.1	yes	4	56.5	odd	6
280.2.bv.c.213.1	yes	4	5.3	odd	4
280.2.bv.d.117.1	yes	4	7.5	odd	6
280.2.bv.d.213.1	yes	4	40.13	odd	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(0.500000 + 1.86603i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-2.36603 + 1.36603i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.633975 + 0.366025i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 1.36603i) q^{2} +(0.500000 + 1.86603i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-2.36603 + 1.36603i) q^{6} +(-2.50000 + 0.866025i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.633975 + 0.366025i) q^{9} +(-1.00000 + 3.00000i) q^{10} +(-0.633975 - 0.366025i) q^{11} +(-2.73205 - 2.73205i) q^{12} +(3.00000 - 3.00000i) q^{13} +(-2.09808 - 3.09808i) q^{14} +(-1.36603 + 4.09808i) q^{15} +(2.00000 - 3.46410i) q^{16} +(1.09808 + 4.09808i) q^{17} +(-0.732051 - 0.732051i) q^{18} +(3.00000 - 1.73205i) q^{19} +(-4.46410 - 0.267949i) q^{20} +(-2.86603 - 4.23205i) q^{21} +(0.267949 - 1.00000i) q^{22} +(-1.50000 - 0.401924i) q^{23} +(2.73205 - 4.73205i) q^{24} +(1.96410 + 4.59808i) q^{25} +(5.19615 + 3.00000i) q^{26} +(3.09808 + 3.09808i) q^{27} +(3.46410 - 4.00000i) q^{28} -4.46410 q^{29} +(-6.09808 - 0.366025i) q^{30} +(-8.83013 - 5.09808i) q^{31} +(5.46410 + 1.46410i) q^{32} +(0.366025 - 1.36603i) q^{33} +(-5.19615 + 3.00000i) q^{34} +(-5.73205 - 1.46410i) q^{35} +(0.732051 - 1.26795i) q^{36} +(6.46410 + 1.73205i) q^{37} +(3.46410 + 3.46410i) q^{38} +(7.09808 + 4.09808i) q^{39} +(-1.26795 - 6.19615i) q^{40} +0.464102i q^{41} +(4.73205 - 5.46410i) q^{42} +(2.36603 + 2.36603i) q^{43} +1.46410 q^{44} +(-1.63397 - 0.0980762i) q^{45} -2.19615i q^{46} +(0.633975 + 0.169873i) q^{47} +(7.46410 + 2.00000i) q^{48} +(5.50000 - 4.33013i) q^{49} +(-5.56218 + 4.36603i) q^{50} +(-7.09808 + 4.09808i) q^{51} +(-2.19615 + 8.19615i) q^{52} +(3.00000 - 0.803848i) q^{53} +(-3.09808 + 5.36603i) q^{54} +(-0.732051 - 1.46410i) q^{55} +(6.73205 + 3.26795i) q^{56} +(4.73205 + 4.73205i) q^{57} +(-1.63397 - 6.09808i) q^{58} +(7.73205 + 4.46410i) q^{59} +(-1.73205 - 8.46410i) q^{60} +(-4.96410 - 8.59808i) q^{61} +(3.73205 - 13.9282i) q^{62} +(1.26795 - 1.46410i) q^{63} +8.00000i q^{64} +(9.29423 - 1.90192i) q^{65} +2.00000 q^{66} +(1.03590 + 3.86603i) q^{67} +(-6.00000 - 6.00000i) q^{68} -3.00000i q^{69} +(-0.0980762 - 8.36603i) q^{70} +15.4641 q^{71} +(2.00000 + 0.535898i) q^{72} +(-8.09808 + 2.16987i) q^{73} +9.46410i q^{74} +(-7.59808 + 5.96410i) q^{75} +(-3.46410 + 6.00000i) q^{76} +(1.90192 + 0.366025i) q^{77} +(-3.00000 + 11.1962i) q^{78} +(-11.1962 + 6.46410i) q^{79} +(8.00000 - 4.00000i) q^{80} +(-5.33013 + 9.23205i) q^{81} +(-0.633975 + 