LMFDB - Embedded newform 280.2.bj.d.131.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(131,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("280.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bj (of order $6$, degree $2$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	280.131
Dual form			280.2.bj.d.171.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.36603 + 0.633975i) q^{6} +(-0.866025 + 2.50000i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.36603 + 0.633975i) q^{6} +(-0.866025 + 2.50000i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.00000 - 1.00000i) q^{10} +(0.732051 + 1.26795i) q^{11} -3.46410 q^{12} +4.73205 q^{13} +(-2.09808 + 3.09808i) q^{14} +1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.09808 + 0.633975i) q^{17} +(-7.09808 - 4.09808i) q^{19} +(1.73205 - 1.00000i) q^{20} +(-0.866025 - 4.50000i) q^{21} +(0.535898 + 2.00000i) q^{22} +(5.13397 + 2.96410i) q^{23} +(-4.73205 - 1.26795i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(6.46410 + 1.73205i) q^{26} -5.19615i q^{27} +(-4.00000 + 3.46410i) q^{28} -10.4641i q^{29} +(-0.633975 + 2.36603i) q^{30} +(1.09808 + 1.90192i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-2.19615 - 1.26795i) q^{33} +(-1.73205 + 0.464102i) q^{34} +(1.73205 + 2.00000i) q^{35} +(1.73205 + 1.00000i) q^{37} +(-8.19615 - 8.19615i) q^{38} +(-7.09808 + 4.09808i) q^{39} +(2.73205 - 0.732051i) q^{40} -5.19615i q^{41} +(0.464102 - 6.46410i) q^{42} +3.92820 q^{43} +2.92820i q^{44} +(5.92820 + 5.92820i) q^{46} +(1.26795 - 2.19615i) q^{47} +(-6.00000 - 3.46410i) q^{48} +(-5.50000 - 4.33013i) q^{49} +(-0.366025 - 1.36603i) q^{50} +(1.09808 - 1.90192i) q^{51} +(8.19615 + 4.73205i) q^{52} +(0.169873 - 0.0980762i) q^{53} +(1.90192 - 7.09808i) q^{54} +1.46410 q^{55} +(-6.73205 + 3.26795i) q^{56} +14.1962 q^{57} +(3.83013 - 14.2942i) q^{58} +(4.09808 - 2.36603i) q^{59} +(-1.73205 + 3.00000i) q^{60} +(2.13397 - 3.69615i) q^{61} +(0.803848 + 3.00000i) q^{62} +8.00000i q^{64} +(2.36603 - 4.09808i) q^{65} +(-2.53590 - 2.53590i) q^{66} +(-5.69615 - 9.86603i) q^{67} -2.53590 q^{68} -10.2679 q^{69} +(1.63397 + 3.36603i) q^{70} -5.26795i q^{71} +(-10.0981 + 5.83013i) q^{73} +(2.00000 + 2.00000i) q^{74} +(1.50000 + 0.866025i) q^{75} +(-8.19615 - 14.1962i) q^{76} +(-3.80385 + 0.732051i) q^{77} +(-11.1962 + 3.00000i) q^{78} +(-4.09808 - 2.36603i) q^{79} +4.00000 q^{80} +(4.50000 + 7.79423i) q^{81} +(1.90192 - 7.09808i) q^{82} +14.6603i q^{83} +(3.00000 - 8.66025i) q^{84} +1.26795i q^{85} +(5.36603 + 1.43782i) q^{86} +(9.06218 + 15.6962i) q^{87} +(-1.07180 + 4.00000i) q^{88} +(12.6962 + 7.33013i) q^{89} +(-4.09808 + 11.8301i) q^{91} +(5.92820 + 10.2679i) q^{92} +(-3.29423 - 1.90192i) q^{93} +(2.53590 - 2.53590i) q^{94} +(-7.09808 + 4.09808i) q^{95} +(-6.92820 - 6.92820i) q^{96} +3.46410i q^{97} +(-5.92820 - 7.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 6 q^{3} + 2 q^{5} - 6 q^{6} + 8 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 6 * q^3 + 2 * q^5 - 6 * q^6 + 8 * q^8	$ 4 q + 2 q^{2} - 6 q^{3} + 2 q^{5} - 6 q^{6} + 8 q^{8} + 4 q^{10} - 4 q^{11} + 12 q^{13} + 2 q^{14} + 8 q^{16} + 6 q^{17} - 18 q^{19} + 16 q^{22} + 24 q^{23} - 12 q^{24} - 2 q^{25} + 12 q^{26} - 16 q^{28} - 6 q^{30} - 6 q^{31} - 8 q^{32} + 12 q^{33} - 12 q^{38} - 18 q^{39} + 4 q^{40} - 12 q^{42} - 12 q^{43} - 4 q^{46} + 12 q^{47} - 24 q^{48} - 22 q^{49} + 2 q^{50} - 6 q^{51} + 12 q^{52} + 18 q^{53} + 18 q^{54} - 8 q^{55} - 20 q^{56} + 36 q^{57} - 2 q^{58} + 6 q^{59} + 12 q^{61} + 24 q^{62} + 6 q^{65} - 24 q^{66} - 2 q^{67} - 24 q^{68} - 48 q^{69} + 10 q^{70} - 30 q^{73} + 8 q^{74} + 6 q^{75} - 12 q^{76} - 36 q^{77} - 24 q^{78} - 6 q^{79} + 16 q^{80} + 18 q^{81} + 18 q^{82} + 12 q^{84} + 18 q^{86} + 12 q^{87} - 32 q^{88} + 30 q^{89} - 6 q^{91} - 4 q^{92} + 18 q^{93} + 24 q^{94} - 18 q^{95} + 4 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 6 * q^3 + 2 * q^5 - 6 * q^6 + 8 * q^8 + 4 * q^10 - 4 * q^11 + 12 * q^13 + 2 * q^14 + 8 * q^16 + 6 * q^17 - 18 * q^19 + 16 * q^22 + 24 * q^23 - 12 * q^24 - 2 * q^25 + 12 * q^26 - 16 * q^28 - 6 * q^30 - 6 * q^31 - 8 * q^32 + 12 * q^33 - 12 * q^38 - 18 * q^39 + 4 * q^40 - 12 * q^42 - 12 * q^43 - 4 * q^46 + 12 * q^47 - 24 * q^48 - 22 * q^49 + 2 * q^50 - 6 * q^51 + 12 * q^52 + 18 * q^53 + 18 * q^54 - 8 * q^55 - 20 * q^56 + 36 * q^57 - 2 * q^58 + 6 * q^59 + 12 * q^61 + 24 * q^62 + 6 * q^65 - 24 * q^66 - 2 * q^67 - 24 * q^68 - 48 * q^69 + 10 * q^70 - 30 * q^73 + 8 * q^74 + 6 * q^75 - 12 * q^76 - 36 * q^77 - 24 * q^78 - 6 * q^79 + 16 * q^80 + 18 * q^81 + 18 * q^82 + 12 * q^84 + 18 * q^86 + 12 * q^87 - 32 * q^88 + 30 * q^89 - 6 * q^91 - 4 * q^92 + 18 * q^93 + 24 * q^94 - 18 * q^95 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.36603	+	0.366025i	0.965926	+	0.258819i
$2$	1.36603	+	0.366025i	0.965926	+	0.258819i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−2.36603	+	0.633975i	−0.965926	+	0.258819i
$7$	−0.866025	+	2.50000i	−0.327327	+	0.944911i
$7$	−0.866025	+	2.50000i	−0.327327	+	0.944911i
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$		0			0
$10$	1.00000	−	1.00000i	0.316228	−	0.316228i
$11$	0.732051	+	1.26795i	0.220722	+	0.382301i	0.955027	−	0.296518i	$-0.0958254\pi$
$11$	0.732051	+	1.26795i	0.220722	+	0.382301i	−0.734306	+	0.678819i	$0.762492\pi$
$12$	−3.46410			−1.00000
$13$	4.73205			1.31243			0.656217	−	0.754572i	$-0.272155\pi$
$13$	4.73205			1.31243			0.656217	+	0.754572i	$0.272155\pi$
$14$	−2.09808	+	3.09808i	−0.560734	+	0.827996i
$15$			1.73205i			0.447214i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−1.09808	+	0.633975i	−0.266323	+	0.153761i	−0.627215	−	0.778846i	$-0.715805\pi$
$17$	−1.09808	+	0.633975i	−0.266323	+	0.153761i	0.360893	+	0.932607i	$0.382472\pi$
$18$		0			0
$19$	−7.09808	−	4.09808i	−1.62841	−	0.940163i	−0.984567	−	0.175005i	$-0.944006\pi$
$19$	−7.09808	−	4.09808i	−1.62841	−	0.940163i	−0.643843	−	0.765158i	$-0.722661\pi$
$20$	1.73205	−	1.00000i	0.387298	−	0.223607i
$21$	−0.866025	−	4.50000i	−0.188982	−	0.981981i
$22$	0.535898	+	2.00000i	0.114254	+	0.426401i
$23$	5.13397	+	2.96410i	1.07051	+	0.618058i	0.928320	−	0.371782i	$-0.121253\pi$
$23$	5.13397	+	2.96410i	1.07051	+	0.618058i	0.142188	+	0.989840i	$0.454586\pi$
$24$	−4.73205	−	1.26795i	−0.965926	−	0.258819i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	6.46410	+	1.73205i	1.26771	+	0.339683i
$27$		−	5.19615i		−	1.00000i
$28$	−4.00000	+	3.46410i	−0.755929	+	0.654654i
$29$		−	10.4641i		−	1.94313i	−0.236763	−	0.971567i	$-0.576086\pi$
$29$		−	10.4641i		−	1.94313i	0.236763	−	0.971567i	$-0.423914\pi$
$30$	−0.633975	+	2.36603i	−0.115747	+	0.431975i
$31$	1.09808	+	1.90192i	0.197220	+	0.341596i	0.947626	−	0.319382i	$-0.103475\pi$
$31$	1.09808	+	1.90192i	0.197220	+	0.341596i	−0.750406	+	0.660977i	$0.770142\pi$
$32$	1.46410	+	5.46410i	0.258819	+	0.965926i
$33$	−2.19615	−	1.26795i	−0.382301	−	0.220722i
$34$	−1.73205	+	0.464102i	−0.297044	+	0.0795928i
$35$	1.73205	+	2.00000i	0.292770	+	0.338062i
$36$		0			0
$37$	1.73205	+	1.00000i	0.284747	+	0.164399i	0.635571	−	0.772043i	$-0.280765\pi$
$37$	1.73205	+	1.00000i	0.284747	+	0.164399i	−0.350823	+	0.936442i	$0.614098\pi$
$38$	−8.19615	−	8.19615i	−1.32959	−	1.32959i
$39$	−7.09808	+	4.09808i	−1.13660	+	0.656217i
$40$	2.73205	−	0.732051i	0.431975	−	0.115747i
$41$		−	5.19615i		−	0.811503i	−0.913984	−	0.405751i	$-0.867010\pi$
$41$		−	5.19615i		−	0.811503i	0.913984	−	0.405751i	$-0.132990\pi$
$42$	0.464102	−	6.46410i	0.0716124	−	0.997433i
$43$	3.92820			0.599045			0.299523	−	0.954089i	$-0.403173\pi$
$43$	3.92820			0.599045			0.299523	+	0.954089i	$0.403173\pi$
$44$			2.92820i			0.441443i
$45$		0			0
$46$	5.92820	+	5.92820i	0.874066	+	0.874066i
$47$	1.26795	−	2.19615i	0.184949	−	0.320342i	−0.758610	−	0.651545i	$-0.774121\pi$
$47$	1.26795	−	2.19615i	0.184949	−	0.320342i	0.943559	+	0.331203i	$0.107455\pi$
$48$	−6.00000	−	3.46410i	−0.866025	−	0.500000i
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$	−0.366025	−	1.36603i	−0.0517638	−	0.193185i
