LMFDB - Embedded newform 280.2.bv.a.173.1

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

Embedding invariants

Embedding label			173.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	280.173
Dual form			280.2.bv.a.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-0.500000 + 1.86603i) q^{3} +2.00000i q^{4} +(-1.86603 + 1.23205i) q^{5} +(2.36603 - 1.36603i) q^{6} +(-2.50000 - 0.866025i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-0.633975 - 0.366025i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.500000 + 1.86603i) q^{3} +2.00000i 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} +(3.09808 + 0.633975i) q^{10} +(0.633975 - 0.366025i) q^{11} +(-3.73205 - 1.00000i) q^{12} +(-3.00000 - 3.00000i) q^{13} +(1.63397 + 3.36603i) q^{14} +(-1.36603 - 4.09808i) q^{15} -4.00000 q^{16} +(1.09808 - 4.09808i) q^{17} +(0.267949 + 1.00000i) q^{18} +(-3.00000 - 1.73205i) q^{19} +(-2.46410 - 3.73205i) q^{20} +(2.86603 - 4.23205i) q^{21} +(-1.00000 - 0.267949i) q^{22} +(-1.50000 + 0.401924i) q^{23} +(2.73205 + 4.73205i) q^{24} +(1.96410 - 4.59808i) q^{25} +6.00000i q^{26} +(-3.09808 + 3.09808i) q^{27} +(1.73205 - 5.00000i) q^{28} +4.46410 q^{29} +(-2.73205 + 5.46410i) q^{30} +(-8.83013 + 5.09808i) q^{31} +(4.00000 + 4.00000i) 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} +(1.26795 + 4.73205i) q^{38} +(7.09808 - 4.09808i) q^{39} +(-1.26795 + 6.19615i) q^{40} -0.464102i q^{41} +(-7.09808 + 1.36603i) q^{42} +(-2.36603 + 2.36603i) q^{43} +(0.732051 + 1.26795i) q^{44} +(1.63397 - 0.0980762i) q^{45} +(1.90192 + 1.09808i) q^{46} +(0.633975 - 0.169873i) q^{47} +(2.00000 - 7.46410i) q^{48} +(5.50000 + 4.33013i) q^{49} +(-6.56218 + 2.63397i) q^{50} +(7.09808 + 4.09808i) q^{51} +(6.00000 - 6.00000i) q^{52} +(-3.00000 - 0.803848i) q^{53} +6.19615 q^{54} +(-0.732051 + 1.46410i) q^{55} +(-6.73205 + 3.26795i) q^{56} +(4.73205 - 4.73205i) q^{57} +(-4.46410 - 4.46410i) q^{58} +(-7.73205 + 4.46410i) q^{59} +(8.19615 - 2.73205i) q^{60} +(4.96410 - 8.59808i) q^{61} +(13.9282 + 3.73205i) q^{62} +(1.26795 + 1.46410i) q^{63} -8.00000i q^{64} +(9.29423 + 1.90192i) q^{65} +(1.00000 - 1.73205i) q^{66} +(-1.03590 + 3.86603i) q^{67} +(8.19615 + 2.19615i) q^{68} -3.00000i q^{69} +(-7.19615 - 4.26795i) q^{70} +15.4641 q^{71} +(-2.00000 + 0.535898i) q^{72} +(-8.09808 - 2.16987i) q^{73} +(8.19615 + 4.73205i) q^{74} +(7.59808 + 5.96410i) q^{75} +(3.46410 - 6.00000i) q^{76} +(-1.90192 + 0.366025i) q^{77} +(-11.1962 - 3.00000i) q^{78} +(-11.1962 - 6.46410i) q^{79} +(7.46410 - 4.92820i) q^{80} +(-5.33013 - 9.23205i) q^{81} +(-0.464102 + 0.464102i) q^{82} +(-4.56218 - 4.56218i) q^{83} +(8.46410 + 5.73205i) q^{84} +(3.00000 + 9.00000i) q^{85} +4.73205 q^{86} +(-2.23205 + 8.33013i) q^{87} +(0.535898 - 2.00000i) q^{88} +(-8.59808 + 14.8923i) q^{89} +(-1.73205 - 1.53590i) q^{90} +(4.90192 + 10.0981i) q^{91} +(-0.803848 - 3.00000i) q^{92} +(-5.09808 - 19.0263i) q^{93} +(-0.803848 - 0.464102i) q^{94} +(7.73205 - 0.464102i) q^{95} +(-9.46410 + 5.46410i) q^{96} +(6.26795 + 6.26795i) q^{97} +(-1.16987 - 9.83013i) q^{98} -0.535898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 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 - 4 * q^2 - 2 * q^3 - 4 * q^5 + 6 * q^6 - 10 * q^7 + 8 * q^8 - 6 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} - 4 q^{5} + 6 q^{6} - 10 q^{7} + 8 q^{8} - 6 q^{9} + 2 q^{10} + 6 q^{11} - 8 q^{12} - 12 q^{13} + 10 q^{14} - 2 q^{15} - 16 q^{16} - 6 q^{17} + 8 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 6 q^{23} + 4 q^{24} - 6 q^{25} - 2 q^{27} + 4 q^{29} - 4 q^{30} - 18 q^{31} + 16 q^{32} - 2 q^{33} + 16 q^{35} - 4 q^{36} - 12 q^{37} + 12 q^{38} + 18 q^{39} - 12 q^{40} - 18 q^{42} - 6 q^{43} - 4 q^{44} + 10 q^{45} + 18 q^{46} + 6 q^{47} + 8 q^{48} + 22 q^{49} - 2 q^{50} + 18 q^{51} + 24 q^{52} - 12 q^{53} + 4 q^{54} + 4 q^{55} - 20 q^{56} + 12 q^{57} - 4 q^{58} - 24 q^{59} + 12 q^{60} + 6 q^{61} + 28 q^{62} + 12 q^{63} + 6 q^{65} + 4 q^{66} - 18 q^{67} + 12 q^{68} - 8 q^{70} + 48 q^{71} - 8 q^{72} - 22 q^{73} + 12 q^{74} + 20 q^{75} - 18 q^{77} - 24 q^{78} - 24 q^{79} + 16 q^{80} - 4 q^{81} + 12 q^{82} + 6 q^{83} + 20 q^{84} + 12 q^{85} + 12 q^{86} - 2 q^{87} + 16 q^{88} - 24 q^{89} + 30 q^{91} - 24 q^{92} - 10 q^{93} - 24 q^{94} + 24 q^{95} - 24 q^{96} + 32 q^{97} - 22 q^{98} - 16 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 - 4 * q^5 + 6 * q^6 - 10 * q^7 + 8 * q^8 - 6 * q^9 + 2 * q^10 + 6 * q^11 - 8 * q^12 - 12 * q^13 + 10 * q^14 - 2 * q^15 - 16 * q^16 - 6 * q^17 + 8 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 6 * q^23 + 4 * q^24 - 6 * q^25 - 2 * q^27 + 4 * q^29 - 4 * q^30 - 18 * q^31 + 16 * q^32 - 2 * q^33 + 16 * q^35 - 4 * q^36 - 12 * q^37 + 12 * q^38 + 18 * q^39 - 12 * q^40 - 18 * q^42 - 6 * q^43 - 4 * q^44 + 10 * q^45 + 18 * q^46 + 6 * q^47 + 8 * q^48 + 22 * q^49 - 2 * q^50 + 18 * q^51 + 24 * q^52 - 12 * q^53 + 4 * q^54 + 4 * q^55 - 20 * q^56 + 12 * q^57 - 4 * q^58 - 24 * q^59 + 12 * q^60 + 6 * q^61 + 28 * q^62 + 12 * q^63 + 6 * q^65 + 4 * q^66 - 18 * q^67 + 12 * q^68 - 8 * q^70 + 48 * q^71 - 8 * q^72 - 22 * q^73 + 12 * q^74 + 20 * q^75 - 18 * q^77 - 24 * q^78 - 24 * q^79 + 16 * q^80 - 4 * q^81 + 12 * q^82 + 6 * q^83 + 20 * q^84 + 12 * q^85 + 12 * q^86 - 2 * q^87 + 16 * q^88 - 24 * q^89 + 30 * q^91 - 24 * q^92 - 10 * q^93 - 24 * q^94 + 24 * q^95 - 24 * q^96 + 32 * q^97 - 22 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$	−0.500000	+	1.86603i	−0.288675	+	1.07735i	0.657437	+	0.753510i	$0.271641\pi$
$3$	−0.500000	+	1.86603i	−0.288675	+	1.07735i	−0.946112	+	0.323840i	$0.895026\pi$
$4$			2.00000i			1.00000i
$5$	−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
$10$	3.09808	+	0.633975i	0.979698	+	0.200480i
$11$	0.633975	−	0.366025i	0.191151	−	0.110361i	−0.401371	−	0.915916i	$-0.631466\pi$
$11$	0.633975	−	0.366025i	0.191151	−	0.110361i	0.592521	+	0.805555i	$0.298133\pi$
$12$	−3.73205	−	1.00000i	−1.07735	−	0.288675i
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	0.155747	−	0.987797i	$-0.450222\pi$
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	−0.987797	+	0.155747i	$0.950222\pi$
$14$	1.63397	+	3.36603i	0.436698	+	0.899608i
$15$	−1.36603	−	4.09808i	−0.352706	−	1.05812i
$16$	−4.00000			−1.00000
$17$	1.09808	−	4.09808i	0.266323	−	0.993929i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	1.09808	−	4.09808i	0.266323	−	0.993929i	0.961436	−	0.275029i	$-0.0886875\pi$
$18$	0.267949	+	1.00000i	0.0631562	+	0.235702i
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	0.114708	−	0.993399i	$-0.463407\pi$
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	−2.46410	−	3.73205i	−0.550990	−	0.834512i
$21$	2.86603	−	4.23205i	0.625418	−	0.923509i
$22$	−1.00000	−	0.267949i	−0.213201	−	0.0571270i
$23$	−1.50000	+	0.401924i	−0.312772	+	0.0838069i	−0.411790	−	0.911279i	$-0.635096\pi$
$23$	−1.50000	+	0.401924i	−0.312772	+	0.0838069i	0.0990186	+	0.995086i	$0.468430\pi$
$24$	2.73205	+	4.73205i	0.557678	+	0.965926i
$25$	1.96410	−	4.59808i	0.392820	−	0.919615i
$26$			6.00000i			1.17670i
$27$	−3.09808	+	3.09808i	−0.596225	+	0.596225i
$28$	1.73205	−	5.00000i	0.327327	−	0.944911i
$29$	4.46410			0.828963			0.414481	−	0.910058i	$-0.363963\pi$
$29$	4.46410			0.828963			0.414481	+	0.910058i	$0.363963\pi$
$30$	−2.73205	+	5.46410i	−0.498802	+	0.997604i
$31$	−8.83013	+	5.09808i	−1.58594	+	0.915642i	−0.591971	+	0.805959i	$0.701650\pi$
$31$	−8.83013	+	5.09808i	−1.58594	+	0.915642i	−0.993967	+	0.109682i	$0.965017\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	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	$-0.768740\pi$
$37$	−6.46410	+	1.73205i	−1.06269	+	0.284747i	−0.315205	+	0.949024i	$0.602073\pi$
$38$	1.26795	+	4.73205i	0.205689	+	0.767640i
$39$	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	$-0.988462\pi$
$41$		−	0.464102i		−	0.0724805i	0.999343	−	0.0362402i	$-0.0115382\pi$
$42$	−7.09808	+	1.36603i	−1.09526	+	0.210782i
$43$	−2.36603	+	2.36603i	−0.360815	+	0.360815i	−0.864113	−	0.503298i	$-0.832120\pi$
$43$	−2.36603	+	2.36603i	−0.360815	+	0.360815i	0.503298	+	0.864113i	$0.332120\pi$
$44$	0.732051	+	1.26795i	0.110361	+	0.191151i
$45$	1.63397	−	0.0980762i	0.243579	−	0.0146203i
$46$	1.90192	+	1.09808i	0.280423	+	0.161903i
$47$	0.633975	−	0.169873i	0.0924747	−	0.0247785i	−0.212285	−	0.977208i	$-0.568091\pi$
$47$	0.633975	−	0.169873i	0.0924747	−	0.0247785i	0.304760	+	0.952429i	$0.401424\pi$
$48$	2.00000	−	7.46410i	0.288675	−	1.07735i
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−6.56218	+	2.63397i	−0.928032	+	0.372500i