0.169873i) q^{82} +(4.56218 - 4.56218i) q^{83} +(9.19615 + 4.46410i) q^{84} +(-3.00000 + 9.00000i) q^{85} +(-2.36603 + 4.09808i) q^{86} +(-2.23205 - 8.33013i) q^{87} +(0.535898 + 2.00000i) q^{88} +(-8.59808 - 14.8923i) q^{89} +(-0.464102 - 2.26795i) q^{90} +(-4.90192 + 10.0981i) q^{91} +(3.00000 - 0.803848i) q^{92} +(5.09808 - 19.0263i) q^{93} +0.928203i q^{94} +(7.73205 + 0.464102i) q^{95} +10.9282i q^{96} +(6.26795 - 6.26795i) q^{97} +(7.92820 + 5.92820i) q^{98} +0.535898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} + 4 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 + 4 * q^5 - 6 * q^6 - 10 * q^7 - 8 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} + 4 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9} - 4 q^{10} - 6 q^{11} - 4 q^{12} + 12 q^{13} + 2 q^{14} - 2 q^{15} + 8 q^{16} - 6 q^{17} + 4 q^{18} + 12 q^{19} - 4 q^{20} - 8 q^{21} + 8 q^{22} - 6 q^{23} + 4 q^{24} - 6 q^{25} + 2 q^{27} - 4 q^{29} - 14 q^{30} - 18 q^{31} + 8 q^{32} - 2 q^{33} - 16 q^{35} - 4 q^{36} + 12 q^{37} + 18 q^{39} - 12 q^{40} + 12 q^{42} + 6 q^{43} - 8 q^{44} - 10 q^{45} + 6 q^{47} + 16 q^{48} + 22 q^{49} + 2 q^{50} - 18 q^{51} + 12 q^{52} + 12 q^{53} - 2 q^{54} + 4 q^{55} + 20 q^{56} + 12 q^{57} - 10 q^{58} + 24 q^{59} - 6 q^{61} + 8 q^{62} + 12 q^{63} + 6 q^{65} + 8 q^{66} + 18 q^{67} - 24 q^{68} + 10 q^{70} + 48 q^{71} + 8 q^{72} - 22 q^{73} - 20 q^{75} + 18 q^{77} - 12 q^{78} - 24 q^{79} + 32 q^{80} - 4 q^{81} - 6 q^{82} - 6 q^{83} + 16 q^{84} - 12 q^{85} - 6 q^{86} - 2 q^{87} + 16 q^{88} - 24 q^{89} + 12 q^{90} - 30 q^{91} + 12 q^{92} + 10 q^{93} + 24 q^{95} + 32 q^{97} + 4 q^{98} + 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 + 4 * q^5 - 6 * q^6 - 10 * q^7 - 8 * q^8 - 6 * q^9 - 4 * q^10 - 6 * q^11 - 4 * q^12 + 12 * q^13 + 2 * q^14 - 2 * q^15 + 8 * q^16 - 6 * q^17 + 4 * q^18 + 12 * q^19 - 4 * q^20 - 8 * q^21 + 8 * q^22 - 6 * q^23 + 4 * q^24 - 6 * q^25 + 2 * q^27 - 4 * q^29 - 14 * q^30 - 18 * q^31 + 8 * q^32 - 2 * q^33 - 16 * q^35 - 4 * q^36 + 12 * q^37 + 18 * q^39 - 12 * q^40 + 12 * q^42 + 6 * q^43 - 8 * q^44 - 10 * q^45 + 6 * q^47 + 16 * q^48 + 22 * q^49 + 2 * q^50 - 18 * q^51 + 12 * q^52 + 12 * q^53 - 2 * q^54 + 4 * q^55 + 20 * q^56 + 12 * q^57 - 10 * q^58 + 24 * q^59 - 6 * q^61 + 8 * q^62 + 12 * q^63 + 6 * q^65 + 8 * q^66 + 18 * q^67 - 24 * q^68 + 10 * q^70 + 48 * q^71 + 8 * q^72 - 22 * q^73 - 20 * q^75 + 18 * q^77 - 12 * q^78 - 24 * q^79 + 32 * q^80 - 4 * q^81 - 6 * q^82 - 6 * q^83 + 16 * q^84 - 12 * q^85 - 6 * q^86 - 2 * q^87 + 16 * q^88 - 24 * q^89 + 12 * q^90 - 30 * q^91 + 12 * q^92 + 10 * q^93 + 24 * q^95 + 32 * q^97 + 4 * q^98 + 16 * q^99

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