$51$	1.09808	−	1.90192i	0.153761	−	0.266323i
$52$	8.19615	+	4.73205i	1.13660	+	0.656217i
$53$	0.169873	−	0.0980762i	0.0233338	−	0.0134718i	−0.488288	−	0.872683i	$-0.662378\pi$
$53$	0.169873	−	0.0980762i	0.0233338	−	0.0134718i	0.511622	+	0.859211i	$0.329045\pi$
$54$	1.90192	−	7.09808i	0.258819	−	0.965926i
$55$	1.46410			0.197419
$56$	−6.73205	+	3.26795i	−0.899608	+	0.436698i
$57$	14.1962			1.88033
$58$	3.83013	−	14.2942i	0.502920	−	1.87692i
$59$	4.09808	−	2.36603i	0.533524	−	0.308030i	−0.208926	−	0.977931i	$-0.566997\pi$
$59$	4.09808	−	2.36603i	0.533524	−	0.308030i	0.742450	+	0.669901i	$0.233664\pi$
$60$	−1.73205	+	3.00000i	−0.223607	+	0.387298i
$61$	2.13397	−	3.69615i	0.273227	−	0.473244i	−0.696459	−	0.717597i	$-0.745242\pi$
$61$	2.13397	−	3.69615i	0.273227	−	0.473244i	0.969686	+	0.244353i	$0.0785755\pi$
$62$	0.803848	+	3.00000i	0.102089	+	0.381000i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	2.36603	−	4.09808i	0.293469	−	0.508304i
$66$	−2.53590	−	2.53590i	−0.312148	−	0.312148i
$67$	−5.69615	−	9.86603i	−0.695896	−	1.20533i	−0.969878	−	0.243592i	$-0.921674\pi$
$67$	−5.69615	−	9.86603i	−0.695896	−	1.20533i	0.273982	−	0.961735i	$-0.411659\pi$
$68$	−2.53590			−0.307523
$69$	−10.2679			−1.23612
$70$	1.63397	+	3.36603i	0.195297	+	0.402317i
$71$		−	5.26795i		−	0.625191i	−0.949886	−	0.312595i	$-0.898802\pi$
$71$		−	5.26795i		−	0.625191i	0.949886	−	0.312595i	$-0.101198\pi$
$72$		0			0
$73$	−10.0981	+	5.83013i	−1.18189	+	0.682365i	−0.956451	−	0.291892i	$-0.905715\pi$
$73$	−10.0981	+	5.83013i	−1.18189	+	0.682365i	−0.225439	+	0.974257i	$0.572382\pi$
$74$	2.00000	+	2.00000i	0.232495	+	0.232495i
$75$	1.50000	+	0.866025i	0.173205	+	0.100000i
$76$	−8.19615	−	14.1962i	−0.940163	−	1.62841i
$77$	−3.80385	+	0.732051i	−0.433489	+	0.0834249i
$78$	−11.1962	+	3.00000i	−1.26771	+	0.339683i
$79$	−4.09808	−	2.36603i	−0.461070	−	0.266199i	0.251424	−	0.967877i	$-0.419101\pi$
$79$	−4.09808	−	2.36603i	−0.461070	−	0.266199i	−0.712494	+	0.701678i	$0.752434\pi$
$80$	4.00000			0.447214
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	1.90192	−	7.09808i	0.210032	−	0.783851i
$83$			14.6603i			1.60917i	0.593836	+	0.804586i	$0.297613\pi$
$83$			14.6603i			1.60917i	−0.593836	+	0.804586i	$0.702387\pi$
$84$	3.00000	−	8.66025i	0.327327	−	0.944911i
$85$			1.26795i			0.137528i
$86$	5.36603	+	1.43782i	0.578633	+	0.155044i
$87$	9.06218	+	15.6962i	0.971567	+	1.68280i
$88$	−1.07180	+	4.00000i	−0.114254	+	0.426401i
$89$	12.6962	+	7.33013i	1.34579	+	0.776992i	0.987650	−	0.156676i	$-0.0500779\pi$
$89$	12.6962	+	7.33013i	1.34579	+	0.776992i	0.358139	+	0.933668i	$0.383411\pi$
$90$		0			0
$91$	−4.09808	+	11.8301i	−0.429595	+	1.24013i
$92$	5.92820	+	10.2679i	0.618058	+	1.07051i
$93$	−3.29423	−	1.90192i	−0.341596	−	0.197220i
$94$	2.53590	−	2.53590i	0.261558	−	0.261558i
$95$	−7.09808	+	4.09808i	−0.728247	+	0.420454i
$96$	−6.92820	−	6.92820i	−0.707107	−	0.707107i
$97$			3.46410i			0.351726i	0.984415	+	0.175863i	$0.0562716\pi$
$97$			3.46410i			0.351726i	−0.984415	+	0.175863i	$0.943728\pi$
$98$	−5.92820	−	7.92820i	−0.598839	−	0.800869i
$99$		0			0
$100$		−	2.00000i		−	0.200000i
$101$	5.59808	+	9.69615i	0.557029	+	0.964803i	0.997743	+	0.0671552i	$0.0213923\pi$
$101$	5.59808	+	9.69615i	0.557029	+	0.964803i	−0.440713	+	0.897648i	$0.645274\pi$
$102$	2.19615	−	2.19615i	0.217451	−	0.217451i
$103$	1.33013	−	2.30385i	0.131061	−	0.227005i	−0.793025	−	0.609190i	$-0.791495\pi$
$103$	1.33013	−	2.30385i	0.131061	−	0.227005i	0.924086	+	0.382185i	$0.124828\pi$
$104$	9.46410	+	9.46410i	0.928032	+	0.928032i
$105$	−4.33013	−	1.50000i	−0.422577	−	0.146385i
$106$	0.267949	−	0.0717968i	0.0260255	−	0.00697352i
$107$	−3.50000	+	6.06218i	−0.338358	+	0.586053i	−0.984124	−	0.177482i	$-0.943205\pi$
$107$	−3.50000	+	6.06218i	−0.338358	+	0.586053i	0.645766	+	0.763535i	$0.276538\pi$
$108$	5.19615	−	9.00000i	0.500000	−	0.866025i
$109$	−15.0622	+	8.69615i	−1.44269	+	0.832940i	−0.998029	−	0.0627561i	$-0.980011\pi$
$109$	−15.0622	+	8.69615i	−1.44269	+	0.832940i	−0.444666	+	0.895696i	$0.646678\pi$
$110$	2.00000	+	0.535898i	0.190693	+	0.0510959i
$111$	−3.46410			−0.328798
$112$	−10.3923	+	2.00000i	−0.981981	+	0.188982i
$113$	−3.26795			−0.307423			−0.153711	−	0.988116i	$-0.549123\pi$
$113$	−3.26795			−0.307423			−0.153711	+	0.988116i	$0.549123\pi$
$114$	19.3923	+	5.19615i	1.81626	+	0.486664i
$115$	5.13397	−	2.96410i	0.478746	−	0.276404i
$116$	10.4641	−	18.1244i	0.971567	−	1.68280i
$117$		0			0
$118$	6.46410	−	1.73205i	0.595069	−	0.159448i
$119$	−0.633975	−	3.29423i	−0.0581164	−	0.301981i
$120$	−3.46410	+	3.46410i	−0.316228	+	0.316228i
$121$	4.42820	−	7.66987i	0.402564	−	0.697261i
$122$	4.26795	−	4.26795i	0.386402	−	0.386402i
$123$	4.50000	+	7.79423i	0.405751	+	0.702782i
$124$			4.39230i			0.394441i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$		−	15.4641i		−	1.37222i	−0.727499	−	0.686109i	$-0.759317\pi$
$127$		−	15.4641i		−	1.37222i	0.727499	−	0.686109i	$-0.240683\pi$
$128$	−2.92820	+	10.9282i	−0.258819	+	0.965926i
$129$	−5.89230	+	3.40192i	−0.518789	+	0.299523i
$130$	4.73205	−	4.73205i	0.415028	−	0.415028i
$131$	−10.3923	−	6.00000i	−0.907980	−	0.524222i	−0.0281993	−	0.999602i	$-0.508977\pi$
$131$	−10.3923	−	6.00000i	−0.907980	−	0.524222i	−0.879781	+	0.475380i	$0.842311\pi$
$132$	−2.53590	−	4.39230i	−0.220722	−	0.382301i
$133$	16.3923	−	14.1962i	1.42139	−	1.23096i
$134$	−4.16987	−	15.5622i	−0.360222	−	1.34437i
$135$	−4.50000	−	2.59808i	−0.387298	−	0.223607i
$136$	−3.46410	−	0.928203i	−0.297044	−	0.0795928i
$137$	6.19615	+	10.7321i	0.529373	+	0.916901i	0.999413	+	0.0342559i	$0.0109061\pi$
$137$	6.19615	+	10.7321i	0.529373	+	0.916901i	−0.470040	+	0.882645i	$0.655761\pi$
$138$	−14.0263	−	3.75833i	−1.19400	−	0.319930i
$139$			9.46410i			0.802735i	0.915917	+	0.401367i	$0.131465\pi$
$139$			9.46410i			0.802735i	−0.915917	+	0.401367i	$0.868535\pi$
$140$	1.00000	+	5.19615i	0.0845154	+	0.439155i
$141$			4.39230i			0.369899i
$142$	1.92820	−	7.19615i	0.161811	−	0.603888i
$143$	3.46410	+	6.00000i	0.289683	+	0.501745i
$144$		0			0
$145$	−9.06218	−	5.23205i	−0.752573	−	0.434498i
$146$	−15.9282	+	4.26795i	−1.31823	+	0.353218i
$147$	12.0000	+	1.73205i	0.989743	+	0.142857i
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$	2.13397	+	1.23205i	0.174822	+	0.100934i	0.584858	−	0.811136i	$-0.301150\pi$
$149$	2.13397	+	1.23205i	0.174822	+	0.100934i	−0.410036	+	0.912070i	$0.634484\pi$
$150$	1.73205	+	1.73205i	0.141421	+	0.141421i
$151$	−5.02628	+	2.90192i	−0.409033	+	0.236155i	−0.690374	−	0.723453i	$-0.742554\pi$
$151$	−5.02628	+	2.90192i	−0.409033	+	0.236155i	0.281341	+	0.959608i	$0.409221\pi$
$152$	−6.00000	−	22.3923i	−0.486664	−	1.81626i
$153$		0			0
$154$	−5.46410	−	0.392305i	−0.440310	−	0.0316128i
$155$	2.19615			0.176399
$156$	−16.3923			−1.31243
$157$	1.26795	+	2.19615i	0.101193	+	0.175272i	0.912177	−	0.409797i	$-0.134401\pi$
$157$	1.26795	+	2.19615i	0.101193	+	0.175272i	−0.810983	+	0.585069i	$0.801067\pi$
$158$	−4.73205	−	4.73205i	−0.376462	−	0.376462i
$159$	−0.169873	+	0.294229i	−0.0134718	+	0.0233338i
$160$	5.46410	+	1.46410i	0.431975	+	0.115747i
$161$	−11.8564	+	10.2679i	−0.934416	+	0.809228i
$162$	3.29423	+	12.2942i	0.258819	+	0.965926i
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	−0.601035	−	0.799223i	$-0.705245\pi$
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	0.992665	+	0.120900i	$0.0385779\pi$
$164$	5.19615	−	9.00000i	0.405751	−	0.702782i
$165$	−2.19615	+	1.26795i	−0.170970	+	0.0987097i
$166$	−5.36603	+	20.0263i	−0.416484	+	1.55434i
$167$	3.33975			0.258437			0.129219	−	0.991616i	$-0.458753\pi$
$167$	3.33975			0.258437			0.129219	+	0.991616i	$0.458753\pi$
$168$	7.26795	−	10.7321i	0.560734	−	0.827996i
$169$	9.39230			0.722485
$170$	−0.464102	+	1.73205i	−0.0355950	+	0.132842i
$171$		0			0
$172$	6.80385	+	3.92820i	0.518789	+	0.299523i
$173$	0.803848	−	1.39230i	0.0611154	−	0.105855i	−0.833849	−	0.551993i	$-0.813868\pi$