$51$	7.09808	+	4.09808i	0.993929	+	0.573845i
$52$	6.00000	−	6.00000i	0.832050	−	0.832050i
$53$	−3.00000	−	0.803848i	−0.412082	−	0.110417i	0.0468214	−	0.998903i	$-0.485091\pi$
$53$	−3.00000	−	0.803848i	−0.412082	−	0.110417i	−0.458903	+	0.888486i	$0.651757\pi$
$54$	6.19615			0.843190
$55$	−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
$58$	−4.46410	−	4.46410i	−0.586165	−	0.586165i
$59$	−7.73205	+	4.46410i	−1.00663	+	0.581177i	−0.910202	−	0.414164i	$-0.864074\pi$
$59$	−7.73205	+	4.46410i	−1.00663	+	0.581177i	−0.0964249	+	0.995340i	$0.530741\pi$
$60$	8.19615	−	2.73205i	1.05812	−	0.352706i
$61$	4.96410	−	8.59808i	0.635588	−	1.10087i	−0.350802	−	0.936450i	$-0.614091\pi$
$61$	4.96410	−	8.59808i	0.635588	−	1.10087i	0.986390	−	0.164421i	$-0.0525756\pi$
$62$	13.9282	+	3.73205i	1.76888	+	0.473971i
$63$	1.26795	+	1.46410i	0.159747	+	0.184459i
$64$		−	8.00000i		−	1.00000i
$65$	9.29423	+	1.90192i	1.15281	+	0.235905i
$66$	1.00000	−	1.73205i	0.123091	−	0.213201i
$67$	−1.03590	+	3.86603i	−0.126555	+	0.472310i	−0.999890	−	0.0148095i	$-0.995286\pi$
$67$	−1.03590	+	3.86603i	−0.126555	+	0.472310i	0.873335	+	0.487120i	$0.161952\pi$
$68$	8.19615	+	2.19615i	0.993929	+	0.266323i
$69$		−	3.00000i		−	0.361158i
$70$	−7.19615	−	4.26795i	−0.860105	−	0.510117i
$71$	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	−0.248376	−	0.968664i	$-0.579897\pi$
$73$	−8.09808	−	2.16987i	−0.947808	−	0.253964i	−0.699432	+	0.714699i	$0.746564\pi$
$74$	8.19615	+	4.73205i	0.952783	+	0.550090i
$75$	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
$78$	−11.1962	−	3.00000i	−1.26771	−	0.339683i
$79$	−11.1962	−	6.46410i	−1.25967	−	0.727268i	−0.286656	−	0.958034i	$-0.592544\pi$
$79$	−11.1962	−	6.46410i	−1.25967	−	0.727268i	−0.973009	+	0.230765i	$0.925877\pi$
$80$	7.46410	−	4.92820i	0.834512	−	0.550990i
$81$	−5.33013	−	9.23205i	−0.592236	−	1.02578i
$82$	−0.464102	+	0.464102i	−0.0512514	+	0.0512514i
$83$	−4.56218	−	4.56218i	−0.500764	−	0.500764i	0.410911	−	0.911675i	$-0.365211\pi$
$83$	−4.56218	−	4.56218i	−0.500764	−	0.500764i	−0.911675	+	0.410911i	$0.865211\pi$
$84$	8.46410	+	5.73205i	0.923509	+	0.625418i
$85$	3.00000	+	9.00000i	0.325396	+	0.976187i
$86$	4.73205			0.510270
$87$	−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	−0.0992979	+	0.995058i	$0.531660\pi$
$89$	−8.59808	+	14.8923i	−0.911394	+	1.57858i	−0.812096	+	0.583523i	$0.801674\pi$
$90$	−1.73205	−	1.53590i	−0.182574	−	0.161898i
$91$	4.90192	+	10.0981i	0.513861	+	1.05857i
$92$	−0.803848	−	3.00000i	−0.0838069	−	0.312772i
$93$	−5.09808	−	19.0263i	−0.528646	−	1.97293i
$94$	−0.803848	−	0.464102i	−0.0829105	−	0.0478684i
$95$	7.73205	−	0.464102i	0.793292	−	0.0476158i
$96$	−9.46410	+	5.46410i	−0.965926	+	0.557678i
$97$	6.26795	+	6.26795i	0.636414	+	0.636414i	0.949669	−	0.313255i	$-0.101420\pi$
$97$	6.26795	+	6.26795i	0.636414	+	0.636414i	−0.313255	+	0.949669i	$0.601420\pi$
$98$	−1.16987	−	9.83013i	−0.118175	−	0.992993i
$99$	−0.535898			−0.0538598
$100$	9.19615	+	3.92820i	0.919615	+	0.392820i
$101$	−5.06218	−	8.76795i	−0.503706	−	0.872444i	−0.999991	−	0.00428406i	$-0.998636\pi$
$101$	−5.06218	−	8.76795i	−0.503706	−	0.872444i	0.496285	−	0.868159i	$-0.334697\pi$
$102$	−3.00000	−	11.1962i	−0.297044	−	1.10858i
$103$	3.33013	+	12.4282i	0.328127	+	1.22459i	0.911131	+	0.412118i	$0.135211\pi$
$103$	3.33013	+	12.4282i	0.328127	+	1.22459i	−0.583003	+	0.812470i	$0.698123\pi$
$104$	−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	$-0.497390\pi$
$107$	5.33013	−	1.42820i	0.515283	−	0.138070i	0.507084	+	0.861897i	$0.330723\pi$
$108$	−6.19615	−	6.19615i	−0.596225	−	0.596225i
$109$	−2.13397	−	3.69615i	−0.204398	−	0.354027i	0.745543	−	0.666458i	$-0.232190\pi$
$109$	−2.13397	−	3.69615i	−0.204398	−	0.354027i	−0.949941	+	0.312430i	$0.898857\pi$
$110$	2.19615	−	0.732051i	0.209395	−	0.0697983i
$111$		−	12.9282i		−	1.22709i
$112$	10.0000	+	3.46410i	0.944911	+	0.327327i
$113$	2.53590	+	2.53590i	0.238557	+	0.238557i	0.816253	−	0.577695i	$-0.196048\pi$
$113$	2.53590	+	2.53590i	0.238557	+	0.238557i	−0.577695	+	0.816253i	$0.696048\pi$
$114$	−9.46410			−0.886394
$115$	2.30385	−	2.59808i	0.214835	−	0.242272i
$116$			8.92820i			0.828963i
$117$	0.803848	+	3.00000i	0.0743157	+	0.277350i
$118$	12.1962	+	3.26795i	1.12275	+	0.300839i
$119$	−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
$122$	−13.5622	+	3.63397i	−1.22786	+	0.329005i
$123$	0.866025	+	0.232051i	0.0780869	+	0.0209233i
$124$	−10.1962	−	17.6603i	−0.915642	−	1.58594i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	0.196152	−	2.73205i	0.0174746	−	0.243390i
$127$	−11.0000	+	11.0000i	−0.976092	+	0.976092i	−0.999721	−	0.0236286i	$-0.992478\pi$
$127$	−11.0000	+	11.0000i	−0.976092	+	0.976092i	0.0236286	+	0.999721i	$0.492478\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$	−3.23205	−	5.59808i	−0.284566	−	0.492883i
$130$	−7.39230	−	11.1962i	−0.648348	−	0.981968i
$131$	3.73205	−	6.46410i	0.326071	−	0.564771i	−0.655658	−	0.755058i	$-0.727609\pi$
$131$	3.73205	−	6.46410i	0.326071	−	0.564771i	0.981728	+	0.190287i	$0.0609419\pi$
$132$	−2.73205	+	0.732051i	−0.237795	+	0.0637168i
$133$	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	−0.108904	−	0.994052i	$-0.534734\pi$
$137$	−8.19615	−	2.19615i	−0.700245	−	0.187630i	−0.591340	+	0.806422i	$0.701401\pi$
$138$	−3.00000	+	3.00000i	−0.255377	+	0.255377i
$139$		−	1.26795i		−	0.107546i	−0.998553	−	0.0537730i	$-0.982875\pi$
$139$		−	1.26795i		−	0.107546i	0.998553	−	0.0537730i	$-0.0171247\pi$
$140$	2.92820	+	11.4641i	0.247478	+	0.968893i
$141$			1.26795i			0.106781i
$142$	−15.4641	−	15.4641i	−1.29772	−	1.29772i
$143$	−3.00000	−	0.803848i	−0.250873	−	0.0672211i
$144$	2.53590	+	1.46410i	0.211325	+	0.122008i
$145$	−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
$148$	−3.46410	−	12.9282i	−0.284747	−	1.06269i
$149$	−11.3301	+	19.6244i	−0.928200	+	1.60769i	−0.141868	+	0.989886i	$0.545311\pi$
$149$	−11.3301	+	19.6244i	−0.928200	+	1.60769i	−0.786332	+	0.617804i	$0.788022\pi$
$150$	−1.63397	−	13.5622i	−0.133413	−	1.10735i
$151$	−6.90192	−	11.9545i	−0.561671	−	0.972842i	−0.997351	−	0.0727405i	$-0.976826\pi$
$151$	−6.90192	−	11.9545i	−0.561671	−	0.972842i	0.435680	−	0.900101i	$-0.356508\pi$
$152$	−9.46410	+	2.53590i	−0.767640	+	0.205689i
$153$	−2.19615	+	2.19615i	−0.177548	+	0.177548i
$154$	2.26795	+	1.53590i	0.182757	+	0.123766i
$155$	10.1962	−	20.3923i	0.818975	−	1.63795i
$156$	8.19615	+	14.1962i	0.656217	+	1.13660i
$157$	17.0263	+	4.56218i	1.35885	+	0.364101i	0.863392	−	0.504533i	$-0.168335\pi$
$157$	17.0263	+	4.56218i	1.35885	+	0.364101i	0.495453	+	0.868635i	$0.335002\pi$
$158$	4.73205	+	17.6603i	0.376462	+	1.40497i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$	−12.3923	−	2.53590i	−0.979698	−	0.200480i
$161$	4.09808	+	0.294229i	0.322974	+	0.0231885i
$162$	−3.90192	+	14.5622i	−0.306564	+	1.14411i
$163$	−0.973721	−	3.63397i	−0.0762677	−	0.284635i	0.917250	−	0.398312i	$-0.130404\pi$
$163$	−0.973721	−	3.63397i	−0.0762677	−	0.284635i	−0.993518	+	0.113677i	$0.963737\pi$
$164$	0.928203			0.0724805
$165$	−2.36603	−	2.09808i	−0.184195	−	0.163335i
$166$			9.12436i			0.708187i
$167$	3.29423	+	3.29423i	0.254915	+	0.254915i	0.822982	−	0.568067i	$-0.192309\pi$
$167$	3.29423	+	3.29423i	0.254915	+	0.254915i	−0.568067	+	0.822982i	$0.692309\pi$
$168$	−2.73205	−	14.1962i	−0.210782	−	1.09526i
$169$			5.00000i			0.384615i
$170$	6.00000	−	12.0000i	0.460179	−	0.920358i
$171$	1.26795	+	2.19615i	0.0969625	+	0.167944i
$172$	−4.73205	−	4.73205i	−0.360815	−	0.360815i
$173$	0.464102	−	0.124356i	0.0352850	−	0.00945459i	−0.241133	−	0.970492i	$-0.577519\pi$
$173$	0.464102	−	0.124356i	0.0352850	−	0.00945459i	0.276418	+	0.961037i	$0.410852\pi$
$174$	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
$178$	23.4904	−	6.29423i	1.76068	−	0.471772i
$179$	−7.02628	−	12.1699i	−0.525169	−	0.909619i	−0.999570	−	0.0293105i	$-0.990669\pi$
$179$	−7.02628	−	12.1699i	−0.525169	−	0.909619i	0.474402	−	0.880309i	$-0.342664\pi$
$180$	0.196152	+	3.26795i	0.0146203	+	0.243579i
$181$	22.5167			1.67365			0.836825	−	0.547470i	$-0.184409\pi$
$181$	22.5167			1.67365			0.836825	+	0.547470i	$0.184409\pi$
$182$	5.19615	−	15.0000i	0.385164	−	1.11187i
$183$	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
$186$	−13.9282	+	24.1244i	−1.02127	+	1.76888i
$187$	−0.803848	−	3.00000i	−0.0587832	−	0.219382i
$188$	0.339746	+	1.26795i	0.0247785	+	0.0924747i
$189$	10.4282	−	5.06218i	0.758540	−	0.368219i
$190$	−8.19615	−	7.26795i	−0.594611	−	0.527272i
$191$	−1.56218	+	2.70577i	−0.113035	+	0.195783i	−0.916993	−	0.398904i	$-0.869391\pi$