$173$	0.803848	−	1.39230i	0.0611154	−	0.105855i	0.894964	+	0.446138i	$0.147201\pi$
$174$	6.63397	+	24.7583i	0.502920	+	1.87692i
$175$	2.59808	−	0.500000i	0.196396	−	0.0377964i
$176$	−2.92820	+	5.07180i	−0.220722	+	0.382301i
$177$	−4.09808	+	7.09808i	−0.308030	+	0.533524i
$178$	14.6603	+	14.6603i	1.09883	+	1.09883i
$179$	−9.09808	−	15.7583i	−0.680022	−	1.17783i	−0.974974	−	0.222321i	$-0.928637\pi$
$179$	−9.09808	−	15.7583i	−0.680022	−	1.17783i	0.294951	−	0.955512i	$-0.404697\pi$
$180$		0			0
$181$	1.73205			0.128742			0.0643712	−	0.997926i	$-0.479496\pi$
$181$	1.73205			0.128742			0.0643712	+	0.997926i	$0.479496\pi$
$182$	−9.92820	+	14.6603i	−0.735927	+	1.08669i
$183$			7.39230i			0.546455i
$184$	4.33975	+	16.1962i	0.319930	+	1.19400i
$185$	1.73205	−	1.00000i	0.127343	−	0.0735215i
$186$	−3.80385	−	3.80385i	−0.278912	−	0.278912i
$187$	−1.60770	−	0.928203i	−0.117566	−	0.0678769i
$188$	4.39230	−	2.53590i	0.320342	−	0.184949i
$189$	12.9904	+	4.50000i	0.944911	+	0.327327i
$190$	−11.1962	+	3.00000i	−0.812254	+	0.217643i
$191$	21.1244	+	12.1962i	1.52850	+	0.882483i	0.999425	+	0.0339106i	$0.0107961\pi$
$191$	21.1244	+	12.1962i	1.52850	+	0.882483i	0.529080	+	0.848572i	$0.322537\pi$
$192$	−6.92820	−	12.0000i	−0.500000	−	0.866025i
$193$	−6.92820	−	12.0000i	−0.498703	−	0.863779i	0.501296	−	0.865276i	$-0.332857\pi$
$193$	−6.92820	−	12.0000i	−0.498703	−	0.863779i	−0.999999	+	0.00149702i	$0.999523\pi$
$194$	−1.26795	+	4.73205i	−0.0910334	+	0.339741i
$195$			8.19615i			0.586939i
$196$	−5.19615	−	13.0000i	−0.371154	−	0.928571i
$197$			4.92820i			0.351120i	0.984469	+	0.175560i	$0.0561736\pi$
$197$			4.92820i			0.351120i	−0.984469	+	0.175560i	$0.943826\pi$
$198$		0			0
$199$	−9.00000	−	15.5885i	−0.637993	−	1.10504i	−0.985873	−	0.167497i	$-0.946431\pi$
$199$	−9.00000	−	15.5885i	−0.637993	−	1.10504i	0.347879	−	0.937539i	$-0.386902\pi$
$200$	0.732051	−	2.73205i	0.0517638	−	0.193185i
$201$	17.0885	+	9.86603i	1.20533	+	0.695896i
$202$	4.09808	+	15.2942i	0.288340	+	1.07610i
$203$	26.1603	+	9.06218i	1.83609	+	0.636040i
$204$	3.80385	−	2.19615i	0.266323	−	0.153761i
$205$	−4.50000	−	2.59808i	−0.314294	−	0.181458i
$206$	2.66025	−	2.66025i	0.185349	−	0.185349i
$207$		0			0
$208$	9.46410	+	16.3923i	0.656217	+	1.13660i
$209$		−	12.0000i		−	0.830057i
$210$	−5.36603	−	3.63397i	−0.370291	−	0.250768i
$211$	−18.5885			−1.27968			−0.639841	−	0.768507i	$-0.721000\pi$
$211$	−18.5885			−1.27968			−0.639841	+	0.768507i	$0.721000\pi$
$212$	0.392305			0.0269436
$213$	4.56218	+	7.90192i	0.312595	+	0.541431i
$214$	−7.00000	+	7.00000i	−0.478510	+	0.478510i
$215$	1.96410	−	3.40192i	0.133951	−	0.232009i
$216$	10.3923	−	10.3923i	0.707107	−	0.707107i
$217$	−5.70577	+	1.09808i	−0.387333	+	0.0745423i
$218$	−23.7583	+	6.36603i	−1.60912	+	0.431162i
$219$	10.0981	−	17.4904i	0.682365	−	1.18189i
$220$	2.53590	+	1.46410i	0.170970	+	0.0987097i
$221$	−5.19615	+	3.00000i	−0.349531	+	0.201802i
$222$	−4.73205	−	1.26795i	−0.317594	−	0.0850992i
$223$	−13.8564			−0.927894			−0.463947	−	0.885863i	$-0.653567\pi$
$223$	−13.8564			−0.927894			−0.463947	+	0.885863i	$0.653567\pi$
$224$	−14.9282	−	1.07180i	−0.997433	−	0.0716124i
$225$		0			0
$226$	−4.46410	−	1.19615i	−0.296948	−	0.0795669i
$227$	−4.39230	+	2.53590i	−0.291528	+	0.168313i	−0.638631	−	0.769514i	$-0.720499\pi$
$227$	−4.39230	+	2.53590i	−0.291528	+	0.168313i	0.347103	+	0.937827i	$0.387165\pi$
$228$	24.5885	+	14.1962i	1.62841	+	0.940163i
$229$	−7.73205	+	13.3923i	−0.510948	+	0.884988i	0.488971	+	0.872300i	$0.337372\pi$
$229$	−7.73205	+	13.3923i	−0.510948	+	0.884988i	−0.999919	+	0.0126885i	$0.995961\pi$
$230$	8.09808	−	2.16987i	0.533971	−	0.143077i
$231$	5.07180	−	4.39230i	0.333700	−	0.288992i
$232$	20.9282	−	20.9282i	1.37400	−	1.37400i
$233$	2.63397	−	4.56218i	0.172557	−	0.298878i	−0.766756	−	0.641939i	$-0.778130\pi$
$233$	2.63397	−	4.56218i	0.172557	−	0.298878i	0.939313	+	0.343061i	$0.111464\pi$
$234$		0			0
$235$	−1.26795	−	2.19615i	−0.0827119	−	0.143261i
$236$	9.46410			0.616061
$237$	8.19615			0.532397
$238$	0.339746	−	4.73205i	0.0220225	−	0.306733i
$239$		−	1.80385i		−	0.116681i	−0.998297	−	0.0583406i	$-0.981419\pi$
$239$		−	1.80385i		−	0.116681i	0.998297	−	0.0583406i	$-0.0185809\pi$
$240$	−6.00000	+	3.46410i	−0.387298	+	0.223607i
$241$	−6.80385	+	3.92820i	−0.438274	+	0.253038i	−0.702865	−	0.711323i	$-0.748096\pi$
$241$	−6.80385	+	3.92820i	−0.438274	+	0.253038i	0.264591	+	0.964361i	$0.414763\pi$
$242$	8.85641	−	8.85641i	0.569311	−	0.569311i
$243$		0			0
$244$	7.39230	−	4.26795i	0.473244	−	0.273227i
$245$	−6.50000	+	2.59808i	−0.415270	+	0.165985i
$246$	3.29423	+	12.2942i	0.210032	+	0.783851i
$247$	−33.5885	−	19.3923i	−2.13718	−	1.23390i
$248$	−1.60770	+	6.00000i	−0.102089	+	0.381000i
$249$	−12.6962	−	21.9904i	−0.804586	−	1.39358i
$250$	−1.36603	−	0.366025i	−0.0863950	−	0.0231495i
$251$		−	15.8038i		−	0.997530i	−0.866737	−	0.498765i	$-0.833787\pi$
$251$		−	15.8038i		−	0.997530i	0.866737	−	0.498765i	$-0.166213\pi$
$252$		0			0
$253$			8.67949i			0.545675i
$254$	5.66025	−	21.1244i	0.355156	−	1.32546i
$255$	−1.09808	−	1.90192i	−0.0687642	−	0.119103i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	5.19615	+	3.00000i	0.324127	+	0.187135i	0.653231	−	0.757159i	$-0.273413\pi$
$257$	5.19615	+	3.00000i	0.324127	+	0.187135i	−0.329104	+	0.944294i	$0.606747\pi$
$258$	−9.29423	+	2.49038i	−0.578633	+	0.155044i
$259$	−4.00000	+	3.46410i	−0.248548	+	0.215249i
$260$	8.19615	−	4.73205i	0.508304	−	0.293469i
$261$		0			0
$262$	−12.0000	−	12.0000i	−0.741362	−	0.741362i
$263$	13.9186	−	8.03590i	0.858257	−	0.495515i	−0.00517143	−	0.999987i	$-0.501646\pi$
$263$	13.9186	−	8.03590i	0.858257	−	0.495515i	0.863428	+	0.504472i	$0.168313\pi$
$264$	−1.85641	−	6.92820i	−0.114254	−	0.426401i
$265$		−	0.196152i		−	0.0120495i
$266$	27.5885	−	13.3923i	1.69156	−	0.821135i
$267$	−25.3923			−1.55398
$268$		−	22.7846i		−	1.39179i
$269$	−4.33013	−	7.50000i	−0.264013	−	0.457283i	0.703292	−	0.710901i	$-0.251713\pi$
$269$	−4.33013	−	7.50000i	−0.264013	−	0.457283i	−0.967304	+	0.253618i	$0.918379\pi$
$270$	−5.19615	−	5.19615i	−0.316228	−	0.316228i
$271$	7.09808	−	12.2942i	0.431177	−	0.746821i	−0.565798	−	0.824544i	$-0.691432\pi$
$271$	7.09808	−	12.2942i	0.431177	−	0.746821i	0.996975	+	0.0777230i	$0.0247650\pi$
$272$	−4.39230	−	2.53590i	−0.266323	−	0.153761i
$273$	−4.09808	−	21.2942i	−0.248027	−	1.28879i
$274$	4.53590	+	16.9282i	0.274024	+	1.02267i
$275$	0.732051	−	1.26795i	0.0441443	−	0.0764602i
$276$	−17.7846	−	10.2679i	−1.07051	−	0.618058i
$277$	1.90192	−	1.09808i	0.114276	−	0.0659770i	−0.441773	−	0.897127i	$-0.645650\pi$
$277$	1.90192	−	1.09808i	0.114276	−	0.0659770i	0.556048	+	0.831150i	$0.312317\pi$
$278$	−3.46410	+	12.9282i	−0.207763	+	0.775382i
$279$		0			0
$280$	−0.535898	+	7.46410i	−0.0320261	+	0.446065i
$281$	21.8564			1.30384			0.651922	−	0.758286i	$-0.273963\pi$
$281$	21.8564			1.30384			0.651922	+	0.758286i	$0.273963\pi$
$282$	−1.60770	+	6.00000i	−0.0957369	+	0.357295i
$283$	3.00000	−	1.73205i	0.178331	−	0.102960i	−0.408177	−	0.912903i	$-0.633835\pi$
$283$	3.00000	−	1.73205i	0.178331	−	0.102960i	0.586509	+	0.809943i	$0.300502\pi$
$284$	5.26795	−	9.12436i	0.312595	−	0.541431i
$285$	7.09808	−	12.2942i	0.420454	−	0.728247i
$286$	2.53590	+	9.46410i	0.149951	+	0.559624i
$287$	12.9904	+	4.50000i	0.766798	+	0.265627i
$288$		0			0
$289$	−7.69615	+	13.3301i	−0.452715	+	0.784125i
$290$	−10.4641	−	10.4641i	−0.614473	−	0.614473i
$291$	−3.00000	−	5.19615i	−0.175863	−	0.304604i
$292$	−23.3205			−1.36473
$293$	−13.8564			−0.809500			−0.404750	−	0.914427i	$-0.632641\pi$
$293$	−13.8564			−0.809500			−0.404750	+	0.914427i	$0.632641\pi$
$294$	15.7583	+	6.75833i	0.919044	+	0.394154i
$295$		−	4.73205i		−	0.275511i
$296$	1.46410	+	5.46410i	0.0850992	+	0.317594i
$297$	6.58846	−	3.80385i	0.382301	−	0.220722i
$298$	2.46410	+	2.46410i	0.142742	+	0.142742i
$299$	24.2942	+	14.0263i	1.40497	+	0.811161i
$300$	1.73205	+	3.00000i	0.100000	+	0.173205i
$301$	−3.40192	+	9.82051i	−0.196084	+	0.566045i
$302$	−7.92820	+	2.12436i	−0.456217	+	0.122243i
$303$	−16.7942	−	9.69615i	−0.964803	−	0.557029i
$304$		−	32.7846i		−	1.88033i
$305$	−2.13397	−	3.69615i	−0.122191	−	0.211641i
$306$		0			0
$307$			6.12436i			0.349535i	0.984610	+	0.174768i	$0.0559175\pi$
$307$			6.12436i			0.349535i	−0.984610	+	0.174768i	$0.944083\pi$
$308$	−7.32051	−	2.53590i	−0.417125	−	0.144496i
$309$			4.60770i			0.262123i
$310$	3.00000	+	0.803848i	0.170389	+	0.0456555i
$311$	−1.90192	−	3.29423i	−0.107848	−	0.186799i	0.807050	−	0.590483i	$-0.201063\pi$
$311$	−1.90192	−	3.29423i	−0.107848	−	0.186799i	−0.914898	+	0.403684i	$0.867729\pi$
$312$	−22.3923	−	6.00000i	−1.26771	−	0.339683i
$313$	−15.0000	−	8.66025i	−0.847850	−	0.489506i	0.0120748	−	0.999927i	$-0.496156\pi$
$313$	−15.0000	−	8.66025i	−0.847850	−	0.489506i	−0.859925	+	0.510421i	$0.829490\pi$
$314$	0.928203	+	3.46410i	0.0523815	+	0.195491i
$315$		0			0
$316$	−4.73205	−	8.19615i	−0.266199	−	0.461070i
$317$	−8.02628	−	4.63397i	−0.450801	−	0.260270i	0.257368	−	0.966314i	$-0.417145\pi$
$317$	−8.02628	−	4.63397i	−0.450801	−	0.260270i	−0.708168	+	0.706044i	$0.750478\pi$
$318$	−0.339746	+	0.339746i	−0.0190520	+	0.0190520i
$319$	13.2679	−	7.66025i	0.742863	−	0.428892i
$320$	6.92820	+	4.00000i	0.387298	+	0.223607i
$321$		−	12.1244i		−	0.676716i
$322$	−19.9545	+	9.68653i	−1.11202	+	0.539809i
$323$	10.3923			0.578243
$324$			18.0000i			1.00000i
$325$	−2.36603	−	4.09808i	−0.131243	−	0.227320i
$326$	10.0000	−	10.0000i	0.553849	−	0.553849i
$327$	15.0622	−	26.0885i	0.832940	−	1.44269i
$328$	10.3923	−	10.3923i	0.573819	−	0.573819i
$329$	4.39230	+	5.07180i	0.242156	+	0.279617i
$330$	−3.46410	+	0.928203i	−0.190693	+	0.0510959i
$331$	11.3660	−	19.6865i	0.624733	−	1.08207i	−0.363859	−	0.931454i	$-0.618541\pi$
$331$	11.3660	−	19.6865i	0.624733	−	1.08207i	0.988592	−	0.150616i	$-0.0481256\pi$
$332$	−14.6603	+	25.3923i	−0.804586	+	1.39358i
$333$		0			0
$334$	4.56218	+	1.22243i	0.249631	+	0.0668885i
$335$	−11.3923			−0.622428
$336$	13.8564	−	12.0000i	0.755929	−	0.654654i
$337$	−28.9808			−1.57868			−0.789341	−	0.613955i	$-0.789578\pi$
$337$	−28.9808			−1.57868			−0.789341	+	0.613955i	$0.789578\pi$
$338$	12.8301	+	3.43782i	0.697867	+	0.186993i
$339$	4.90192	−	2.83013i	0.266236	−	0.153711i
$340$	−1.26795	+	2.19615i	−0.0687642	+	0.119103i
$341$	−1.60770	+	2.78461i	−0.0870616	+	0.150795i
$342$		0			0
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$	7.85641	+	7.85641i	0.423589	+	0.423589i
$345$	−5.13397	+	8.89230i	−0.276404	+	0.478746i
$346$	1.60770	−	1.60770i	0.0864302	−	0.0864302i
$347$	−8.62436	−	14.9378i	−0.462980	−	0.801904i	0.536128	−	0.844137i	$-0.319886\pi$
$347$	−8.62436	−	14.9378i	−0.462980	−	0.801904i	−0.999108	+	0.0422323i	$0.986553\pi$
$348$			36.2487i			1.94313i
$349$	34.5167			1.84763			0.923817	−	0.382834i	$-0.125052\pi$
$349$	34.5167			1.84763			0.923817	+	0.382834i	$0.125052\pi$
$350$	3.73205	+	0.267949i	0.199487	+	0.0143225i
$351$		−	24.5885i		−	1.31243i
$352$	−5.85641	+	5.85641i	−0.312148	+	0.312148i
$353$	−30.0788	+	17.3660i	−1.60094	+	0.924300i	−0.609634	+	0.792683i	$0.708684\pi$
$353$	−30.0788	+	17.3660i	−1.60094	+	0.924300i	−0.991301	+	0.131618i	$0.957983\pi$
$354$	−8.19615	+	8.19615i	−0.435621	+	0.435621i
$355$	−4.56218	−	2.63397i	−0.242135	−	0.139797i
$356$	14.6603	+	25.3923i	0.776992	+	1.34579i
$357$	3.80385	+	4.39230i	0.201321	+	0.232465i
$358$	−6.66025	−	24.8564i	−0.352005	−	1.31370i
$359$	23.9545	+	13.8301i	1.26427	+	0.729926i	0.973898	−	0.226988i	$-0.0728877\pi$
$359$	23.9545	+	13.8301i	1.26427	+	0.729926i	0.290372	+	0.956914i	$0.406221\pi$
$360$		0			0
$361$	24.0885	+	41.7224i	1.26781	+	2.19592i
$362$	2.36603	+	0.633975i	0.124356	+	0.0333210i
$363$			15.3397i			0.805128i
$364$	−18.9282	+	16.3923i	−0.992107	+	0.859190i
$365$			11.6603i			0.610326i
$366$	−2.70577	+	10.0981i	−0.141433	+	0.527835i
$367$	9.86603	+	17.0885i	0.515002	+	0.892010i	0.999848	+	0.0174107i	$0.00554228\pi$
$367$	9.86603	+	17.0885i	0.515002	+	0.892010i	−0.484846	+	0.874599i	$0.661124\pi$
$368$			23.7128i			1.23612i
$369$		0			0
$370$	2.73205	−	0.732051i	0.142033	−	0.0380575i
$371$	0.0980762	+	0.509619i	0.00509186	+	0.0264581i
$372$	−3.80385	−	6.58846i	−0.197220	−	0.341596i
$373$	0.803848	+	0.464102i	0.0416216	+	0.0240303i	0.520666	−	0.853760i	$-0.325684\pi$
$373$	0.803848	+	0.464102i	0.0416216	+	0.0240303i	−0.479045	+	0.877790i	$0.659017\pi$
$374$	−1.85641	−	1.85641i	−0.0959925	−	0.0959925i
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$	6.92820	−	1.85641i	0.357295	−	0.0957369i
$377$		−	49.5167i		−	2.55024i
$378$	16.0981	+	10.9019i	0.827996	+	0.560734i
$379$	−26.4449			−1.35838			−0.679191	−	0.733962i	$-0.737669\pi$
$379$	−26.4449			−1.35838			−0.679191	+	0.733962i	$0.737669\pi$
$380$	−16.3923			−0.840907
$381$	13.3923	+	23.1962i	0.686109	+	1.18837i
$382$	24.3923	+	24.3923i	1.24802	+	1.24802i
$383$	−8.59808	+	14.8923i	−0.439341	+	0.760961i	−0.997639	−	0.0686795i	$-0.978121\pi$
$383$	−8.59808	+	14.8923i	−0.439341	+	0.760961i	0.558298	+	0.829641i	$0.311455\pi$
$384$	−5.07180	−	18.9282i	−0.258819	−	0.965926i
$385$	−1.26795	+	3.66025i	−0.0646207	+	0.186544i
$386$	−5.07180	−	18.9282i	−0.258148	−	0.963420i
$387$		0			0
$388$	−3.46410	+	6.00000i	−0.175863	+	0.304604i
$389$	−21.7128	+	12.5359i	−1.10088	+	0.635595i	−0.936453	−	0.350793i	$-0.885912\pi$
$389$	−21.7128	+	12.5359i	−1.10088	+	0.635595i	−0.164430	+	0.986389i	$0.552579\pi$
$390$	−3.00000	+	11.1962i	−0.151911	+	0.566939i
$391$	−7.51666			−0.380134
$392$	−2.33975	−	19.6603i	−0.118175	−	0.992993i
$393$	20.7846			1.04844
$394$	−1.80385	+	6.73205i	−0.0908765	+	0.339156i
$395$	−4.09808	+	2.36603i	−0.206197	+	0.119048i
$396$		0			0
$397$	−13.3923	+	23.1962i	−0.672141	+	1.16418i	0.305155	+	0.952303i	$0.401292\pi$
$397$	−13.3923	+	23.1962i	−0.672141	+	1.16418i	−0.977296	+	0.211879i	$0.932042\pi$
$398$	−6.58846	−	24.5885i	−0.330250	−	1.23251i
$399$	−12.2942	+	35.4904i	−0.615481	+	1.77674i
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	−4.23205	+	7.33013i	−0.211339	+	0.366049i	−0.952134	−	0.305682i	$-0.901116\pi$
$401$	−4.23205	+	7.33013i	−0.211339	+	0.366049i	0.740795	+	0.671731i	$0.234449\pi$
$402$	19.7321	+	19.7321i	0.984145	+	0.984145i
$403$	5.19615	+	9.00000i	0.258839	+	0.448322i
$404$			22.3923i			1.11406i
$405$	9.00000			0.447214
$406$	32.4186	+	21.9545i	1.60891	+	1.08958i
$407$			2.92820i			0.145146i
$408$	6.00000	−	1.60770i	0.297044	−	0.0795928i
$409$	17.8923	−	10.3301i	0.884718	−	0.510792i	0.0125066	−	0.999922i	$-0.496019\pi$
$409$	17.8923	−	10.3301i	0.884718	−	0.510792i	0.872211	+	0.489130i	$0.162686\pi$
$410$	−5.19615	−	5.19615i	−0.256620	−	0.256620i
$411$	−18.5885	−	10.7321i	−0.916901	−	0.529373i
$412$	4.60770	−	2.66025i	0.227005	−	0.131061i
$413$	2.36603	+	12.2942i	0.116424	+	0.604959i
$414$		0			0
$415$	12.6962	+	7.33013i	0.623230	+	0.359822i
$416$	6.92820	+	25.8564i	0.339683	+	1.26771i
$417$	−8.19615	−	14.1962i	−0.401367	−	0.695189i
$418$	4.39230	−	16.3923i	0.214835	−	0.801774i
$419$			11.3205i			0.553043i	0.961008	+	0.276522i	$0.0891817\pi$
$419$			11.3205i			0.553043i	−0.961008	+	0.276522i	$0.910818\pi$
$420$	−6.00000	−	6.92820i	−0.292770	−	0.338062i
$421$		−	21.2487i		−	1.03560i	−0.855502	−	0.517799i	$-0.826751\pi$
$421$		−	21.2487i		−	1.03560i	0.855502	−	0.517799i	$-0.173249\pi$
$422$	−25.3923	−	6.80385i	−1.23608	−	0.331206i
$423$		0			0
$424$	0.535898	+	0.143594i	0.0260255	+	0.00697352i
$425$	1.09808	+	0.633975i	0.0532645	+	0.0307523i
$426$	3.33975	+	12.4641i	0.161811	+	0.603888i
$427$	7.39230	+	8.53590i	0.357739	+	0.413081i
$428$	−12.1244	+	7.00000i	−0.586053	+	0.338358i
$429$	−10.3923	−	6.00000i	−0.501745	−	0.289683i
$430$	3.92820	−	3.92820i	0.189435	−	0.189435i
$431$	6.92820	−	4.00000i	0.333720	−	0.192673i	−0.323772	−	0.946135i	$-0.604951\pi$
$431$	6.92820	−	4.00000i	0.333720	−	0.192673i	0.657491	+	0.753462i	$0.271618\pi$
$432$	18.0000	−	10.3923i	0.866025	−	0.500000i
$433$		−	28.9808i		−	1.39273i	−0.717689	−	0.696363i	$-0.754800\pi$