$191$	−1.56218	+	2.70577i	−0.113035	+	0.195783i	0.803957	+	0.594687i	$0.202724\pi$
$192$	14.9282	+	4.00000i	1.07735	+	0.288675i
$193$	3.09808	−	11.5622i	0.223004	−	0.832264i	−0.760190	−	0.649701i	$-0.774894\pi$
$193$	3.09808	−	11.5622i	0.223004	−	0.832264i	0.983194	−	0.182563i	$-0.0584393\pi$
$194$		−	12.5359i		−	0.900025i
$195$	−8.19615	+	16.3923i	−0.586939	+	1.17388i
$196$	−8.66025	+	11.0000i	−0.618590	+	0.785714i
$197$	5.53590	+	5.53590i	0.394416	+	0.394416i	0.876258	−	0.481842i	$-0.160032\pi$
$197$	5.53590	+	5.53590i	0.394416	+	0.394416i	−0.481842	+	0.876258i	$0.660032\pi$
$198$	0.535898	+	0.535898i	0.0380846	+	0.0380846i
$199$	−1.73205	−	3.00000i	−0.122782	−	0.212664i	0.798082	−	0.602549i	$-0.205848\pi$
$199$	−1.73205	−	3.00000i	−0.122782	−	0.212664i	−0.920864	+	0.389885i	$0.872515\pi$
$200$	−5.26795	−	13.1244i	−0.372500	−	0.928032i
$201$	−6.69615	−	3.86603i	−0.472310	−	0.272688i
$202$	−3.70577	+	13.8301i	−0.260737	+	0.973084i
$203$	−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
$206$	9.09808	−	15.7583i	0.633893	−	1.09793i
$207$	1.09808	+	0.294229i	0.0763216	+	0.0204503i
$208$	12.0000	+	12.0000i	0.832050	+	0.832050i
$209$	−2.53590			−0.175412
$210$	11.5622	−	11.2942i	0.797866	−	0.779376i
$211$		−	20.5359i		−	1.41375i	−0.707339	−	0.706875i	$-0.750104\pi$
$211$		−	20.5359i		−	1.41375i	0.707339	−	0.706875i	$-0.249896\pi$
$212$	1.60770	−	6.00000i	0.110417	−	0.412082i
$213$	−7.73205	+	28.8564i	−0.529791	+	1.97721i
$214$	−6.75833	−	3.90192i	−0.461990	−	0.266730i
$215$	1.50000	−	7.33013i	0.102299	−	0.499911i
$216$			12.3923i			0.843190i
$217$	26.4904	−	5.09808i	1.79828	−	0.346080i
$218$	−1.56218	+	5.83013i	−0.105804	+	0.394866i
$219$	8.09808	−	14.0263i	0.547217	−	0.947808i
$220$	−2.92820	−	1.46410i	−0.197419	−	0.0987097i
$221$	−15.5885	+	9.00000i	−1.04859	+	0.605406i
$222$	−12.9282	+	12.9282i	−0.867684	+	0.867684i
$223$	7.92820	−	7.92820i	0.530912	−	0.530912i	−0.389932	−	0.920844i	$-0.627501\pi$
$223$	7.92820	−	7.92820i	0.530912	−	0.530912i	0.920844	+	0.389932i	$0.127501\pi$
$224$	−6.53590	−	13.4641i	−0.436698	−	0.899608i
$225$	−2.92820	+	2.19615i	−0.195214	+	0.146410i
$226$		−	5.07180i		−	0.337371i
$227$	12.8301	+	3.43782i	0.851565	+	0.228176i	0.658100	−	0.752931i	$-0.271361\pi$
$227$	12.8301	+	3.43782i	0.851565	+	0.228176i	0.193466	+	0.981107i	$0.438027\pi$
$228$	9.46410	+	9.46410i	0.626775	+	0.626775i
$229$	−13.3923	−	7.73205i	−0.884988	−	0.510948i	−0.0126885	−	0.999919i	$-0.504039\pi$
$229$	−13.3923	−	7.73205i	−0.884988	−	0.510948i	−0.872300	+	0.488971i	$0.837372\pi$
$230$	−4.90192	+	0.294229i	−0.323223	+	0.0194009i
$231$	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	−0.0187040	−	0.999825i	$-0.505954\pi$
$233$	7.09808	−	1.90192i	0.465010	−	0.124599i	0.483714	+	0.875226i	$0.339287\pi$
$234$	2.19615	−	3.80385i	0.143567	−	0.248665i
$235$	−0.973721	+	1.09808i	−0.0635185	+	0.0716306i
$236$	−8.92820	−	15.4641i	−0.581177	−	1.00663i
$237$	17.6603	−	17.6603i	1.14716	−	1.14716i
$238$	15.5885	−	3.00000i	1.01045	−	0.194461i
$239$		−	4.73205i		−	0.306091i	−0.988219	−	0.153045i	$-0.951092\pi$
$239$		−	4.73205i		−	0.306091i	0.988219	−	0.153045i	$-0.0489081\pi$
$240$	5.46410	+	16.3923i	0.352706	+	1.05812i
$241$	−17.6603	+	10.1962i	−1.13760	+	0.656792i	−0.945834	−	0.324649i	$-0.894754\pi$
$241$	−17.6603	+	10.1962i	−1.13760	+	0.656792i	−0.191763	+	0.981441i	$0.561420\pi$
$242$	14.2942	−	3.83013i	0.918868	−	0.246210i
$243$	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
$250$	9.00000	−	13.0000i	0.569210	−	0.822192i
$251$	−19.6603			−1.24094			−0.620472	−	0.784229i	$-0.713059\pi$
$251$	−19.6603			−1.24094			−0.620472	+	0.784229i	$0.713059\pi$
$252$	−2.92820	+	2.53590i	−0.184459	+	0.159747i
$253$	−0.803848	+	0.803848i	−0.0505375	+	0.0505375i
$254$	22.0000			1.38040
$255$	−18.2942	+	1.09808i	−1.14563	+	0.0687642i
$256$	16.0000			1.00000
$257$	25.8564	−	6.92820i	1.61288	−	0.432169i	0.663980	−	0.747751i	$-0.268866\pi$
$257$	25.8564	−	6.92820i	1.61288	−	0.432169i	0.948899	+	0.315581i	$0.102199\pi$
$258$	−2.36603	+	8.83013i	−0.147302	+	0.549740i
$259$	17.6603	+	1.26795i	1.09735	+	0.0787865i
$260$	−3.80385	+	18.5885i	−0.235905	+	1.15281i
$261$	−2.83013	−	1.63397i	−0.175180	−	0.101140i
$262$	−10.1962	+	2.73205i	−0.629920	+	0.168787i
$263$	−0.107695	+	0.401924i	−0.00664077	+	0.0247837i	−0.969167	−	0.246406i	$-0.920750\pi$
$263$	−0.107695	+	0.401924i	−0.00664077	+	0.0247837i	0.962526	+	0.271190i	$0.0874170\pi$
$264$	3.46410	+	2.00000i	0.213201	+	0.123091i
$265$	6.58846	−	2.19615i	0.404726	−	0.134909i
$266$	0.928203	−	12.9282i	0.0569118	−	0.792679i
$267$	−23.4904	−	23.4904i	−1.43759	−	1.43759i
$268$	−7.73205	−	2.07180i	−0.472310	−	0.126555i
$269$	3.06218	−	1.76795i	0.186704	−	0.107794i	−0.403734	−	0.914876i	$-0.632288\pi$
$269$	3.06218	−	1.76795i	0.186704	−	0.107794i	0.590439	+	0.807082i	$0.298955\pi$
$270$	−11.5622	+	7.63397i	−0.703652	+	0.464589i
$271$	10.3923	+	6.00000i	0.631288	+	0.364474i	0.781251	−	0.624218i	$-0.214582\pi$
$271$	10.3923	+	6.00000i	0.631288	+	0.364474i	−0.149963	+	0.988692i	$0.547915\pi$
$272$	−4.39230	+	16.3923i	−0.266323	+	0.993929i
$273$	−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
$276$	6.00000			0.361158
$277$	−5.02628	+	18.7583i	−0.302000	+	1.12708i	0.633497	+	0.773745i	$0.281619\pi$
$277$	−5.02628	+	18.7583i	−0.302000	+	1.12708i	−0.935497	+	0.353334i	$0.885048\pi$
$278$	−1.26795	+	1.26795i	−0.0760465	+	0.0760465i
$279$	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	$0.757366\pi$
$282$	1.26795	−	1.26795i	0.0755053	−	0.0755053i
$283$	−3.63397	+	13.5622i	−0.216017	+	0.806188i	0.769789	+	0.638299i	$0.220362\pi$
$283$	−3.63397	+	13.5622i	−0.216017	+	0.806188i	−0.985806	+	0.167889i	$0.946305\pi$
$284$			30.9282i			1.83525i
$285$	−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
$288$	−1.07180	−	4.00000i	−0.0631562	−	0.235702i
$289$	−0.866025	−	0.500000i	−0.0509427	−	0.0294118i
$290$	13.8301	+	2.83013i	0.812133	+	0.166191i
$291$	−14.8301	+	8.56218i	−0.869357	+	0.501924i
$292$	4.33975	−	16.1962i	0.253964	−	0.947808i
$293$	4.19615	+	4.19615i	0.245142	+	0.245142i	0.818973	−	0.573832i	$-0.194544\pi$
$293$	4.19615	+	4.19615i	0.245142	+	0.245142i	−0.573832	+	0.818973i	$0.694544\pi$
$294$	18.9282	+	2.73205i	1.10392	+	0.159336i
$295$	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
$298$	30.9545	−	8.29423i	1.79315	−	0.480472i
$299$	5.70577	+	3.29423i	0.329973	+	0.190510i
$300$	−11.9282	+	15.1962i	−0.688675	+	0.877350i
$301$	7.96410	−	3.86603i	0.459043	−	0.222834i
$302$	−5.05256	+	18.8564i	−0.290742	+	1.08506i
$303$	18.8923	−	5.06218i	1.08533	−	0.290815i
$304$	12.0000	+	6.92820i	0.688247	+	0.397360i
$305$	1.33013	+	22.1603i	0.0761629	+	1.26889i
$306$	4.39230			0.251091
$307$	−0.758330	+	0.758330i	−0.0432802	+	0.0432802i	−0.728416	−	0.685135i	$-0.759743\pi$
$307$	−0.758330	+	0.758330i	−0.0432802	+	0.0432802i	0.685135	+	0.728416i	$0.259743\pi$
$308$	−0.732051	−	3.80385i	−0.0417125	−	0.216744i
$309$	−24.8564			−1.41403
$310$	−30.5885	+	10.1962i	−1.73731	+	0.579103i
$311$	21.5885	−	12.4641i	1.22417	−	0.706774i	0.258365	−	0.966047i	$-0.416816\pi$
$311$	21.5885	−	12.4641i	1.22417	−	0.706774i	0.965804	+	0.259273i	$0.0834829\pi$
$312$	6.00000	−	22.3923i	0.339683	−	1.26771i
$313$	−4.32051	−	16.1244i	−0.244210	−	0.911402i	−0.973779	−	0.227496i	$-0.926946\pi$
$313$	−4.32051	−	16.1244i	−0.244210	−	0.911402i	0.729570	−	0.683907i	$-0.239720\pi$
$314$	−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	$-0.542819\pi$
$317$	4.36603	−	1.16987i	0.245220	−	0.0657066i	0.379336	+	0.925259i	$0.376153\pi$
$318$	−8.19615	+	2.19615i	−0.459617	+	0.123154i
$319$	2.83013	−	1.63397i	0.158457	−	0.0914850i
$320$	9.85641	+	14.9282i	0.550990	+	0.834512i
$321$			10.6603i			0.594997i
$322$	−3.80385	−	4.39230i	−0.211980	−	0.244774i
$323$	−10.3923	+	10.3923i	−0.578243	+	0.578243i
$324$	18.4641	−	10.6603i	1.02578	−	0.592236i
$325$	−19.6865	+	7.90192i	−1.09201	+	0.438320i
$326$	−2.66025	+	4.60770i	−0.147338	+	0.255197i
$327$	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
$330$	0.267949	+	4.46410i	0.0147501	+	0.245741i
$331$	6.29423	+	3.63397i	0.345962	+	0.199741i	0.662905	−	0.748703i	$-0.269323\pi$
$331$	6.29423	+	3.63397i	0.345962	+	0.199741i	−0.316943	+	0.948444i	$0.602656\pi$
$332$	9.12436	−	9.12436i	0.500764	−	0.500764i
$333$	4.73205	+	1.26795i	0.259315	+	0.0694832i
$334$		−	6.58846i		−	0.360504i
$335$	−2.83013	−	8.49038i	−0.154626	−	0.463879i
$336$	−11.4641	+	16.9282i	−0.625418	+	0.923509i
$337$	−19.6603	+	19.6603i	−1.07096	+	1.07096i	−0.0736804	+	0.997282i	$0.523474\pi$