$433$		−	28.9808i		−	1.39273i	0.717689	−	0.696363i	$-0.245200\pi$
$434$	−8.19615	−	0.588457i	−0.393428	−	0.0282469i
$435$	18.1244			0.868996
$436$	−34.7846			−1.66588
$437$	−24.2942	−	42.0788i	−1.16215	−	2.01290i
$438$	20.1962	−	20.1962i	0.965009	−	0.965009i
$439$	−6.92820	+	12.0000i	−0.330665	+	0.572729i	−0.982642	−	0.185510i	$-0.940606\pi$
$439$	−6.92820	+	12.0000i	−0.330665	+	0.572729i	0.651977	+	0.758238i	$0.273940\pi$
$440$	2.92820	+	2.92820i	0.139597	+	0.139597i
$441$		0			0
$442$	−8.19615	+	2.19615i	−0.389851	+	0.104460i
$443$	−3.50000	+	6.06218i	−0.166290	+	0.288023i	−0.937113	−	0.349027i	$-0.886512\pi$
$443$	−3.50000	+	6.06218i	−0.166290	+	0.288023i	0.770823	+	0.637050i	$0.219845\pi$
$444$	−6.00000	−	3.46410i	−0.284747	−	0.164399i
$445$	12.6962	−	7.33013i	0.601855	−	0.347481i
$446$	−18.9282	−	5.07180i	−0.896276	−	0.240157i
$447$	−4.26795			−0.201867
$448$	−20.0000	−	6.92820i	−0.944911	−	0.327327i
$449$	19.5359			0.921956			0.460978	−	0.887412i	$-0.347499\pi$
$449$	19.5359			0.921956			0.460978	+	0.887412i	$0.347499\pi$
$450$		0			0
$451$	6.58846	−	3.80385i	0.310238	−	0.179116i
$452$	−5.66025	−	3.26795i	−0.266236	−	0.153711i
$453$	5.02628	−	8.70577i	0.236155	−	0.409033i
$454$	−6.92820	+	1.85641i	−0.325157	+	0.0871255i
$455$	8.19615	+	9.46410i	0.384242	+	0.443684i
$456$	28.3923	+	28.3923i	1.32959	+	1.32959i
$457$	−20.3205	+	35.1962i	−0.950553	+	1.64641i	−0.206322	+	0.978484i	$0.566150\pi$
$457$	−20.3205	+	35.1962i	−0.950553	+	1.64641i	−0.744231	+	0.667923i	$0.767184\pi$
$458$	−15.4641	+	15.4641i	−0.722590	+	0.722590i
$459$	3.29423	+	5.70577i	0.153761	+	0.266323i
$460$	11.8564			0.552808
$461$	−10.1436			−0.472434			−0.236217	−	0.971700i	$-0.575908\pi$
$461$	−10.1436			−0.472434			−0.236217	+	0.971700i	$0.575908\pi$
$462$	8.53590	−	4.14359i	0.397126	−	0.192777i
$463$			19.3923i			0.901237i	0.892717	+	0.450618i	$0.148796\pi$
$463$			19.3923i			0.901237i	−0.892717	+	0.450618i	$0.851204\pi$
$464$	36.2487	−	20.9282i	1.68280	−	0.971567i
$465$	−3.29423	+	1.90192i	−0.152766	+	0.0881996i
$466$	5.26795	−	5.26795i	0.244033	−	0.244033i
$467$	24.4808	+	14.1340i	1.13283	+	0.654042i	0.944646	−	0.328091i	$-0.106405\pi$
$467$	24.4808	+	14.1340i	1.13283	+	0.654042i	0.188188	+	0.982133i	$0.439738\pi$
$468$		0			0
$469$	29.5981	−	5.69615i	1.36671	−	0.263024i
$470$	−0.928203	−	3.46410i	−0.0428148	−	0.159787i
$471$	−3.80385	−	2.19615i	−0.175272	−	0.101193i
$472$	12.9282	+	3.46410i	0.595069	+	0.159448i
$473$	2.87564	+	4.98076i	0.132222	+	0.229016i
$474$	11.1962	+	3.00000i	0.514256	+	0.137795i
$475$			8.19615i			0.376065i
$476$	2.19615	−	6.33975i	0.100660	−	0.290582i
$477$		0			0
$478$	0.660254	−	2.46410i	0.0301993	−	0.112705i
$479$	−2.83013	−	4.90192i	−0.129312	−	0.223975i	0.794098	−	0.607789i	$-0.207943\pi$
$479$	−2.83013	−	4.90192i	−0.129312	−	0.223975i	−0.923410	+	0.383815i	$0.874610\pi$
$480$	−9.46410	+	2.53590i	−0.431975	+	0.115747i
$481$	8.19615	+	4.73205i	0.373712	+	0.215763i
$482$	−10.7321	+	2.87564i	−0.488832	+	0.130982i
$483$	8.89230	−	25.6699i	0.404614	−	1.16802i
$484$	15.3397	−	8.85641i	0.697261	−	0.402564i
$485$	3.00000	+	1.73205i	0.136223	+	0.0786484i
$486$		0			0
$487$	−21.4641	+	12.3923i	−0.972631	+	0.561549i	−0.900037	−	0.435813i	$-0.856461\pi$
$487$	−21.4641	+	12.3923i	−0.972631	+	0.561549i	−0.0725939	+	0.997362i	$0.523128\pi$
$488$	11.6603	−	3.12436i	0.527835	−	0.141433i
$489$			17.3205i			0.783260i
$490$	−9.83013	+	1.16987i	−0.444080	+	0.0528495i
$491$	−26.7321			−1.20640			−0.603200	−	0.797590i	$-0.706108\pi$
$491$	−26.7321			−1.20640			−0.603200	+	0.797590i	$0.706108\pi$
$492$			18.0000i			0.811503i
$493$	6.63397	+	11.4904i	0.298779	+	0.517501i
$494$	−38.7846	−	38.7846i	−1.74500	−	1.74500i
$495$		0			0
$496$	−4.39230	+	7.60770i	−0.197220	+	0.341596i
$497$	13.1699	+	4.56218i	0.590750	+	0.204642i
$498$	−9.29423	−	34.6865i	−0.416484	−	1.55434i
$499$	−11.1962	+	19.3923i	−0.501209	+	0.868119i	0.498790	+	0.866723i	$0.333778\pi$
$499$	−11.1962	+	19.3923i	−0.501209	+	0.868119i	−0.999999	+	0.00139615i	$0.999556\pi$
$500$	−1.73205	−	1.00000i	−0.0774597	−	0.0447214i
$501$	−5.00962	+	2.89230i	−0.223813	+	0.129219i
$502$	5.78461	−	21.5885i	0.258180	−	0.963540i
$503$	−2.66025			−0.118615			−0.0593074	−	0.998240i	$-0.518889\pi$
$503$	−2.66025			−0.118615			−0.0593074	+	0.998240i	$0.518889\pi$
$504$		0			0
$505$	11.1962			0.498222
$506$	−3.17691	+	11.8564i	−0.141231	+	0.527082i
$507$	−14.0885	+	8.13397i	−0.625690	+	0.361242i
$508$	15.4641	−	26.7846i	0.686109	−	1.18837i
$509$	14.2583	−	24.6962i	0.631989	−	1.09464i	−0.355155	−	0.934807i	$-0.615572\pi$
$509$	14.2583	−	24.6962i	0.631989	−	1.09464i	0.987145	−	0.159830i	$-0.0510947\pi$
$510$	−0.803848	−	3.00000i	−0.0355950	−	0.132842i
$511$	−5.83013	−	30.2942i	−0.257910	−	1.34014i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−21.2942	+	36.8827i	−0.940163	+	1.62841i
$514$	6.00000	+	6.00000i	0.264649	+	0.264649i
$515$	−1.33013	−	2.30385i	−0.0586124	−	0.101520i
$516$	−13.6077			−0.599045
$517$	3.71281			0.163289
$518$	−6.73205	+	3.26795i	−0.295789	+	0.143585i
$519$			2.78461i			0.122231i
$520$	12.9282	−	3.46410i	0.566939	−	0.151911i
$521$	10.6077	−	6.12436i	0.464732	−	0.268313i	−0.249300	−	0.968426i	$-0.580201\pi$
$521$	10.6077	−	6.12436i	0.464732	−	0.268313i	0.714032	+	0.700113i	$0.246867\pi$
$522$		0			0
$523$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$523$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$524$	−12.0000	−	20.7846i	−0.524222	−	0.907980i
$525$	−3.46410	+	3.00000i	−0.151186	+	0.130931i
$526$	21.9545	−	5.88269i	0.957261	−	0.256497i
$527$	−2.41154	−	1.39230i	−0.105048	−	0.0606498i
$528$		−	10.1436i		−	0.441443i
$529$	6.07180	+	10.5167i	0.263991	+	0.457246i
$530$	0.0717968	−	0.267949i	0.00311865	−	0.0116390i
$531$		0			0
$532$	42.5885	−	8.19615i	1.84644	−	0.355348i
$533$		−	24.5885i		−	1.06504i
$534$	−34.6865	−	9.29423i	−1.50103	−	0.402201i
$535$	3.50000	+	6.06218i	0.151318	+	0.262091i
$536$	8.33975	−	31.1244i	0.360222	−	1.34437i
$537$	27.2942	+	15.7583i	1.17783	+	0.680022i
$538$	−3.16987	−	11.8301i	−0.136663	−	0.510033i
$539$	1.46410	−	10.1436i	0.0630633	−	0.436916i
$540$	−5.19615	−	9.00000i	−0.223607	−	0.387298i
$541$	−39.1865	−	22.6244i	−1.68476	−	0.972697i	−0.958420	−	0.285363i	$-0.907886\pi$
$541$	−39.1865	−	22.6244i	−1.68476	−	0.972697i	−0.726341	−	0.687335i	$-0.758781\pi$
$542$	14.1962	−	14.1962i	0.609777	−	0.609777i
$543$	−2.59808	+	1.50000i	−0.111494	+	0.0643712i
$544$	−5.07180	−	5.07180i	−0.217451	−	0.217451i
$545$			17.3923i			0.745004i
$546$	2.19615	−	30.5885i	0.0939866	−	1.30907i
$547$	1.00000			0.0427569			0.0213785	−	0.999771i	$-0.493195\pi$
$547$	1.00000			0.0427569			0.0213785	+	0.999771i	$0.493195\pi$
$548$			24.7846i			1.05875i
$549$		0			0
$550$	1.46410	−	1.46410i	0.0624295	−	0.0624295i
$551$	−42.8827	+	74.2750i	−1.82686	+	3.16422i
$552$	−20.5359	−	20.5359i	−0.874066	−	0.874066i
$553$	9.46410	−	8.19615i	0.402455	−	0.348536i
$554$	3.00000	−	0.803848i	0.127458	−	0.0341522i
$555$	−1.73205	+	3.00000i	−0.0735215	+	0.127343i
$556$	−9.46410	+	16.3923i	−0.401367	+	0.695189i
$557$	36.1244	−	20.8564i	1.53064	−	0.883714i	0.531306	−	0.847180i	$-0.321702\pi$
$557$	36.1244	−	20.8564i	1.53064	−	0.883714i	0.999332	−	0.0365341i	$-0.0116318\pi$
$558$		0			0
$559$	18.5885			0.786208
$560$	−3.46410	+	10.0000i	−0.146385	+	0.422577i
$561$	3.21539			0.135754
$562$	29.8564	+	8.00000i	1.25942	+	0.337460i
$563$	−14.3038	+	8.25833i	−0.602835	+	0.348047i	−0.770156	−	0.637855i	$-0.779822\pi$
$563$	−14.3038	+	8.25833i	−0.602835	+	0.348047i	0.167321	+	0.985902i	$0.446488\pi$
$564$	−4.39230	+	7.60770i	−0.184949	+	0.320342i
$565$	−1.63397	+	2.83013i	−0.0687418	+	0.119064i
$566$	4.73205	−	1.26795i	0.198903	−	0.0532959i
$567$	−23.3827	+	4.50000i	−0.981981	+	0.188982i
$568$	10.5359	−	10.5359i	0.442076	−	0.442076i
$569$	−3.26795	+	5.66025i	−0.137000	+	0.237290i	−0.926360	−	0.376640i	$-0.877079\pi$
$569$	−3.26795	+	5.66025i	−0.137000	+	0.237290i	0.789360	+	0.613931i	$0.210413\pi$
$570$	14.1962	−	14.1962i	0.594611	−	0.594611i
$571$	−1.29423	−	2.24167i	−0.0541618	−	0.0938110i	0.837673	−	0.546172i	$-0.183915\pi$
$571$	−1.29423	−	2.24167i	−0.0541618	−	0.0938110i	−0.891835	+	0.452361i	$0.850582\pi$
$572$			13.8564i			0.579365i
$573$	−42.2487			−1.76497
$574$	16.0981	+	10.9019i	0.671921	+	0.455038i
$575$		−	5.92820i		−	0.247223i
$576$		0			0
$577$	14.7846	−	8.53590i	0.615491	−	0.355354i	−0.159620	−	0.987178i	$-0.551027\pi$
$577$	14.7846	−	8.53590i	0.615491	−	0.355354i	0.775112	+	0.631824i	$0.217694\pi$
$578$	−15.3923	+	15.3923i	−0.640235	+	0.640235i
$579$	20.7846	+	12.0000i	0.863779	+	0.498703i
$580$	−10.4641	−	18.1244i	−0.434498	−	0.752573i
$581$	−36.6506	−	12.6962i	−1.52052	−	0.526725i
$582$	−2.19615	−	8.19615i	−0.0910334	−	0.339741i
$583$	0.248711	+	0.143594i	0.0103006	+	0.00594704i
$584$	−31.8564	−	8.53590i	−1.31823	−	0.353218i
$585$		0			0
$586$	−18.9282	−	5.07180i	−0.781917	−	0.209514i
$587$			9.46410i			0.390625i	0.980741	+	0.195313i	$0.0625722\pi$
$587$			9.46410i			0.390625i	−0.980741	+	0.195313i	$0.937428\pi$
$588$	19.0526	+	15.0000i	0.785714	+	0.618590i
$589$		−	18.0000i		−	0.741677i
$590$	1.73205	−	6.46410i	0.0713074	−	0.266123i
$591$	−4.26795	−	7.39230i	−0.175560	−	0.304079i
$592$			8.00000i			0.328798i
$593$	−35.2750	−	20.3660i	−1.44857	−	0.836332i	−0.450174	−	0.892941i	$-0.648638\pi$
$593$	−35.2750	−	20.3660i	−1.44857	−	0.836332i	−0.998396	+	0.0566085i	$0.981971\pi$
$594$	10.3923	−	2.78461i	0.426401	−	0.114254i
$595$	−3.16987	−	1.09808i	−0.129952	−	0.0450167i
$596$	2.46410	+	4.26795i	0.100934	+	0.174822i
$597$	27.0000	+	15.5885i	1.10504	+	0.637993i
$598$	28.0526	+	28.0526i	1.14715	+	1.14715i
$599$	13.2679	−	7.66025i	0.542114	−	0.312989i	−0.203821	−	0.979008i	$-0.565336\pi$
$599$	13.2679	−	7.66025i	0.542114	−	0.312989i	0.745935	+	0.666019i	$0.232003\pi$
$600$	1.26795	+	4.73205i	0.0517638	+	0.193185i
$601$		−	1.60770i		−	0.0655793i	−0.999462	−	0.0327896i	$-0.989561\pi$
$601$		−	1.60770i		−	0.0655793i	0.999462	−	0.0327896i	$-0.0104391\pi$
$602$	−8.24167	+	12.1699i	−0.335905	+	0.496007i
$603$		0			0
$604$	−11.6077			−0.472310
$605$	−4.42820	−	7.66987i	−0.180032	−	0.311825i
$606$	−19.3923	−	19.3923i	−0.787759	−	0.787759i
$607$	−15.5263	+	26.8923i	−0.630192	+	1.09152i	0.357320	+	0.933982i	$0.383691\pi$
$607$	−15.5263	+	26.8923i	−0.630192	+	1.09152i	−0.987512	+	0.157543i	$0.949643\pi$
$608$	12.0000	−	44.7846i	0.486664	−	1.81626i
$609$	−47.0885	+	9.06218i	−1.90812	+	0.367218i
$610$	−1.56218	−	5.83013i	−0.0632507	−	0.236055i
$611$	6.00000	−	10.3923i	0.242734	−	0.420428i
$612$		0			0
$613$	21.8827	−	12.6340i	0.883833	−	0.510281i	0.0119129	−	0.999929i	$-0.496208\pi$
$613$	21.8827	−	12.6340i	0.883833	−	0.510281i	0.871920	+	0.489648i	$0.162875\pi$
$614$	−2.24167	+	8.36603i	−0.0904664	+	0.337625i
$615$	9.00000			0.362915
$616$	−9.07180	−	6.14359i	−0.365513	−	0.247532i
$617$	28.9282			1.16461			0.582303	−	0.812972i	$-0.302152\pi$
$617$	28.9282			1.16461			0.582303	+	0.812972i	$0.302152\pi$
$618$	−1.68653	+	6.29423i	−0.0678423	+	0.253191i
$619$	6.58846	−	3.80385i	0.264812	−	0.152890i	−0.361715	−	0.932289i	$-0.617809\pi$
$619$	6.58846	−	3.80385i	0.264812	−	0.152890i	0.626528	+	0.779399i	$0.284475\pi$
$620$	3.80385	+	2.19615i	0.152766	+	0.0881996i
$621$	15.4019	−	26.6769i	0.618058	−	1.07051i
$622$	−1.39230	−	5.19615i	−0.0558263	−	0.208347i
$623$	−29.3205	+	25.3923i	−1.17470	+	1.01732i
$624$	−28.3923	−	16.3923i	−1.13660	−	0.656217i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−17.3205	−	17.3205i	−0.692267	−	0.692267i
$627$	10.3923	+	18.0000i	0.415029	+	0.718851i
$628$			5.07180i			0.202387i
$629$	−2.53590			−0.101113
$630$		0			0
$631$			21.4641i			0.854472i	0.904140	+	0.427236i	$0.140513\pi$
$631$			21.4641i			0.854472i	−0.904140	+	0.427236i	$0.859487\pi$
$632$	−3.46410	−	12.9282i	−0.137795	−	0.514256i
$633$	27.8827	−	16.0981i	1.10824	−	0.639841i
$634$	−9.26795	−	9.26795i	−0.368077	−	0.368077i
$635$	−13.3923	−	7.73205i	−0.531457	−	0.306837i
$636$	−0.588457	+	0.339746i	−0.0233338	+	0.0134718i
$637$	−26.0263	−	20.4904i	−1.03120	−	0.811858i
$638$	20.9282	−	5.60770i	0.828556	−	0.222011i
$639$		0			0
$640$	8.00000	+	8.00000i	0.316228	+	0.316228i
$641$	−17.2321	−	29.8468i	−0.680625	−	1.17888i	−0.974790	−	0.223123i	$-0.928375\pi$
$641$	−17.2321	−	29.8468i	−0.680625	−	1.17888i	0.294165	−	0.955755i	$-0.404958\pi$
$642$	4.43782	−	16.5622i	0.175147	−	0.653657i
$643$			19.6077i			0.773252i	0.922237	+	0.386626i	$0.126360\pi$
$643$			19.6077i			0.773252i	−0.922237	+	0.386626i	$0.873640\pi$
$644$	−30.8038	+	5.92820i	−1.21384	+	0.233604i
$645$			6.80385i			0.267901i
$646$	14.1962	+	3.80385i	0.558540	+	0.149660i
$647$	13.7942	+	23.8923i	0.542307	+	0.939303i	0.998771	+	0.0495615i	$0.0157824\pi$
$647$	13.7942	+	23.8923i	0.542307	+	0.939303i	−0.456464	+	0.889742i	$0.650884\pi$
$648$	−6.58846	+	24.5885i	−0.258819	+	0.965926i
$649$	6.00000	+	3.46410i	0.235521	+	0.135978i
$650$	−1.73205	−	6.46410i	−0.0679366	−	0.253543i
$651$	7.60770	−	6.58846i	0.298169	−	0.258222i
$652$	17.3205	−	10.0000i	0.678323	−	0.391630i
$653$	−16.4378	−	9.49038i	−0.643262	−	0.371387i	0.142608	−	0.989779i	$-0.454451\pi$
$653$	−16.4378	−	9.49038i	−0.643262	−	0.371387i	−0.785870	+	0.618392i	$0.787784\pi$
$654$	30.1244	−	30.1244i	1.17796	−	1.17796i
$655$	−10.3923	+	6.00000i	−0.406061	+	0.234439i
$656$	18.0000	−	10.3923i	0.702782	−	0.405751i
$657$		0			0
$658$	4.14359	+	8.53590i	0.161534	+	0.332764i
$659$	−17.8038			−0.693539			−0.346770	−	0.937950i	$-0.612721\pi$
$659$	−17.8038			−0.693539			−0.346770	+	0.937950i	$0.612721\pi$
$660$	−5.07180			−0.197419
$661$	−1.79423	−	3.10770i	−0.0697874	−	0.120875i	0.829020	−	0.559219i	$-0.188899\pi$
$661$	−1.79423	−	3.10770i	−0.0697874	−	0.120875i	−0.898808	+	0.438343i	$0.855565\pi$
$662$	22.7321	−	22.7321i	0.883506	−	0.883506i
$663$	5.19615	−	9.00000i	0.201802	−	0.349531i
$664$	−29.3205	+	29.3205i	−1.13786	+	1.13786i
$665$	−4.09808	−	21.2942i	−0.158917	−	0.825755i
$666$		0			0
$667$	31.0167	−	53.7224i	1.20097	−	2.08014i
$668$	5.78461	+	3.33975i	0.223813	+	0.129219i
$669$	20.7846	−	12.0000i	0.803579	−	0.463947i
$670$	−15.5622	−	4.16987i	−0.601219	−	0.161096i
$671$	6.24871			0.241229
$672$	23.3205	−	11.3205i	0.899608	−	0.436698i
$673$	38.7846			1.49504			0.747518	−	0.664241i	$-0.231245\pi$
$673$	38.7846			1.49504			0.747518	+	0.664241i	$0.231245\pi$
$674$	−39.5885	−	10.6077i	−1.52489	−	0.408593i
$675$	−4.50000	+	2.59808i	−0.173205	+	0.100000i
$676$	16.2679	+	9.39230i	0.625690	+	0.361242i
$677$	−18.2942	+	31.6865i	−0.703104	+	1.21781i	0.264267	+	0.964450i	$0.414870\pi$
$677$	−18.2942	+	31.6865i	−0.703104	+	1.21781i	−0.967371	+	0.253363i	$0.918463\pi$
$678$	7.73205	−	2.07180i	0.296948	−	0.0795669i
$679$	−8.66025	−	3.00000i	−0.332350	−	0.115129i
$680$	−2.53590	+	2.53590i	−0.0972473	+	0.0972473i
$681$	4.39230	−	7.60770i	0.168313	−	0.291528i
$682$	−3.21539	+	3.21539i	−0.123124	+	0.123124i
$683$	−12.4282	−	21.5263i	−0.475552	−	0.823680i	0.524056	−	0.851684i	$-0.324418\pi$
$683$	−12.4282	−	21.5263i	−0.475552	−	0.823680i	−0.999608	+	0.0280037i	$0.991085\pi$
$684$		0			0
$685$	12.3923			0.473486
$686$	24.9545	−	7.95448i	0.952767	−	0.303704i
$687$		−	26.7846i		−	1.02190i
$688$	7.85641	+	13.6077i	0.299523	+	0.518789i
$689$	0.803848	−	0.464102i	0.0306242	−	0.0176809i
$690$	−10.2679	+	10.2679i	−0.390894	+	0.390894i
$691$	19.3923	+	11.1962i	0.737718	+	0.425922i	0.821239	−	0.570584i	$-0.193283\pi$
$691$	19.3923	+	11.1962i	0.737718	+	0.425922i	−0.0835210	+	0.996506i	$0.526617\pi$
$692$	2.78461	−	1.60770i	0.105855	−	0.0611154i
$693$		0			0
$694$	−6.31347	−	23.5622i	−0.239656	−	0.894408i
$695$	8.19615	+	4.73205i	0.310898	+	0.179497i
$696$	−13.2679	+	49.5167i	−0.502920	+	1.87692i
$697$	3.29423	+	5.70577i	0.124778	+	0.216122i
$698$	47.1506	+	12.6340i	1.78468	+	0.478203i
$699$			9.12436i			0.345115i
$700$	5.00000	+	1.73205i	0.188982	+	0.0654654i
$701$			33.7846i			1.27603i	0.770025	+	0.638014i	$0.220244\pi$
$701$			33.7846i			1.27603i	−0.770025	+	0.638014i	$0.779756\pi$