$337$	−19.6603	+	19.6603i	−1.07096	+	1.07096i	−0.997282	+	0.0736804i	$0.976526\pi$
$338$	5.00000	−	5.00000i	0.271964	−	0.271964i
$339$	−6.00000	+	3.46410i	−0.325875	+	0.188144i
$340$	−18.0000	+	6.00000i	−0.976187	+	0.325396i
$341$	−3.73205	+	6.46410i	−0.202102	+	0.350051i
$342$	0.928203	−	3.46410i	0.0501915	−	0.187317i
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$			9.46410i			0.510270i
$345$	3.69615	+	5.59808i	0.198994	+	0.301390i
$346$	−0.588457	−	0.339746i	−0.0316357	−	0.0182649i
$347$	9.35641	−	34.9186i	0.502278	−	1.87453i	0.0175817	−	0.999845i	$-0.494403\pi$
$347$	9.35641	−	34.9186i	0.502278	−	1.87453i	0.484697	−	0.874682i	$-0.338930\pi$
$348$	−16.6603	−	4.46410i	−0.893083	−	0.239301i
$349$		−	19.9808i		−	1.06955i	−0.844996	−	0.534773i	$-0.820397\pi$
$349$		−	19.9808i		−	1.06955i	0.844996	−	0.534773i	$-0.179603\pi$
$350$	18.6865	−	0.901924i	0.998837	−	0.0482099i
$351$	18.5885			0.992178
$352$	4.00000	+	1.07180i	0.213201	+	0.0571270i
$353$	−25.3923	−	6.80385i	−1.35150	−	0.362132i	−0.490809	−	0.871267i	$-0.663299\pi$
$353$	−25.3923	−	6.80385i	−1.35150	−	0.362132i	−0.860687	+	0.509135i	$0.829965\pi$
$354$	−12.1962	+	21.1244i	−0.648218	+	1.12275i
$355$	−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
$358$	−5.14359	+	19.1962i	−0.271847	+	1.01455i
$359$	4.09808	+	2.36603i	0.216288	+	0.124874i	0.604230	−	0.796810i	$-0.293481\pi$
$359$	4.09808	+	2.36603i	0.216288	+	0.124874i	−0.387942	+	0.921684i	$0.626814\pi$
$360$	3.07180	−	3.46410i	0.161898	−	0.182574i
$361$	−3.50000	−	6.06218i	−0.184211	−	0.319062i
$362$	−22.5167	−	22.5167i	−1.18345	−	1.18345i
$363$	−14.2942	−	14.2942i	−0.750252	−	0.750252i
$364$	−20.1962	+	9.80385i	−1.05857	+	0.513861i
$365$	17.7846	−	5.92820i	0.930889	−	0.310296i
$366$		−	27.1244i		−	1.41781i
$367$	2.16025	−	8.06218i	0.112764	−	0.420842i	−0.886346	−	0.463024i	$-0.846764\pi$
$367$	2.16025	−	8.06218i	0.112764	−	0.420842i	0.999110	+	0.0421820i	$0.0134309\pi$
$368$	6.00000	−	1.60770i	0.312772	−	0.0838069i
$369$	−0.169873	+	0.294229i	−0.00884323	+	0.0153169i
$370$	−21.1244	+	1.26795i	−1.09820	+	0.0659175i
$371$	6.80385	+	4.60770i	0.353238	+	0.239220i
$372$	38.0526	−	10.1962i	1.97293	−	0.528646i
$373$	−2.53590	−	9.46410i	−0.131304	−	0.490033i	0.868682	−	0.495370i	$-0.164968\pi$
$373$	−2.53590	−	9.46410i	−0.131304	−	0.490033i	−0.999986	+	0.00533769i	$0.998301\pi$
$374$	−2.19615	+	3.80385i	−0.113560	+	0.196692i
$375$	−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
$378$	−15.4904	−	5.36603i	−0.796739	−	0.275999i
$379$	30.2487			1.55377			0.776886	−	0.629641i	$-0.216798\pi$
$379$	30.2487			1.55377			0.776886	+	0.629641i	$0.216798\pi$
$380$	0.928203	+	15.4641i	0.0476158	+	0.793292i
$381$	−15.0263	−	26.0263i	−0.769820	−	1.33337i
$382$	4.26795	−	1.14359i	0.218367	−	0.0585113i
$383$	−1.96410	−	7.33013i	−0.100361	−	0.374552i	0.897417	−	0.441184i	$-0.145441\pi$
$383$	−1.96410	−	7.33013i	−0.100361	−	0.374552i	−0.997778	+	0.0666319i	$0.978775\pi$
$384$	−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
$388$	−12.5359	+	12.5359i	−0.636414	+	0.636414i
$389$	7.53590	+	13.0526i	0.382085	+	0.661791i	0.991360	−	0.131168i	$-0.0418727\pi$
$389$	7.53590	+	13.0526i	0.382085	+	0.661791i	−0.609275	+	0.792959i	$0.708539\pi$
$390$	24.5885	−	8.19615i	1.24508	−	0.415028i
$391$			6.58846i			0.333193i
$392$	19.6603	−	2.33975i	0.992993	−	0.118175i
$393$	10.1962	+	10.1962i	0.514328	+	0.514328i
$394$		−	11.0718i		−	0.557789i
$395$	28.8564	−	1.73205i	1.45192	−	0.0871489i
$396$		−	1.07180i		−	0.0538598i
$397$	5.83013	+	21.7583i	0.292606	+	1.09202i	0.943100	+	0.332508i	$0.107895\pi$
$397$	5.83013	+	21.7583i	0.292606	+	1.09202i	−0.650495	+	0.759511i	$0.725438\pi$
$398$	−1.26795	+	4.73205i	−0.0635566	+	0.237196i
$399$	−15.9282	+	7.73205i	−0.797408	+	0.387087i
$400$	−7.85641	+	18.3923i	−0.392820	+	0.919615i
$401$	15.3564	−	26.5981i	0.766862	−	1.32824i	−0.172394	−	0.985028i	$-0.555150\pi$
$401$	15.3564	−	26.5981i	0.766862	−	1.32824i	0.939256	−	0.343216i	$-0.111516\pi$
$402$	2.83013	+	10.5622i	0.141154	+	0.526794i
$403$	41.7846	+	11.1962i	2.08144	+	0.557720i
$404$	17.5359	−	10.1244i	0.872444	−	0.503706i
$405$	21.3205	+	10.6603i	1.05942	+	0.529712i
$406$	7.29423	+	15.0263i	0.362006	+	0.745742i
$407$	−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	0.971793	−	0.235836i	$-0.0757828\pi$
$409$	5.69615	+	9.86603i	0.281657	+	0.487844i	−0.690136	+	0.723679i	$0.742449\pi$
$410$	0.294229	−	1.43782i	0.0145309	−	0.0710090i
$411$	8.19615	−	14.1962i	0.404286	−	0.700245i
$412$	−24.8564	+	6.66025i	−1.22459	+	0.328127i
$413$	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
$416$		−	24.0000i		−	1.17670i
$417$	2.36603	+	0.633975i	0.115865	+	0.0310459i
$418$	2.53590	+	2.53590i	0.124035	+	0.124035i
$419$		−	2.39230i		−	0.116872i	−0.998291	−	0.0584359i	$-0.981389\pi$
$419$		−	2.39230i		−	0.116872i	0.998291	−	0.0584359i	$-0.0186113\pi$
$420$	−22.8564	−	0.267949i	−1.11528	−	0.0130746i
$421$			30.1244i			1.46817i	0.679057	+	0.734086i	$0.262389\pi$
$421$			30.1244i			1.46817i	−0.679057	+	0.734086i	$0.737611\pi$
$422$	−20.5359	+	20.5359i	−0.999672	+	0.999672i
$423$	−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
$428$	2.85641	+	10.6603i	0.138070	+	0.515283i
$429$	3.00000	−	5.19615i	0.144841	−	0.250873i
$430$	−8.83013	+	5.83013i	−0.425827	+	0.281154i
$431$	6.63397	+	11.4904i	0.319547	+	0.553472i	0.980394	−	0.197049i	$-0.0631358\pi$
$431$	6.63397	+	11.4904i	0.319547	+	0.553472i	−0.660846	+	0.750521i	$0.729802\pi$
$432$	12.3923	−	12.3923i	0.596225	−	0.596225i
$433$	−11.4641	+	11.4641i	−0.550930	+	0.550930i	−0.926709	−	0.375780i	$-0.877375\pi$
$433$	−11.4641	+	11.4641i	−0.550930	+	0.550930i	0.375780	+	0.926709i	$0.377375\pi$
$434$	−31.5885	−	21.3923i	−1.51629	−	1.02686i
$435$	−6.09808	−	18.2942i	−0.292380	−	0.877141i
$436$	7.39230	−	4.26795i	0.354027	−	0.204398i
$437$	5.19615	+	1.39230i	0.248566	+	0.0666030i
$438$	−22.1244	+	5.92820i	−1.05714	+	0.283261i
$439$	−2.66025	+	4.60770i	−0.126967	+	0.219913i	−0.922500	−	0.385997i	$-0.873858\pi$
$439$	−2.66025	+	4.60770i	−0.126967	+	0.219913i	0.795533	+	0.605910i	$0.207191\pi$
$440$	1.46410	+	4.39230i	0.0697983	+	0.209395i
$441$	−1.90192	−	4.75833i	−0.0905678	−	0.226587i
$442$	24.5885	+	6.58846i	1.16955	+	0.313381i
$443$	8.93782	+	33.3564i	0.424649	+	1.58481i	0.764689	+	0.644400i	$0.222893\pi$
$443$	8.93782	+	33.3564i	0.424649	+	1.58481i	−0.340040	+	0.940411i	$0.610441\pi$
$444$	25.8564			1.22709
$445$	−2.30385	−	38.3827i	−0.109213	−	1.81951i
$446$	−15.8564			−0.750823
$447$	−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	$-0.815638\pi$
$449$		−	23.1962i		−	1.09469i	0.836906	−	0.547347i	$-0.184362\pi$
$450$	5.12436	+	0.732051i	0.241564	+	0.0345092i
$451$	−0.169873	−	0.294229i	−0.00799901	−	0.0138547i
$452$	−5.07180	+	5.07180i	−0.238557	+	0.238557i
$453$	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	−0.996623	−	0.0821116i	$-0.973834\pi$
$457$	−3.73205	−	13.9282i	−0.174578	−	0.651534i	0.822045	−	0.569422i	$-0.192833\pi$
$458$	5.66025	+	21.1244i	0.264486	+	0.987076i
$459$	9.29423	+	16.0981i	0.433817	+	0.751394i
$460$	5.19615	+	4.60770i	0.242272	+	0.214835i
$461$	−12.1436			−0.565584			−0.282792	−	0.959181i	$-0.591261\pi$
$461$	−12.1436			−0.565584			−0.282792	+	0.959181i	$0.591261\pi$
$462$	−4.00000	+	3.46410i	−0.186097	+	0.161165i
$463$	0.830127	+	0.830127i	0.0385793	+	0.0385793i	0.726133	−	0.687554i	$-0.241316\pi$
$463$	0.830127	+	0.830127i	0.0385793	+	0.0385793i	−0.687554	+	0.726133i	$0.741316\pi$
$464$	−17.8564			−0.828963
$465$	32.9545	+	29.2224i	1.52823	+	1.35516i
$466$	−9.00000	−	5.19615i	−0.416917	−	0.240707i
$467$	−1.66987	−	6.23205i	−0.0772725	−	0.288385i	0.916466	−	0.400111i	$-0.131029\pi$
$467$	−1.66987	−	6.23205i	−0.0772725	−	0.288385i	−0.993739	+	0.111727i	$0.964362\pi$
$468$	−6.00000	+	1.60770i	−0.277350	+	0.0743157i
$469$	5.93782	−	8.76795i	0.274183	−	0.404866i
$470$	2.07180	−	0.124356i	0.0955649	−	0.00573610i
$471$	−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
$474$	−35.3205			−1.62232
$475$	−13.8564	+	10.3923i	−0.635776	+	0.476832i
$476$	−18.5885	−	12.5885i	−0.852001	−	0.576991i
$477$	1.60770	+	1.60770i	0.0736113	+	0.0736113i
$478$	−4.73205	+	4.73205i	−0.216439	+	0.216439i
$479$	1.90192	+	3.29423i	0.0869011	+	0.150517i	0.906200	−	0.422850i	$-0.138970\pi$
$479$	1.90192	+	3.29423i	0.0869011	+	0.150517i	−0.819299	+	0.573367i	$0.805637\pi$
$480$	10.9282	−	21.8564i	0.498802	−	0.997604i
$481$	24.5885	+	14.1962i	1.12114	+	0.647289i
$482$	27.8564	+	7.46410i	1.26882	+	0.339981i
$483$	−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