$702$	9.00000	−	33.5885i	0.339683	−	1.26771i
$703$	−8.19615	−	14.1962i	−0.309124	−	0.535418i
$704$	−10.1436	+	5.85641i	−0.382301	+	0.220722i
$705$	3.80385	+	2.19615i	0.143261	+	0.0827119i
$706$	−47.4449	+	12.7128i	−1.78561	+	0.478453i
$707$	−29.0885	+	5.59808i	−1.09398	+	0.210537i
$708$	−14.1962	+	8.19615i	−0.533524	+	0.308030i
$709$	22.6699	+	13.0885i	0.851385	+	0.491547i	0.861118	−	0.508405i	$-0.169765\pi$
$709$	22.6699	+	13.0885i	0.851385	+	0.491547i	−0.00973296	+	0.999953i	$0.503098\pi$
$710$	−5.26795	−	5.26795i	−0.197703	−	0.197703i
$711$		0			0
$712$	10.7321	+	40.0526i	0.402201	+	1.50103i
$713$			13.0192i			0.487574i
$714$	3.58846	+	7.39230i	0.134295	+	0.276650i
$715$	6.92820			0.259100
$716$		−	36.3923i		−	1.36004i
$717$	1.56218	+	2.70577i	0.0583406	+	0.101049i
$718$	27.6603	+	27.6603i	1.03227	+	1.03227i
$719$	21.4641	−	37.1769i	0.800476	−	1.38646i	−0.118827	−	0.992915i	$-0.537913\pi$
$719$	21.4641	−	37.1769i	0.800476	−	1.38646i	0.919303	−	0.393550i	$-0.128753\pi$
$720$		0			0
$721$	4.60770	+	5.32051i	0.171600	+	0.198146i
$722$	17.6340	+	65.8109i	0.656269	+	2.44923i
$723$	6.80385	−	11.7846i	0.253038	−	0.438274i
$724$	3.00000	+	1.73205i	0.111494	+	0.0643712i
$725$	−9.06218	+	5.23205i	−0.336561	+	0.194313i
$726$	−5.61474	+	20.9545i	−0.208382	+	0.777694i
$727$	25.0526			0.929148			0.464574	−	0.885534i	$-0.346207\pi$
$727$	25.0526			0.929148			0.464574	+	0.885534i	$0.346207\pi$
$728$	−31.8564	+	15.4641i	−1.18068	+	0.573138i
$729$	−27.0000			−1.00000
$730$	−4.26795	+	15.9282i	−0.157964	+	0.589529i
$731$	−4.31347	+	2.49038i	−0.159539	+	0.0921101i
$732$	−7.39230	+	12.8038i	−0.273227	+	0.473244i
$733$	−5.19615	+	9.00000i	−0.191924	+	0.332423i	−0.945888	−	0.324494i	$-0.894806\pi$
$733$	−5.19615	+	9.00000i	−0.191924	+	0.332423i	0.753964	+	0.656916i	$0.228139\pi$
$734$	7.22243	+	26.9545i	0.266585	+	0.994908i
$735$	7.50000	−	9.52628i	0.276642	−	0.351382i
$736$	−8.67949	+	32.3923i	−0.319930	+	1.19400i
$737$	8.33975	−	14.4449i	0.307198	−	0.532083i
$738$		0			0
$739$	−2.80385	−	4.85641i	−0.103141	−	0.178646i	0.809836	−	0.586656i	$-0.199556\pi$
$739$	−2.80385	−	4.85641i	−0.103141	−	0.178646i	−0.912977	+	0.408010i	$0.866223\pi$
$740$	4.00000			0.147043
$741$	67.1769			2.46781
$742$	−0.0525589	+	0.732051i	−0.00192950	+	0.0268744i
$743$			9.39230i			0.344570i	0.985047	+	0.172285i	$0.0551150\pi$
$743$			9.39230i			0.344570i	−0.985047	+	0.172285i	$0.944885\pi$
$744$	−2.78461	−	10.3923i	−0.102089	−	0.381000i
$745$	2.13397	−	1.23205i	0.0781828	−	0.0451388i
$746$	0.928203	+	0.928203i	0.0339839	+	0.0339839i
$747$		0			0
$748$	−1.85641	−	3.21539i	−0.0678769	−	0.117566i
$749$	−12.1244	−	14.0000i	−0.443014	−	0.511549i
$750$	2.36603	−	0.633975i	0.0863950	−	0.0231495i
$751$	40.8564	+	23.5885i	1.49087	+	0.860755i	0.999945	−	0.0104462i	$-0.00332520\pi$
$751$	40.8564	+	23.5885i	1.49087	+	0.860755i	0.490926	+	0.871201i	$0.336659\pi$
$752$	10.1436			0.369899
$753$	13.6865	+	23.7058i	0.498765	+	0.863886i
$754$	18.1244	−	67.6410i	0.660050	−	2.46334i
$755$			5.80385i			0.211224i
$756$	18.0000	+	20.7846i	0.654654	+	0.755929i
$757$			18.1962i			0.661350i	0.943745	+	0.330675i	$0.107276\pi$
$757$			18.1962i			0.661350i	−0.943745	+	0.330675i	$0.892724\pi$
$758$	−36.1244	−	9.67949i	−1.31210	−	0.351575i
$759$	−7.51666	−	13.0192i	−0.272837	−	0.472568i
$760$	−22.3923	−	6.00000i	−0.812254	−	0.217643i
$761$	−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	$0.889681\pi$
$762$	9.80385	+	36.5885i	0.355156	+	1.32546i
$763$	−8.69615	−	45.1865i	−0.314822	−	1.63586i
$764$	24.3923	+	42.2487i	0.882483	+	1.52850i
$765$		0			0
$766$	−17.1962	+	17.1962i	−0.621322	+	0.621322i
$767$	19.3923	−	11.1962i	0.700216	−	0.404270i
$768$		−	27.7128i		−	1.00000i
$769$		−	10.3923i		−	0.374756i	−0.982288	−	0.187378i	$-0.940001\pi$
$769$		−	10.3923i		−	0.374756i	0.982288	−	0.187378i	$-0.0599989\pi$
$770$	−3.07180	+	4.53590i	−0.110700	+	0.163462i
$771$	−10.3923			−0.374270
$772$		−	27.7128i		−	0.997406i
$773$	−24.2942	−	42.0788i	−0.873803	−	1.51347i	−0.858033	−	0.513595i	$-0.828313\pi$
$773$	−24.2942	−	42.0788i	−0.873803	−	1.51347i	−0.0157699	−	0.999876i	$-0.505020\pi$
$774$		0			0
$775$	1.09808	−	1.90192i	0.0394441	−	0.0683191i
$776$	−6.92820	+	6.92820i	−0.248708	+	0.248708i
$777$	3.00000	−	8.66025i	0.107624	−	0.310685i
$778$	−34.2487	+	9.17691i	−1.22788	+	0.329008i
$779$	−21.2942	+	36.8827i	−0.762945	+	1.32146i
$780$	−8.19615	+	14.1962i	−0.293469	+	0.508304i
$781$	6.67949	−	3.85641i	0.239011	−	0.137993i
$782$	−10.2679	−	2.75129i	−0.367181	−	0.0983859i
$783$	−54.3731			−1.94313
$784$	4.00000	−	27.7128i	0.142857	−	0.989743i
$785$	2.53590			0.0905101
$786$	28.3923	+	7.60770i	1.01272	+	0.271357i
$787$	29.3038	−	16.9186i	1.04457	−	0.603082i	0.123445	−	0.992351i	$-0.460606\pi$
$787$	29.3038	−	16.9186i	1.04457	−	0.603082i	0.921124	+	0.389269i	$0.127272\pi$
$788$	−4.92820	+	8.53590i	−0.175560	+	0.304079i
$789$	−13.9186	+	24.1077i	−0.495515	+	0.858257i
$790$	−6.46410	+	1.73205i	−0.229982	+	0.0616236i
$791$	2.83013	−	8.16987i	0.100628	−	0.290487i
$792$		0			0
$793$	10.0981	−	17.4904i	0.358593	−	0.621102i
$794$	−26.7846	+	26.7846i	−0.950550	+	0.950550i
$795$	0.169873	+	0.294229i	0.00602477	+	0.0104352i
$796$		−	36.0000i		−	1.27599i
$797$	−5.32051			−0.188462			−0.0942310	−	0.995550i	$-0.530039\pi$
$797$	−5.32051			−0.188462			−0.0942310	+	0.995550i	$0.530039\pi$
$798$	−29.7846	+	43.9808i	−1.05436	+	1.55690i
$799$			3.21539i			0.113752i
$800$	4.00000	−	4.00000i	0.141421	−	0.141421i
$801$		0			0
$802$	−8.46410	+	8.46410i	−0.298878	+	0.298878i
$803$	−14.7846	−	8.53590i	−0.521738	−	0.301225i
$804$	19.7321	+	34.1769i	0.695896	+	1.20533i
$805$	2.96410	+	15.4019i	0.104471	+	0.542846i
$806$	3.80385	+	14.1962i	0.133985	+	0.500038i
$807$	12.9904	+	7.50000i	0.457283	+	0.264013i
$808$	−8.19615	+	30.5885i	−0.288340	+	1.07610i
$809$	9.16025	+	15.8660i	0.322057	+	0.557820i	0.980912	−	0.194450i	$-0.0622923\pi$
$809$	9.16025	+	15.8660i	0.322057	+	0.557820i	−0.658855	+	0.752270i	$0.728959\pi$
$810$	12.2942	+	3.29423i	0.431975	+	0.115747i
$811$			17.6603i			0.620135i	0.950714	+	0.310068i	$0.100352\pi$
$811$			17.6603i			0.620135i	−0.950714	+	0.310068i	$0.899648\pi$
$812$	36.2487	+	41.8564i	1.27208	+	1.46887i
$813$			24.5885i			0.862355i
$814$	−1.07180	+	4.00000i	−0.0375665	+	0.140200i
$815$	−5.00000	−	8.66025i	−0.175142	−	0.303355i
$816$	8.78461			0.307523
$817$	−27.8827	−	16.0981i	−0.975492	−	0.563200i
$818$	28.2224	−	7.56218i	0.986774	−	0.264405i
$819$		0			0
$820$	−5.19615	−	9.00000i	−0.181458	−	0.314294i
$821$	−1.73205	−	1.00000i	−0.0604490	−	0.0349002i	0.469471	−	0.882948i	$-0.344445\pi$
$821$	−1.73205	−	1.00000i	−0.0604490	−	0.0349002i	−0.529920	+	0.848048i	$0.677778\pi$
$822$	−21.4641	−	21.4641i	−0.748647	−	0.748647i
$823$	20.3827	−	11.7679i	0.710496	−	0.410205i	−0.100749	−	0.994912i	$-0.532124\pi$
$823$	20.3827	−	11.7679i	0.710496	−	0.410205i	0.811245	+	0.584707i	$0.198791\pi$
$824$	7.26795	−	1.94744i	0.253191	−	0.0678423i
$825$			2.53590i			0.0882886i
$826$	−1.26795	+	17.6603i	−0.0441176	+	0.614479i
$827$	−8.85641			−0.307967			−0.153984	−	0.988073i	$-0.549210\pi$
$827$	−8.85641			−0.307967			−0.153984	+	0.988073i	$0.549210\pi$
$828$		0			0
$829$	7.60770	+	13.1769i	0.264226	+	0.457653i	0.967361	−	0.253404i	$-0.0815501\pi$
$829$	7.60770	+	13.1769i	0.264226	+	0.457653i	−0.703134	+	0.711057i	$0.748217\pi$
$830$	14.6603	+	14.6603i	0.508865	+	0.508865i
$831$	−1.90192	+	3.29423i	−0.0659770	+	0.114276i
$832$			37.8564i			1.31243i
$833$	8.78461	+	1.26795i	0.304369	+	0.0439318i
$834$	−6.00000	−	22.3923i	−0.207763	−	0.775382i
$835$	1.66987	−	2.89230i	0.0577883	−	0.100092i
$836$	12.0000	−	20.7846i	0.415029	−	0.718851i
$837$	9.88269	−	5.70577i	0.341596	−	0.197220i
$838$	−4.14359	+	15.4641i	−0.143138	+	0.534199i
$839$	44.5359			1.53755			0.768775	−	0.639519i	$-0.220867\pi$
$839$	44.5359			1.53755			0.768775	+	0.639519i	$0.220867\pi$
$840$	−5.66025	−	11.6603i	−0.195297	−	0.402317i
$841$	−80.4974			−2.77577