$486$	−9.12436	−	5.26795i	−0.413889	−	0.238959i
$487$	−19.0263	−	5.09808i	−0.862163	−	0.231016i	−0.199467	−	0.979905i	$-0.563921\pi$
$487$	−19.0263	−	5.09808i	−0.862163	−	0.231016i	−0.662696	+	0.748889i	$0.730588\pi$
$488$	−7.26795	−	27.1244i	−0.329005	−	1.22786i
$489$	7.26795			0.328668
$490$	14.2942	+	16.9019i	0.645747	+	0.763551i
$491$			12.1962i			0.550405i	0.961386	+	0.275202i	$0.0887448\pi$
$491$			12.1962i			0.550405i	−0.961386	+	0.275202i	$0.911255\pi$
$492$	−0.464102	+	1.73205i	−0.0209233	+	0.0780869i
$493$	4.90192	−	18.2942i	0.220772	−	0.823931i
$494$	10.3923	−	18.0000i	0.467572	−	0.809858i
$495$	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
$498$	−17.0263	−	4.56218i	−0.762966	−	0.204436i
$499$	−6.75833	+	11.7058i	−0.302544	+	0.524022i	−0.976712	−	0.214556i	$-0.931169\pi$
$499$	−6.75833	+	11.7058i	−0.302544	+	0.524022i	0.674167	+	0.738579i	$0.264503\pi$
$500$	−22.0000	+	4.00000i	−0.983870	+	0.178885i
$501$	−7.79423	+	4.50000i	−0.348220	+	0.201045i
$502$	19.6603	+	19.6603i	0.877480	+	0.877480i
$503$	−22.6865	+	22.6865i	−1.01154	+	1.01154i	−0.0116099	+	0.999933i	$0.503696\pi$
$503$	−22.6865	+	22.6865i	−1.01154	+	1.01154i	−0.999933	+	0.0116099i	$0.996304\pi$
$504$	5.46410	+	0.392305i	0.243390	+	0.0174746i
$505$	20.2487	+	10.1244i	0.901056	+	0.450528i
$506$	1.60770			0.0714708
$507$	−9.33013	−	2.50000i	−0.414365	−	0.111029i
$508$	−22.0000	−	22.0000i	−0.976092	−	0.976092i
$509$	−9.57180	−	5.52628i	−0.424262	−	0.244948i	0.272637	−	0.962117i	$-0.412104\pi$
$509$	−9.57180	−	5.52628i	−0.424262	−	0.244948i	−0.696899	+	0.717169i	$0.745438\pi$
$510$	19.3923	+	17.1962i	0.858706	+	0.761458i
$511$	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
$514$	−32.7846	−	18.9282i	−1.44607	−	0.834887i
$515$	−21.5263	−	19.0885i	−0.948561	−	0.841138i
$516$	11.1962	−	6.46410i	0.492883	−	0.284566i
$517$	0.339746	−	0.339746i	0.0149420	−	0.0149420i
$518$	−16.3923	−	18.9282i	−0.720237	−	0.831658i
$519$			0.928203i			0.0407436i
$520$	22.3923	−	14.7846i	0.981968	−	0.648348i
$521$	7.39230	−	4.26795i	0.323863	−	0.186982i	−0.329250	−	0.944243i	$-0.606796\pi$
$521$	7.39230	−	4.26795i	0.323863	−	0.186982i	0.653113	+	0.757260i	$0.273463\pi$
$522$	1.19615	+	4.46410i	0.0523542	+	0.195388i
$523$	−24.2942	+	6.50962i	−1.06231	+	0.284646i	−0.747331	−	0.664452i	$-0.768665\pi$
$523$	−24.2942	+	6.50962i	−1.06231	+	0.284646i	−0.314982	+	0.949098i	$0.601998\pi$
$524$	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
$528$	−1.46410	−	5.46410i	−0.0637168	−	0.237795i
$529$	−17.8301	+	10.2942i	−0.775223	+	0.447575i
$530$	−8.78461	−	4.39230i	−0.381579	−	0.190790i
$531$	6.53590			0.283634
$532$	−13.8564	+	12.0000i	−0.600751	+	0.520266i
$533$	−1.39230	+	1.39230i	−0.0603074	+	0.0603074i
$534$			46.9808i			2.03306i
$535$	−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
$538$	−4.83013	−	1.29423i	−0.208242	−	0.0557982i
$539$	5.07180	+	0.732051i	0.218458	+	0.0315317i
$540$	19.1962	+	3.92820i	0.826071	+	0.169043i
$541$	1.79423	+	1.03590i	0.0771399	+	0.0445368i	0.538074	−	0.842898i	$-0.319152\pi$
$541$	1.79423	+	1.03590i	0.0771399	+	0.0445368i	−0.460934	+	0.887434i	$0.652485\pi$
$542$	−4.39230	−	16.3923i	−0.188666	−	0.704110i
$543$	−11.2583	+	42.0167i	−0.483141	+	1.80311i
$544$	20.7846	−	12.0000i	0.891133	−	0.514496i
$545$	8.53590	+	4.26795i	0.365638	+	0.182819i
$546$	25.3923	+	17.1962i	1.08669	+	0.735927i
$547$	14.4904	+	14.4904i	0.619564	+	0.619564i	0.945420	−	0.325856i	$-0.105652\pi$
$547$	14.4904	+	14.4904i	0.619564	+	0.619564i	−0.325856	+	0.945420i	$0.605652\pi$
$548$	4.39230	−	16.3923i	0.187630	−	0.700245i
$549$	−6.29423	+	3.63397i	−0.268631	+	0.155094i
$550$	−3.19615	+	4.07180i	−0.136284	+	0.173622i
$551$	−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
$556$	2.53590			0.107546
$557$	−8.24167	+	30.7583i	−0.349211	+	1.30327i	0.538404	+	0.842687i	$0.319027\pi$
$557$	−8.24167	+	30.7583i	−0.349211	+	1.30327i	−0.887615	+	0.460586i	$0.847639\pi$
$558$	−7.46410	−	7.46410i	−0.315981	−	0.315981i
$559$	14.1962			0.600433
$560$	−22.9282	+	5.85641i	−0.968893	+	0.247478i
$561$	6.00000			0.253320
$562$	24.2487	+	24.2487i	1.02287	+	1.02287i
$563$	7.06218	−	26.3564i	0.297635	−	1.11079i	−0.641466	−	0.767151i	$-0.721674\pi$
$563$	7.06218	−	26.3564i	0.297635	−	1.11079i	0.939102	−	0.343639i	$-0.111660\pi$
$564$	−2.53590			−0.106781
$565$	−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	0.839363	−	0.543571i	$-0.182928\pi$
$569$	18.8038	+	10.8564i	0.788298	+	0.455124i	−0.0510648	+	0.998695i	$0.516262\pi$
$570$	17.6603	−	11.6603i	0.739707	−	0.488394i
$571$	−14.7846	+	8.53590i	−0.618717	+	0.357216i	−0.776369	−	0.630278i	$-0.782941\pi$
$571$	−14.7846	+	8.53590i	−0.618717	+	0.357216i	0.157653	+	0.987495i	$0.449607\pi$
$572$	1.60770	−	6.00000i	0.0672211	−	0.250873i
$573$	−4.26795	−	4.26795i	−0.178296	−	0.178296i
$574$	1.56218	−	0.758330i	0.0652040	−	0.0316521i
$575$	−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	0.810905	+	0.585178i	$0.198975\pi$
$577$	−4.41858	+	16.4904i	−0.183948	+	0.686504i	−0.994853	+	0.101326i	$0.967691\pi$
$578$	0.366025	+	1.36603i	0.0152246	+	0.0568192i
$579$	20.0263	+	11.5622i	0.832264	+	0.480508i
$580$	−11.0000	−	16.6603i	−0.456750	−	0.691779i
$581$	7.45448	+	15.3564i	0.309264	+	0.637091i
$582$	23.3923	+	6.26795i	0.969642	+	0.259815i
$583$	−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
$586$		−	8.39230i		−	0.346683i
$587$	9.00000	−	9.00000i	0.371470	−	0.371470i	−0.496543	−	0.868012i	$-0.665397\pi$
$587$	9.00000	−	9.00000i	0.371470	−	0.371470i	0.868012	+	0.496543i	$0.165397\pi$
$588$	−16.1962	−	21.6603i	−0.667918	−	0.893254i
$589$	35.3205			1.45536
$590$	−26.7846	+	8.92820i	−1.10270	+	0.367568i
$591$	−13.0981	+	7.56218i	−0.538783	+	0.311066i
$592$	25.8564	−	6.92820i	1.06269	−	0.284747i
$593$	−3.80385	−	14.1962i	−0.156205	−	0.582966i	−0.998999	−	0.0447296i	$-0.985757\pi$
$593$	−3.80385	−	14.1962i	−0.156205	−	0.582966i	0.842794	−	0.538237i	$-0.180909\pi$
$594$	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
$598$	−2.41154	−	9.00000i	−0.0986153	−	0.368037i
$599$	21.0000	−	12.1244i	0.858037	−	0.495388i	−0.00531761	−	0.999986i	$-0.501693\pi$
$599$	21.0000	−	12.1244i	0.858037	−	0.495388i	0.863354	+	0.504598i	$0.168359\pi$
$600$	27.1244	−	3.26795i	1.10735	−	0.133413i
$601$			28.3923i			1.15815i	0.815276	+	0.579073i	$0.196585\pi$
$601$			28.3923i			1.15815i	−0.815276	+	0.579073i	$0.803415\pi$
$602$	−11.8301	−	4.09808i	−0.482160	−	0.167025i
$603$	2.07180	−	2.07180i	0.0843701	−	0.0843701i
$604$	23.9090	−	13.8038i	0.972842	−	0.561671i
$605$	−1.40192	−	23.3564i	−0.0569963	−	0.949573i
$606$	−23.9545	−	13.8301i	−0.973084	−	0.561811i
$607$	−22.9904	+	6.16025i	−0.933151	+	0.250037i	−0.693198	−	0.720747i	$-0.743799\pi$
$607$	−22.9904	+	6.16025i	−0.933151	+	0.250037i	−0.239953	+	0.970784i	$0.577132\pi$
$608$	−5.07180	−	18.9282i	−0.205689	−	0.767640i
$609$	12.7942	−	18.8923i	0.518448	−	0.765555i
$610$	20.8301	−	23.4904i	0.843387	−	0.951098i
$611$	−2.41154	−	1.39230i	−0.0975606	−	0.0563266i
$612$	−4.39230	−	4.39230i	−0.177548	−	0.177548i
$613$	−5.36603	−	1.43782i	−0.216732	−	0.0580731i	0.148819	−	0.988864i	$-0.452453\pi$
$613$	−5.36603	−	1.43782i	−0.216732	−	0.0580731i	−0.365551	+	0.930791i	$0.619119\pi$
$614$	1.51666			0.0612074
$615$	−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	−0.725544	−	0.688176i	$-0.758412\pi$
$617$	−0.928203	+	0.928203i	−0.0373681	+	0.0373681i	0.688176	+	0.725544i	$0.258412\pi$
$618$	24.8564	+	24.8564i	0.999871	+	0.999871i
$619$	−15.2942	+	8.83013i	−0.614727	+	0.354913i	−0.774813	−	0.632190i	$-0.782156\pi$
$619$	−15.2942	+	8.83013i	−0.614727	+	0.354913i	0.160086	+	0.987103i	$0.448823\pi$
$620$	40.7846	+	20.3923i	1.63795	+	0.818975i
$621$	3.40192	−	5.89230i	0.136514	−	0.236450i
$622$	−34.0526	−	9.12436i	−1.36538	−	0.365853i
$623$	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
$626$	−11.8038	+	20.4449i	−0.471777	+	0.817141i
$627$	1.26795	−	4.73205i	0.0506370	−	0.188980i
$628$	−9.12436	+	34.0526i	−0.364101	+	1.35885i
$629$			28.3923i			1.13208i
$630$	3.00000	+	5.33975i	0.119523	+	0.212741i
$631$	−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
$634$	−5.53590	−	3.19615i	−0.219859	−	0.126935i
$635$	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
$638$	−4.46410	−	1.19615i	−0.176735	−	0.0473561i
$639$	−9.80385	−	5.66025i	−0.387834	−	0.223916i
$640$	5.07180	−	24.7846i	0.200480	−	0.979698i
$641$	16.3301	+	28.2846i	0.645001	+	1.11717i	0.984301	+	0.176497i	$0.0564765\pi$
$641$	16.3301	+	28.2846i	0.645001	+	1.11717i	−0.339300	+	0.940678i	$0.610190\pi$
$642$	10.6603	−	10.6603i	0.420727	−	0.420727i
$643$	9.00000	+	9.00000i	0.354925	+	0.354925i	0.861938	−	0.507013i	$-0.169250\pi$
$643$	9.00000	+	9.00000i	0.354925	+	0.354925i	−0.507013	+	0.861938i	$0.669250\pi$
$644$	−0.588457	+	8.19615i	−0.0231885	+	0.322974i
$645$	12.9282	+	6.46410i	0.509048	+	0.254524i
$646$	20.7846			0.817760
$647$	7.03590	−	26.2583i	0.276610	−	1.03232i	−0.678145	−	0.734928i	$-0.737216\pi$
$647$	7.03590	−	26.2583i	0.276610	−	1.03232i	0.954755	−	0.297394i	$-0.0961174\pi$
$648$	−29.1244	−	7.80385i	−1.14411	−	0.306564i
$649$	−3.26795	+	5.66025i	−0.128278	+	0.222184i
$650$	27.5885	+	11.7846i	1.08211	+	0.462230i
$651$	−3.73205	+	51.9808i	−0.146271	+	2.03729i
$652$	7.26795	−	1.94744i	0.284635	−	0.0762677i
$653$	−8.41858	−	31.4186i	−0.329445	−	1.22950i	−0.909768	−	0.415118i	$-0.863740\pi$
$653$	−8.41858	−	31.4186i	−0.329445	−	1.22950i	0.580323	−	0.814386i	$-0.302926\pi$
$654$	−10.0981	−	5.83013i	−0.394866	−	0.227976i
$655$	1.00000	+	16.6603i	0.0390732	+	0.650970i
$656$			1.85641i			0.0724805i
$657$	4.33975	+	4.33975i	0.169310	+	0.169310i
$658$	1.60770	+	1.85641i	0.0626745	+	0.0723703i
$659$	−39.3205			−1.53171			−0.765855	−	0.643014i	$-0.777684\pi$
$659$	−39.3205			−1.53171			−0.765855	+	0.643014i	$0.777684\pi$
$660$	4.19615	−	4.73205i	0.163335	−	0.184195i
$661$	−19.9641	−	34.5788i	−0.776514	−	1.34496i	−0.933940	−	0.357430i	$-0.883653\pi$
$661$	−19.9641	−	34.5788i	−0.776514	−	1.34496i	0.157426	−	0.987531i	$-0.449680\pi$
$662$	−2.66025	−	9.92820i	−0.103394	−	0.385871i
$663$	−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
$668$	−6.58846	+	6.58846i	−0.254915	+	0.254915i
$669$	10.8301	+	18.7583i	0.418717	+	0.725239i
$670$	−5.66025	+	11.3205i	−0.218675	+	0.437349i
$671$		−	7.26795i		−	0.280576i
$672$	28.3923	−	5.46410i	1.09526	−	0.210782i
$673$	−10.1962	−	10.1962i	−0.393033	−	0.393033i	0.482734	−	0.875767i	$-0.339644\pi$
$673$	−10.1962	−	10.1962i	−0.393033	−	0.393033i	−0.875767	+	0.482734i	$0.839644\pi$
$674$	39.3205			1.51457
$675$	8.16025	+	20.3301i	0.314088	+	0.782507i
$676$	−10.0000			−0.384615
$677$	1.22243	+	4.56218i	0.0469819	+	0.175339i	0.985430	−	0.170081i	$-0.0544031\pi$
$677$	1.22243	+	4.56218i	0.0469819	+	0.175339i	−0.938448	+	0.345420i	$0.887736\pi$
$678$	9.46410	+	2.53590i	0.363467	+	0.0973906i
$679$	−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
$682$	10.1962	−	2.73205i	0.390431	−	0.104616i
$683$	29.3564	+	7.86603i	1.12329	+	0.300985i	0.772215	−	0.635362i	$-0.219149\pi$
$683$	29.3564	+	7.86603i	1.12329	+	0.300985i	0.351077	+	0.936347i	$0.385816\pi$
$684$	−4.39230	+	2.53590i	−0.167944	+	0.0969625i
$685$	18.0000	−	6.00000i	0.687745	−	0.229248i
$686$	−5.58846	+	25.5885i	−0.213368	+	0.976972i
$687$	21.1244	−	21.1244i	0.805944	−	0.805944i
$688$	9.46410	−	9.46410i	0.360815	−	0.360815i
$689$	6.58846	+	11.4115i	0.251000	+	0.434745i
$690$	1.90192	−	9.29423i	0.0724050	−	0.353825i
$691$	21.7583	−	37.6865i	0.827726	−	1.43366i	−0.0720922	−	0.997398i	$-0.522968\pi$
$691$	21.7583	−	37.6865i	0.827726	−	1.43366i	0.899818	−	0.436265i	$-0.143699\pi$
$692$	0.248711	+	0.928203i	0.00945459	+	0.0352850i
$693$	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
$698$	−19.9808	+	19.9808i	−0.756283	+	0.756283i
$699$			14.1962i			0.536948i
$700$	−19.5885	−	17.7846i	−0.740374	−	0.672195i
$701$			33.9808i			1.28344i	0.766941	+	0.641718i	$0.221778\pi$
$701$			33.9808i			1.28344i	−0.766941	+	0.641718i	$0.778222\pi$
$702$	−18.5885	−	18.5885i	−0.701576	−	0.701576i
$703$	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
$708$	33.3205	−	8.92820i	1.25226	−	0.335542i
$709$	−7.96410	+	13.7942i	−0.299098	+	0.518053i	−0.975930	−	0.218085i	$-0.930019\pi$
$709$	−7.96410	+	13.7942i	−0.299098	+	0.518053i	0.676832	+	0.736138i	$0.263352\pi$
$710$	47.9090	+	9.80385i	1.79799	+	0.367932i
$711$	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
$714$	−2.19615	+	30.5885i	−0.0821889	+	1.14474i
$715$	6.58846	−	2.19615i	0.246394	−	0.0821314i
$716$	24.3397	−	14.0526i	0.909619	−	0.525169i
$717$	8.83013	+	2.36603i	0.329767	+	0.0883608i
$718$	−1.73205	−	6.46410i	−0.0646396	−	0.241238i
$719$	−5.36603	+	9.29423i	−0.200119	+	0.346616i	−0.948567	−	0.316578i	$-0.897466\pi$
$719$	−5.36603	+	9.29423i	−0.200119	+	0.346616i	0.748448	+	0.663194i	$0.230800\pi$
$720$	−6.53590	+	0.392305i	−0.243579	+	0.0146203i
$721$	2.43782	−	33.9545i	0.0907892	−	1.26453i
$722$	−2.56218	+	9.56218i	−0.0953544	+	0.355867i
$723$	−10.1962	−	38.0526i	−0.379199	−	1.41519i
$724$			45.0333i			1.67365i
$725$	8.76795	−	20.5263i	0.325633	−	0.762327i
$726$			28.5885i			1.06102i
$727$	−17.2942	−	17.2942i	−0.641407	−	0.641407i	0.309494	−	0.950901i	$-0.399840\pi$
$727$	−17.2942	−	17.2942i	−0.641407	−	0.641407i	−0.950901	+	0.309494i	$0.899840\pi$
$728$	30.0000	+	10.3923i	1.11187	+	0.385164i
$729$		−	17.5885i		−	0.651424i
$730$	−23.7128	−	11.8564i	−0.877651	−	0.438825i
$731$	7.09808	+	12.2942i	0.262532	+	0.454718i
$732$	−27.1244	+	27.1244i	−1.00255	+	1.00255i
$733$	21.2942	−	5.70577i	0.786520	−	0.210747i	0.156863	−	0.987620i	$-0.449862\pi$
$733$	21.2942	−	5.70577i	0.786520	−	0.210747i	0.629657	+	0.776873i	$0.283195\pi$
$734$	−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
$738$	0.464102	−	0.124356i	0.0170838	−	0.00457759i
$739$	−5.83013	−	10.0981i	−0.214465	−	0.371464i	0.738642	−	0.674098i	$-0.235467\pi$
$739$	−5.83013	−	10.0981i	−0.214465	−	0.371464i	−0.953107	+	0.302634i	$0.902134\pi$
$740$	22.3923	+	19.8564i	0.823157	+	0.729936i
$741$	−28.3923			−1.04302
$742$	−2.19615	−	11.4115i	−0.0806233	−	0.418931i
$743$	−33.4186	−	33.4186i	−1.22601	−	1.22601i	−0.965461	−	0.260548i	$-0.916097\pi$
$743$	−33.4186	−	33.4186i	−1.22601	−	1.22601i	−0.260548	−	0.965461i	$-0.583903\pi$
$744$	−48.2487	−	27.8564i	−1.76888	−	1.02127i
$745$	−3.03590	−	50.5788i	−0.111227	−	1.85307i
$746$	−6.92820	+	12.0000i	−0.253660	+	0.439351i
$747$	1.22243	+	4.56218i	0.0447264	+	0.166921i
$748$	6.00000	−	1.60770i	0.219382	−	0.0587832i
$749$	−14.5622	−	1.04552i	−0.532090	−	0.0382024i
$750$	19.7583	+	23.2942i	0.721472	+	0.850585i
$751$	5.19615	−	9.00000i	0.189610	−	0.328415i	−0.755510	−	0.655137i	$-0.772611\pi$
$751$	5.19615	−	9.00000i	0.189610	−	0.328415i	0.945120	+	0.326722i	$0.105944\pi$
$752$	−2.53590	+	0.679492i	−0.0924747	+	0.0247785i
$753$	9.83013	−	36.6865i	0.358230	−	1.33693i
$754$			26.7846i			0.975438i
$755$	27.6077	+	13.8038i	1.00475	+	0.502373i
$756$	10.1244	+	20.8564i	0.368219	+	0.758540i
$757$	−37.0526	−	37.0526i	−1.34670	−	1.34670i	−0.889222	−	0.457476i	$-0.848753\pi$
$757$	−37.0526	−	37.0526i	−1.34670	−	1.34670i	−0.457476	−	0.889222i	$-0.651247\pi$
$758$	−30.2487	−	30.2487i	−1.09868	−	1.09868i
$759$	−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	−0.176098	−	0.984373i	$-0.556348\pi$
$761$	−30.8038	−	17.7846i	−1.11664	−	0.644692i	−0.940541	+	0.339681i	$0.889681\pi$
$762$	−11.0000	+	41.0526i	−0.398488	+	1.48718i
$763$	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
$766$	−5.36603	+	9.29423i	−0.193882	+	0.335814i
$767$	36.5885	+	9.80385i	1.32113	+	0.353996i
$768$	−8.00000	+	29.8564i	−0.288675	+	1.07735i
$769$	22.6410			0.816456			0.408228	−	0.912880i	$-0.366147\pi$
$769$	22.6410			0.816456			0.408228	+	0.912880i	$0.366147\pi$
$770$	−6.12436	−	0.0717968i	−0.220706	−	0.00258738i
$771$			51.7128i			1.86239i
$772$	23.1244	+	6.19615i	0.832264	+	0.223004i
$773$	−3.50962	+	13.0981i	−0.126232	+	0.471105i	−0.999881	−	0.0154528i	$-0.995081\pi$
$773$	−3.50962	+	13.0981i	−0.126232	+	0.471105i	0.873648	+	0.486558i	$0.161748\pi$
$774$	−3.00000	−	1.73205i	−0.107833	−	0.0622573i
$775$	6.09808	+	50.6147i	0.219049	+	1.81814i
$776$	25.0718			0.900025
$777$	−11.1962	+	32.3205i	−0.401660	+	1.15949i
$778$	5.51666	−	20.5885i	0.197782	−	0.738132i
$779$	−0.803848	+	1.39230i	−0.0288008	+	0.0498845i
$780$	−32.7846	−	16.3923i	−1.17388	−	0.586939i
$781$	9.80385	−	5.66025i	0.350809	−	0.202540i
$782$	6.58846	−	6.58846i	0.235603	−	0.235603i
$783$	−13.8301	+	13.8301i	−0.494248	+	0.494248i
$784$	−22.0000	−	17.3205i	−0.785714	−	0.618590i
$785$	−37.3923	+	12.4641i	−1.33459	+	0.444863i
$786$		−	20.3923i		−	0.727369i
$787$	10.1603	+	2.72243i	0.362174	+	0.0970442i	0.435317	−	0.900277i	$-0.356636\pi$
$787$	10.1603	+	2.72243i	0.362174	+	0.0970442i	−0.0731430	+	0.997321i	$0.523303\pi$
$788$	−11.0718	+	11.0718i	−0.394416	+	0.394416i
$789$	−0.696152	−	0.401924i	−0.0247837	−	0.0143089i
$790$	−30.5885	−	27.1244i	−1.08829	−	0.965041i
$791$	−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
$794$	15.9282	−	27.5885i	0.565271	−	0.979078i
$795$	0.803848	+	13.3923i	0.0285095	+	0.474976i
$796$	6.00000	−	3.46410i	0.212664	−	0.122782i
$797$	−0.928203	+	0.928203i	−0.0328786	+	0.0328786i	−0.723355	−	0.690476i	$-0.757401\pi$
$797$	−0.928203	+	0.928203i	−0.0328786	+	0.0328786i	0.690476	+	0.723355i	$0.257401\pi$
$798$	23.6603	+	8.19615i	0.837564	+	0.290141i
$799$		−	2.78461i		−	0.0985124i
$800$	26.2487	−	10.5359i	0.928032	−	0.372500i
$801$	10.9019	−	6.29423i	0.385201	−	0.222396i
$802$	−41.9545	+	11.2417i	−1.48146	+	0.396957i
$803$	−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	−0.996857	−	0.0792233i	$-0.974756\pi$
$809$	−40.5788	+	23.4282i	−1.42668	+	0.823692i	−0.429819	+	0.902915i	$0.641423\pi$
$810$	−10.6603	−	31.9808i	−0.374563	−	1.12369i
$811$	−30.3397			−1.06537			−0.532686	−	0.846313i	$-0.678817\pi$
$811$	−30.3397			−1.06537			−0.532686	+	0.846313i	$0.678817\pi$
$812$	7.73205	−	22.3205i	0.271342	−	0.783296i
$813$	−16.3923	+	16.3923i	−0.574903	+	0.574903i
$814$	6.92820			0.242833
$815$	6.29423	+	5.58142i	0.220477	+	0.195508i
$816$	−28.3923	−	16.3923i	−0.993929	−	0.573845i
$817$	11.1962	−	3.00000i	0.391704	−	0.104957i
$818$	4.16987	−	15.5622i	0.145796	−	0.544119i
$819$	0.588457	−	8.19615i	0.0205624	−	0.286397i
$820$	−1.73205	+	1.14359i	−0.0604858	+	0.0399360i
$821$	9.92820	+	5.73205i	0.346497	+	0.200050i	0.663141	−	0.748494i	$-0.269223\pi$
$821$	9.92820	+	5.73205i	0.346497	+	0.200050i	−0.316645	+	0.948544i	$0.602556\pi$
$822$	−22.3923	+	6.00000i	−0.781021	+	0.209274i
$823$	3.66987	−	13.6962i	0.127924	−	0.477418i	−0.872003	−	0.489500i	$-0.837179\pi$
$823$	3.66987	−	13.6962i	0.127924	−	0.477418i	0.999927	+	0.0120822i	$0.00384597\pi$
$824$	31.5167	+	18.1962i	1.09793	+	0.633893i
$825$	7.00000	+	1.00000i	0.243709	+	0.0348155i
$826$	−27.6603	−	18.7321i	−0.962423	−	0.651771i
$827$	−17.1506	−	17.1506i	−0.596386	−	0.596386i	0.342963	−	0.939349i	$-0.388569\pi$
$827$	−17.1506	−	17.1506i	−0.596386	−	0.596386i	−0.939349	+	0.342963i	$0.888569\pi$
$828$	−0.588457	+	2.19615i	−0.0204503	+	0.0763216i
$829$	8.19615	−	4.73205i	0.284664	−	0.164351i	−0.350869	−	0.936425i	$-0.614114\pi$
$829$	8.19615	−	4.73205i	0.284664	−	0.164351i	0.635533	+	0.772074i	$0.280780\pi$
$830$	−11.2417	−	17.0263i	−0.390204	−	0.590991i
$831$	−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
$836$		−	5.07180i		−	0.175412i
$837$	11.5622	−	43.1506i	0.399647	−	1.49150i
$838$	−2.39230	+	2.39230i	−0.0826408	+	0.0826408i
$839$	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
$842$	30.1244	−	30.1244i	1.03815	−	1.03815i
$843$	12.1244	−	45.2487i	0.417585	−	1.55845i
$844$	41.0718			1.41375
$845$	−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
$848$	12.0000	+	3.21539i	0.412082	+	0.110417i
$849$	−23.4904	−	13.5622i	−0.806188	−	0.465453i
$850$	3.58846	+	29.7846i	0.123083	+	1.02160i
$851$	9.00000	−	5.19615i	0.308516	−	0.178122i
$852$	−57.7128	−	15.4641i	−1.97721	−	0.529791i
$853$	−29.3205	−	29.3205i	−1.00392	−	1.00392i	−0.999992	−	0.00392277i	$-0.998751\pi$
$853$	−29.3205	−	29.3205i	−1.00392	−	1.00392i	−0.00392277	−	0.999992i	$-0.501249\pi$
$854$	37.0526	+	2.66025i	1.26791	+	0.0910320i
$855$	−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	−0.855553	−	0.517716i	$-0.826782\pi$
$857$	4.22243	−	15.7583i	0.144236	−	0.538294i	0.999788	−	0.0205786i	$-0.00655083\pi$
$858$	−8.19615	+	2.19615i	−0.279812	+	0.0749754i
$859$	−14.1962	−	8.19615i	−0.484366	−	0.279649i	0.237868	−	0.971298i	$-0.423551\pi$
$859$	−14.1962	−	8.19615i	−0.484366	−	0.279649i	−0.722234	+	0.691648i	$0.756885\pi$
$860$	14.6603	+	3.00000i	0.499911	+	0.102299i
$861$	−1.96410	−	1.33013i	−0.0669364	−	0.0453306i
$862$	4.85641	−	18.1244i	0.165410	−	0.617318i
$863$	−23.2583	+	6.23205i	−0.791723	+	0.212141i	−0.631947	−	0.775012i	$-0.717744\pi$
$863$	−23.2583	+	6.23205i	−0.791723	+	0.212141i	−0.159776	+	0.987153i	$0.551077\pi$
$864$	−24.7846			−0.843190
$865$	−0.712813	+	0.803848i	−0.0242364	+	0.0273316i
$866$	22.9282			0.779132
$867$	1.36603	−	1.36603i	0.0463927	−	0.0463927i
$868$	10.1962	+	52.9808i	0.346080	+	1.79828i
$869$	−9.46410			−0.321048
$870$	−12.1962	+	24.3923i	−0.413488	+	0.826977i
$871$	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	$-0.693410\pi$
$877$	−19.3923	+	5.19615i	−0.654832	+	0.175462i	−0.0839192	+	0.996473i	$0.526744\pi$
$878$	7.26795	−	1.94744i	0.245281	−	0.0657230i
$879$	−9.92820	+	5.73205i	−0.334870	+	0.193337i
$880$	2.92820	−	5.85641i	0.0987097	−	0.197419i
$881$			27.2487i			0.918032i	0.888428	+	0.459016i	$0.151798\pi$
$881$			27.2487i			0.918032i	−0.888428	+	0.459016i	$0.848202\pi$
$882$	−2.85641	+	6.66025i	−0.0961802	+	0.224262i
$883$	−15.2487	+	15.2487i	−0.513160	+	0.513160i	−0.915493	−	0.402333i	$-0.868199\pi$
$883$	−15.2487	+	15.2487i	−0.513160	+	0.513160i	0.402333	+	0.915493i	$0.368199\pi$
$884$	−18.0000	−	31.1769i	−0.605406	−	1.04859i
$885$	28.8564	+	25.5885i	0.969997	+	0.860147i
$886$	24.4186	−	42.2942i	0.820358	−	1.42090i
$887$	−3.06218	+	0.820508i	−0.102818	+	0.0275500i	−0.309861	−	0.950782i	$-0.600283\pi$
$887$	−3.06218	+	0.820508i	−0.102818	+	0.0275500i	0.207043	+	0.978332i	$0.433616\pi$
$888$	−25.8564	−	25.8564i	−0.867684	−	0.867684i
$889$	37.0263	−	17.9737i	1.24182	−	0.602819i
$890$	−36.0788	+	40.6865i	−1.20937	+	1.36382i
$891$	−6.75833	−	3.90192i	−0.226413	−	0.130719i
$892$	15.8564	+	15.8564i	0.530912	+	0.530912i
$893$	−2.19615	−	0.588457i	−0.0734914	−	0.0196920i
$894$			61.9090i			2.07055i
$895$	28.1051	+	14.0526i	0.939450	+	0.469725i
$896$	26.9282	−	13.0718i	0.899608	−	0.436698i
$897$	−9.00000	+	9.00000i	−0.300501	+	0.300501i
$898$	−23.1962	+	23.1962i	−0.774066	+	0.774066i
$899$	−39.4186	+	22.7583i	−1.31468	+	0.759033i
$900$	−4.39230	−	5.85641i	−0.146410	−	0.195214i
$901$	−6.58846	+	11.4115i	−0.219493	+	0.380174i
$902$	−0.124356	+	0.464102i	−0.00414059	+	0.0154529i
$903$	3.23205	+	16.7942i	0.107556	+	0.558877i
$904$	10.1436			0.337371
$905$	−42.0167	+	27.7417i	−1.39668	+	0.922164i
$906$	−32.6603	−	18.8564i	−1.08506	−	0.626462i
$907$	1.20577	−	4.50000i	0.0400370	−	0.149420i	−0.943014	−	0.332754i	$-0.892022\pi$
$907$	1.20577	−	4.50000i	0.0400370	−	0.149420i	0.983051	+	0.183334i	$0.0586889\pi$
$908$	−6.87564	+	25.6603i	−0.228176	+	0.851565i
$909$			7.41154i			0.245825i
$910$	8.78461	+	34.3923i	0.291207	+	1.14009i
$911$	8.19615			0.271551			0.135775	−	0.990740i	$-0.456647\pi$
$911$	8.19615			0.271551			0.135775	+	0.990740i	$0.456647\pi$
$912$	−18.9282	+	18.9282i	−0.626775	+	0.626775i
$913$	−4.56218	−	1.22243i	−0.150986	−	0.0404566i
$914$	−10.1962	+	17.6603i	−0.337259	+	0.584149i
$915$	−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
$918$	6.80385	−	25.3923i	0.224560	−	0.838071i
$919$	−39.0000	−	22.5167i	−1.28649	−	0.742756i	−0.308465	−	0.951236i	$-0.599815\pi$
$919$	−39.0000	−	22.5167i	−1.28649	−	0.742756i	−0.978027	+	0.208480i	$0.933148\pi$
$920$	−0.588457	−	9.80385i	−0.0194009	−	0.323223i
$921$	−1.03590	−	1.79423i	−0.0341340	−	0.0591218i
$922$	12.1436	+	12.1436i	0.399928	+	0.399928i
$923$	−46.3923	−	46.3923i	−1.52702	−	1.52702i
$924$	7.46410	+	0.535898i	0.245551	+	0.0176298i
$925$	−4.73205	+	33.1244i	−0.155589	+	1.08912i
$926$		−	1.66025i		−	0.0545593i
$927$	2.43782	−	9.09808i	0.0800686	−	0.298820i
$928$	17.8564	+	17.8564i	0.586165	+	0.586165i
$929$	−4.16025	+	7.20577i	−0.136494	+	0.236414i	−0.926167	−	0.377114i	$-0.876917\pi$
$929$	−4.16025	+	7.20577i	−0.136494	+	0.236414i	0.789673	+	0.613527i	$0.210250\pi$
$930$	−3.73205	−	62.1769i	−0.122379	−	2.03886i
$931$	−9.00000	−	22.5167i	−0.294963	−	0.737954i
$932$	3.80385	+	14.1962i	0.124599	+	0.465010i
$933$	12.4641	+	46.5167i	0.408056	+	1.52289i
$934$	−4.56218	+	7.90192i	−0.149279	+	0.258559i
$935$	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	0.713486	−	0.700670i	$-0.247115\pi$
$937$	0.392305	+	0.392305i	0.0128160	+	0.0128160i	−0.700670	+	0.713486i	$0.747115\pi$
$938$	−14.7058	+	2.83013i	−0.480160	+	0.0924069i
$939$	32.2487			1.05240
$940$	−2.19615	−	1.94744i	−0.0716306	−	0.0635185i
$941$	9.73205	+	16.8564i	0.317256	+	0.549503i	0.979914	−	0.199418i	$-0.0639053\pi$
$941$	9.73205	+	16.8564i	0.317256	+	0.549503i	−0.662659	+	0.748922i	$0.730572\pi$
$942$	46.5167	−	12.4641i	1.51559	−	0.406102i
$943$	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	$-0.460765\pi$
$947$	22.3301	−	5.98334i	0.725632	−	0.194432i	0.602683	+	0.797981i	$0.294098\pi$
$948$	35.3205	+	35.3205i	1.14716	+	1.14716i
$949$	17.7846	+	30.8038i	0.577313	+	0.999935i
$950$	24.2487	+	3.46410i	0.786732	+	0.112390i
$951$			8.73205i			0.283156i
$952$	6.00000	+	31.1769i	0.194461	+	1.01045i
$953$	3.46410	+	3.46410i	0.112213	+	0.112213i	0.760984	−	0.648771i	$-0.224717\pi$
$953$	3.46410	+	3.46410i	0.112213	+	0.112213i	−0.648771	+	0.760984i	$0.724717\pi$
$954$		−	3.21539i		−	0.104102i
$955$	−0.418584	−	6.97372i	−0.0135451	−	0.225664i
$956$	9.46410			0.306091
$957$	1.63397	+	6.09808i	0.0528189	+	0.197123i
$958$	1.39230	−	5.19615i	0.0449833	−	0.167880i
$959$	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
$962$	−10.3923	−	38.7846i	−0.335061	−	1.25047i
$963$	−3.90192	−	1.04552i	−0.125738	−	0.0336913i
$964$	−20.3923	−	35.3205i	−0.656792	−	1.13760i
$965$	8.46410	+	25.3923i	0.272469	+	0.817407i
$966$	10.0981	−	4.90192i	0.324900	−	0.157717i
$967$	−10.5096	+	10.5096i	−0.337967	+	0.337967i	−0.855602	−	0.517635i	$-0.826813\pi$
$967$	−10.5096	+	10.5096i	−0.337967	+	0.337967i	0.517635	+	0.855602i	$0.326813\pi$
$968$	7.66025	+	28.5885i	0.246210	+	0.918868i
$969$	−14.1962	−	24.5885i	−0.456046	−	0.789895i
$970$	15.4449	+	23.3923i	0.495905	+	0.751082i
$971$	−10.0000	+	17.3205i	−0.320915	+	0.555842i	−0.980677	−	0.195633i	$-0.937324\pi$
$971$	−10.0000	+	17.3205i	−0.320915	+	0.555842i	0.659762	+	0.751475i	$0.270657\pi$
$972$	3.85641	+	14.3923i	0.123694	+	0.461633i
$973$	−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
$976$	−19.8564	+	34.3923i	−0.635588	+	1.10087i
$977$	20.0263	+	5.36603i	0.640697	+	0.171674i	0.564519	−	0.825420i	$-0.309062\pi$
$977$	20.0263	+	5.36603i	0.640697	+	0.171674i	0.0761781	+	0.997094i	$0.475728\pi$
$978$	−7.26795	−	7.26795i	−0.232403	−	0.232403i
$979$			12.5885i			0.402329i
$980$	2.60770	−	31.1962i	0.0832998	−	0.996525i
$981$			3.12436i			0.0997530i
$982$	12.1962	−	12.1962i	0.389195	−	0.389195i
$983$	12.2321	+	3.27757i	0.390142	+	0.104538i	0.448557	−	0.893754i	$-0.351938\pi$
$983$	12.2321	+	3.27757i	0.390142	+	0.104538i	−0.0584153	+	0.998292i	$0.518605\pi$
$984$	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
$988$	−28.3923	+	7.60770i	−0.903280	+	0.242033i
$989$	2.59808	−	4.50000i	0.0826140	−	0.143092i
$990$	−1.66025	−	0.339746i	−0.0527663	−	0.0107978i
$991$	−17.6865	−	30.6340i	−0.561831	−	0.973120i	−0.997337	−	0.0729342i	$-0.976764\pi$
$991$	−17.6865	−	30.6340i	−0.561831	−	0.973120i	0.435506	−	0.900186i	$-0.356570\pi$
$992$	−55.7128	−	14.9282i	−1.76888	−	0.473971i
$993$	−9.92820	+	9.92820i	−0.315062	+	0.315062i
$994$	25.2679	+	52.0526i	0.801451	+	1.65101i
$995$	6.92820	+	3.46410i	0.219639	+	0.109819i
$996$	12.4641	+	21.5885i	0.394940	+	0.684056i
$997$	−11.1962	−	3.00000i	−0.354586	−	0.0950110i	0.0771291	−	0.997021i	$-0.475425\pi$
$997$	−11.1962	−	3.00000i	−0.354586	−	0.0950110i	−0.431715	+	0.902010i	$0.642091\pi$
$998$	18.4641	−	4.94744i	0.584471	−	0.156609i
$999$	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.a.173.1	yes	4
5.2	odd	4		280.2.bv.d.117.1	yes	4
7.3	odd	6		280.2.bv.c.213.1	yes	4
8.5	even	2		280.2.bv.b.173.1	yes	4
35.17	even	12		280.2.bv.b.157.1	yes	4
40.37	odd	4		280.2.bv.c.117.1	yes	4
56.45	odd	6		280.2.bv.d.213.1	yes	4
280.157	even	12	inner	280.2.bv.a.157.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bv.a.157.1	✓	4	280.157	even	12	inner
280.2.bv.a.173.1	yes	4	1.1	even	1	trivial
280.2.bv.b.157.1	yes	4	35.17	even	12
280.2.bv.b.173.1	yes	4	8.5	even	2
280.2.bv.c.117.1	yes	4	40.37	odd	4
280.2.bv.c.213.1	yes	4	7.3	odd	6
280.2.bv.d.117.1	yes	4	5.2	odd	4
280.2.bv.d.213.1	yes	4	56.45	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.500000 + 1.86603i) q^{3} +2.00000i q^{4} +(-1.86603 + 1.23205i) q^{5} +(2.36603 - 1.36603i) q^{6} +(-2.50000 - 0.866025i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-0.633975 - 0.366025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.500000 + 1.86603i) q^{3} +2.00000i 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} +(3.09808 + 0.633975i) q^{10} +(0.633975 - 0.366025i) q^{11} +(-3.73205 - 1.00000i) q^{12} +(-3.00000 - 3.00000i) q^{13} +(1.63397 + 3.36603i) q^{14} +(-1.36603 - 4.09808i) q^{15} -4.00000 q^{16} +(1.09808 - 4.09808i) q^{17} +(0.267949 + 1.00000i) q^{18} +(-3.00000 - 1.73205i) q^{19} +(-2.46410 - 3.73205i) q^{20} +(2.86603 - 4.23205i) q^{21} +(-1.00000 - 0.267949i) q^{22} +(-1.50000 + 0.401924i) q^{23} +(2.73205 + 4.73205i) q^{24} +(1.96410 - 4.59808i) q^{25} +6.00000i q^{26} +(-3.09808 + 3.09808i) q^{27} +(1.73205 - 5.00000i) q^{28} +4.46410 q^{29} +(-2.73205 + 5.46410i) q^{30} +(-8.83013 + 5.09808i) q^{31} +(4.00000 + 4.00000i) 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} +(1.26795 + 4.73205i) q^{38} +(7.09808 - 4.09808i) q^{39} +(-1.26795 + 6.19615i) q^{40} -0.464102i q^{41} +(-7.09808 + 1.36603i) q^{42} +(-2.36603 + 2.36603i) q^{43} +(0.732051 + 1.26795i) q^{44} +(1.63397 - 0.0980762i) q^{45} +(1.90192 + 1.09808i) q^{46} +(0.633975 - 0.169873i) q^{47} +(2.00000 - 7.46410i) q^{48} +(5.50000 + 4.33013i) q^{49} +(-6.56218 + 2.63397i) q^{50} +(7.09808 + 4.09808i) q^{51} +(6.00000 - 6.00000i) q^{52} +(-3.00000 - 0.803848i) q^{53} +6.19615 q^{54} +(-0.732051 + 1.46410i) q^{55} +(-6.73205 + 3.26795i) q^{56} +(4.73205 - 4.73205i) q^{57} +(-4.46410 - 4.46410i) q^{58} +(-7.73205 + 4.46410i) q^{59} +(8.19615 - 2.73205i) q^{60} +(4.96410 - 8.59808i) q^{61} +(13.9282 + 3.73205i) q^{62} +(1.26795 + 1.46410i) q^{63} -8.00000i q^{64} +(9.29423 + 1.90192i) q^{65} +(1.00000 - 1.73205i) q^{66} +(-1.03590 + 3.86603i) q^{67} +(8.19615 + 2.19615i) q^{68} -3.00000i q^{69} +(-7.19615 - 4.26795i) q^{70} +15.4641 q^{71} +(-2.00000 + 0.535898i) q^{72} +(-8.09808 - 2.16987i) q^{73} +(8.19615 + 4.73205i) q^{74} +(7.59808 + 5.96410i) q^{75} +(3.46410 - 6.00000i) q^{76} +(-1.90192 + 0.366025i) q^{77} +(-11.1962 - 3.00000i) q^{78} +(-11.1962 - 6.46410i) q^{79} +(7.46410 - 4.92820i) q^{80} +(-5.33013 - 9.23205i) q^{81} +(-0.464102 + 0.464102i) q^{82} +(-4.56218 - 4.56218i) q^{83} +(8.46410 + 5.73205i) q^{84} +(3.00000 + 9.00000i) q^{85} +4.73205 q^{86} +(-2.23205 + 8.33013i) q^{87} +(0.535898 - 2.00000i) q^{88} +(-8.59808 + 14.8923i) q^{89} +(-1.73205 - 1.53590i) q^{90} +(4.90192 + 10.0981i) q^{91} +(-0.803848 - 3.00000i) q^{92} +(-5.09808 - 19.0263i) q^{93} +(-0.803848 - 0.464102i) q^{94} +(7.73205 - 0.464102i) q^{95} +(-9.46410 + 5.46410i) q^{96} +(6.26795 + 6.26795i) q^{97} +(-1.16987 - 9.83013i) q^{98} -0.535898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{3} - 4 q^{5} + 6 q^{6} - 10 q^{7} + 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 2 * q^3 - 4 * q^5 + 6 * q^6 - 10 * q^7 + 8 * q^8 - 6 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} - 4 q^{5} + 6 q^{6} - 10 q^{7} + 8 q^{8} - 6 q^{9} + 2 q^{10} + 6 q^{11} - 8 q^{12} - 12 q^{13} + 10 q^{14} - 2 q^{15} - 16 q^{16} - 6 q^{17} + 8 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 6 q^{23} + 4 q^{24} - 6 q^{25} - 2 q^{27} + 4 q^{29} - 4 q^{30} - 18 q^{31} + 16 q^{32} - 2 q^{33} + 16 q^{35} - 4 q^{36} - 12 q^{37} + 12 q^{38} + 18 q^{39} - 12 q^{40} - 18 q^{42} - 6 q^{43} - 4 q^{44} + 10 q^{45} + 18 q^{46} + 6 q^{47} + 8 q^{48} + 22 q^{49} - 2 q^{50} + 18 q^{51} + 24 q^{52} - 12 q^{53} + 4 q^{54} + 4 q^{55} - 20 q^{56} + 12 q^{57} - 4 q^{58} - 24 q^{59} + 12 q^{60} + 6 q^{61} + 28 q^{62} + 12 q^{63} + 6 q^{65} + 4 q^{66} - 18 q^{67} + 12 q^{68} - 8 q^{70} + 48 q^{71} - 8 q^{72} - 22 q^{73} + 12 q^{74} + 20 q^{75} - 18 q^{77} - 24 q^{78} - 24 q^{79} + 16 q^{80} - 4 q^{81} + 12 q^{82} + 6 q^{83} + 20 q^{84} + 12 q^{85} + 12 q^{86} - 2 q^{87} + 16 q^{88} - 24 q^{89} + 30 q^{91} - 24 q^{92} - 10 q^{93} - 24 q^{94} + 24 q^{95} - 24 q^{96} + 32 q^{97} - 22 q^{98} - 16 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 - 4 * q^5 + 6 * q^6 - 10 * q^7 + 8 * q^8 - 6 * q^9 + 2 * q^10 + 6 * q^11 - 8 * q^12 - 12 * q^13 + 10 * q^14 - 2 * q^15 - 16 * q^16 - 6 * q^17 + 8 * q^18 - 12 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 6 * q^23 + 4 * q^24 - 6 * q^25 - 2 * q^27 + 4 * q^29 - 4 * q^30 - 18 * q^31 + 16 * q^32 - 2 * q^33 + 16 * q^35 - 4 * q^36 - 12 * q^37 + 12 * q^38 + 18 * q^39 - 12 * q^40 - 18 * q^42 - 6 * q^43 - 4 * q^44 + 10 * q^45 + 18 * q^46 + 6 * q^47 + 8 * q^48 + 22 * q^49 - 2 * q^50 + 18 * q^51 + 24 * q^52 - 12 * q^53 + 4 * q^54 + 4 * q^55 - 20 * q^56 + 12 * q^57 - 4 * q^58 - 24 * q^59 + 12 * q^60 + 6 * q^61 + 28 * q^62 + 12 * q^63 + 6 * q^65 + 4 * q^66 - 18 * q^67 + 12 * q^68 - 8 * q^70 + 48 * q^71 - 8 * q^72 - 22 * q^73 + 12 * q^74 + 20 * q^75 - 18 * q^77 - 24 * q^78 - 24 * q^79 + 16 * q^80 - 4 * q^81 + 12 * q^82 + 6 * q^83 + 20 * q^84 + 12 * q^85 + 12 * q^86 - 2 * q^87 + 16 * q^88 - 24 * q^89 + 30 * q^91 - 24 * q^92 - 10 * q^93 - 24 * q^94 + 24 * q^95 - 24 * q^96 + 32 * q^97 - 22 * q^98 - 16 * q^99

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