$842$	7.77757	−	29.0263i	0.268033	−	1.00031i
$843$	−32.7846	+	18.9282i	−1.12916	+	0.651922i
$844$	−32.1962	−	18.5885i	−1.10824	−	0.639841i
$845$	4.69615	−	8.13397i	0.161553	−	0.279817i
$846$		0			0
$847$	15.3397	+	17.7128i	0.527080	+	0.608619i
$848$	0.679492	+	0.392305i	0.0233338	+	0.0134718i
$849$	−3.00000	+	5.19615i	−0.102960	+	0.178331i
$850$	1.26795	+	1.26795i	0.0434903	+	0.0434903i
$851$	5.92820	+	10.2679i	0.203216	+	0.351981i
$852$			18.2487i			0.625191i
$853$	1.51666			0.0519295			0.0259647	−	0.999663i	$-0.491734\pi$
$853$	1.51666			0.0519295			0.0259647	+	0.999663i	$0.491734\pi$
$854$	6.97372	+	14.3660i	0.238636	+	0.491595i
$855$		0			0
$856$	−19.1244	+	5.12436i	−0.653657	+	0.175147i
$857$	−8.41154	+	4.85641i	−0.287333	+	0.165892i	−0.636738	−	0.771080i	$-0.719717\pi$
$857$	−8.41154	+	4.85641i	−0.287333	+	0.165892i	0.349406	+	0.936972i	$0.386384\pi$
$858$	−12.0000	−	12.0000i	−0.409673	−	0.409673i
$859$	−43.9808	−	25.3923i	−1.50060	−	0.866374i	−1.00000		0.000698137i	$-0.999778\pi$
$859$	−43.9808	−	25.3923i	−1.50060	−	0.866374i	−0.500604	−	0.865676i	$-0.666889\pi$
$860$	6.80385	−	3.92820i	0.232009	−	0.133951i
$861$	−23.3827	+	4.50000i	−0.796880	+	0.153360i
$862$	10.9282	−	2.92820i	0.372216	−	0.0997350i
$863$	18.2776	+	10.5526i	0.622176	+	0.359213i	0.777716	−	0.628616i	$-0.216378\pi$
$863$	18.2776	+	10.5526i	0.622176	+	0.359213i	−0.155540	+	0.987830i	$0.549712\pi$
$864$	28.3923	−	7.60770i	0.965926	−	0.258819i
$865$	−0.803848	−	1.39230i	−0.0273316	−	0.0473398i
$866$	10.6077	−	39.5885i	0.360464	−	1.34527i
$867$		−	26.6603i		−	0.905430i
$868$	−10.9808	−	3.80385i	−0.372711	−	0.129111i
$869$		−	6.92820i		−	0.235023i
$870$	24.7583	+	6.63397i	0.839386	+	0.224913i
$871$	−26.9545	−	46.6865i	−0.913318	−	1.58191i
$872$	−47.5167	−	12.7321i	−1.60912	−	0.431162i
$873$		0			0
$874$	−17.7846	−	66.3731i	−0.601573	−	2.24510i
$875$	0.866025	−	2.50000i	0.0292770	−	0.0845154i
$876$	34.9808	−	20.1962i	1.18189	−	0.682365i
$877$	36.8827	+	21.2942i	1.24544	+	0.719055i	0.970196	−	0.242320i	$-0.0779082\pi$
$877$	36.8827	+	21.2942i	1.24544	+	0.719055i	0.275243	+	0.961375i	$0.411242\pi$
$878$	−13.8564	+	13.8564i	−0.467631	+	0.467631i
$879$	20.7846	−	12.0000i	0.701047	−	0.404750i
$880$	2.92820	+	5.07180i	0.0987097	+	0.170970i
$881$		−	26.6603i		−	0.898207i	−0.893480	−	0.449103i	$-0.851743\pi$
$881$		−	26.6603i		−	0.898207i	0.893480	−	0.449103i	$-0.148257\pi$
$882$		0			0
$883$	−3.46410			−0.116576			−0.0582882	−	0.998300i	$-0.518564\pi$
$883$	−3.46410			−0.116576			−0.0582882	+	0.998300i	$0.518564\pi$
$884$	−12.0000			−0.403604
$885$	4.09808	+	7.09808i	0.137755	+	0.238599i
$886$	−7.00000	+	7.00000i	−0.235170	+	0.235170i
$887$	20.1340	−	34.8731i	0.676033	−	1.17092i	−0.300133	−	0.953897i	$-0.597031\pi$
$887$	20.1340	−	34.8731i	0.676033	−	1.17092i	0.976166	−	0.217026i	$-0.0696355\pi$
$888$	−6.92820	−	6.92820i	−0.232495	−	0.232495i
$889$	38.6603	+	13.3923i	1.29662	+	0.449163i
$890$	20.0263	−	5.36603i	0.671282	−	0.179870i
$891$	−6.58846	+	11.4115i	−0.220722	+	0.382301i
$892$	−24.0000	−	13.8564i	−0.803579	−	0.463947i
$893$	−18.0000	+	10.3923i	−0.602347	+	0.347765i
$894$	−5.83013	−	1.56218i	−0.194989	−	0.0522470i
$895$	−18.1962			−0.608230
$896$	−24.7846	−	16.7846i	−0.827996	−	0.560734i
$897$	−48.5885			−1.62232
$898$	26.6865	+	7.15064i	0.890541	+	0.238620i
$899$	19.9019	−	11.4904i	0.663766	−	0.383226i
$900$		0			0
$901$	−0.124356	+	0.215390i	−0.00414289	+	0.00717569i
$902$	10.3923	−	2.78461i	0.346026	−	0.0927174i
$903$	−3.40192	−	17.6769i	−0.113209	−	0.588251i
$904$	−6.53590	−	6.53590i	−0.217381	−	0.217381i
$905$	0.866025	−	1.50000i	0.0287877	−	0.0498617i
$906$	10.0526	−	10.0526i	0.333974	−	0.333974i
$907$	17.0885	+	29.5981i	0.567413	+	0.982788i	0.996821	+	0.0796773i	$0.0253890\pi$
$907$	17.0885	+	29.5981i	0.567413	+	0.982788i	−0.429408	+	0.903111i	$0.641278\pi$
$908$	−10.1436			−0.336627
$909$		0			0
$910$	7.73205	+	15.9282i	0.256315	+	0.528015i
$911$			1.71281i			0.0567480i	0.999597	+	0.0283740i	$0.00903294\pi$
$911$			1.71281i			0.0567480i	−0.999597	+	0.0283740i	$0.990967\pi$
$912$	28.3923	+	49.1769i	0.940163	+	1.62841i
$913$	−18.5885	+	10.7321i	−0.615188	+	0.355179i
$914$	−40.6410	+	40.6410i	−1.34429	+	1.34429i
$915$	6.40192	+	3.69615i	0.211641	+	0.122191i
$916$	−26.7846	+	15.4641i	−0.884988	+	0.510948i
$917$	24.0000	−	20.7846i	0.792550	−	0.686368i
$918$	2.41154	+	9.00000i	0.0795928	+	0.297044i
$919$	−28.5622	−	16.4904i	−0.942179	−	0.543967i	−0.0515365	−	0.998671i	$-0.516412\pi$
$919$	−28.5622	−	16.4904i	−0.942179	−	0.543967i	−0.890643	+	0.454704i	$0.849745\pi$
$920$	16.1962	+	4.33975i	0.533971	+	0.143077i
$921$	−5.30385	−	9.18653i	−0.174768	−	0.302707i
$922$	−13.8564	−	3.71281i	−0.456336	−	0.122275i
$923$		−	24.9282i		−	0.820522i
$924$	13.1769	−	2.53590i	0.433489	−	0.0834249i
$925$		−	2.00000i		−	0.0657596i
$926$	−7.09808	+	26.4904i	−0.233257	+	0.870528i
$927$		0			0
$928$	57.1769	−	15.3205i	1.87692	−	0.502920i
$929$	−26.8923	−	15.5263i	−0.882308	−	0.509401i	−0.0108892	−	0.999941i	$-0.503466\pi$
$929$	−26.8923	−	15.5263i	−0.882308	−	0.509401i	−0.871419	+	0.490540i	$0.836800\pi$
$930$	−5.19615	+	1.39230i	−0.170389	+	0.0456555i
$931$	21.2942	+	53.2750i	0.697890	+	1.74602i
$932$	9.12436	−	5.26795i	0.298878	−	0.172557i
$933$	5.70577	+	3.29423i	0.186799	+	0.107848i
$934$	28.2679	+	28.2679i	0.924956	+	0.924956i
$935$	−1.60770	+	0.928203i	−0.0525773	+	0.0303555i
$936$		0			0
$937$			13.8564i			0.452669i	0.974050	+	0.226335i	$0.0726743\pi$
$937$			13.8564i			0.452669i	−0.974050	+	0.226335i	$0.927326\pi$
$938$	42.5167	+	3.05256i	1.38822	+	0.0996696i
$939$	30.0000			0.979013
$940$		−	5.07180i		−	0.165424i
$941$	12.4641	+	21.5885i	0.406318	+	0.703764i	0.994474	−	0.104984i	$-0.0334792\pi$
$941$	12.4641	+	21.5885i	0.406318	+	0.703764i	−0.588156	+	0.808748i	$0.700146\pi$
$942$	−4.39230	−	4.39230i	−0.143109	−	0.143109i
$943$	15.4019	−	26.6769i	0.501556	−	0.868720i
$944$	16.3923	+	9.46410i	0.533524	+	0.308030i
$945$	10.3923	−	9.00000i	0.338062	−	0.292770i
$946$	2.10512	+	7.85641i	0.0684433	+	0.255434i
$947$	7.08846	−	12.2776i	0.230344	−	0.398967i	−0.727565	−	0.686038i	$-0.759348\pi$
$947$	7.08846	−	12.2776i	0.230344	−	0.398967i	0.957909	+	0.287071i	$0.0926816\pi$
$948$	14.1962	+	8.19615i	0.461070	+	0.266199i
$949$	−47.7846	+	27.5885i	−1.55115	+	0.895559i
$950$	−3.00000	+	11.1962i	−0.0973329	+	0.363251i
$951$	16.0526			0.520540
$952$	5.32051	−	7.85641i	0.172439	−	0.254628i
$953$	30.1051			0.975200			0.487600	−	0.873067i	$-0.337872\pi$
$953$	30.1051			0.975200			0.487600	+	0.873067i	$0.337872\pi$
$954$		0			0
$955$	21.1244	−	12.1962i	0.683568	−	0.394658i
$956$	1.80385	−	3.12436i	0.0583406	−	0.101049i
$957$	−13.2679	+	22.9808i	−0.428892	+	0.742863i
$958$	−2.07180	−	7.73205i	−0.0669367	−	0.249811i
$959$	−32.1962	+	6.19615i	−1.03967	+	0.200084i
$960$	−13.8564			−0.447214
$961$	13.0885	−	22.6699i	0.422208	−	0.731286i
$962$	9.46410	+	9.46410i	0.305135	+	0.305135i
$963$		0			0
$964$	−15.7128			−0.506076
$965$	−13.8564			−0.446054
$966$	21.5429	−	31.8109i	0.693133	−	1.02350i
$967$			34.1769i			1.09906i	0.835475	+	0.549528i	$0.185192\pi$
$967$			34.1769i			1.09906i	−0.835475	+	0.549528i	$0.814808\pi$
$968$	24.1962	−	6.48334i	0.777694	−	0.208382i
$969$	−15.5885	+	9.00000i	−0.500773	+	0.289122i
$970$	3.46410	+	3.46410i	0.111226	+	0.111226i
$971$	40.1769	+	23.1962i	1.28934	+	0.744400i	0.978536	−	0.206075i	$-0.0660690\pi$
$971$	40.1769	+	23.1962i	1.28934	+	0.744400i	0.310802	+	0.950475i	$0.399402\pi$
$972$		0			0
$973$	−23.6603	−	8.19615i	−0.758513	−	0.262757i
$974$	−33.8564	+	9.07180i	−1.08483	+	0.290679i
$975$	7.09808	+	4.09808i	0.227320	+	0.131243i
$976$	17.0718			0.546455
$977$	20.9282	+	36.2487i	0.669553	+	1.15970i	0.978029	+	0.208467i	$0.0668474\pi$
$977$	20.9282	+	36.2487i	0.669553	+	1.15970i	−0.308477	+	0.951232i	$0.599819\pi$
$978$	−6.33975	+	23.6603i	−0.202723	+	0.756571i
$979$			21.4641i			0.685996i
$980$	−13.8564	−	2.00000i	−0.442627	−	0.0638877i
$981$		0			0
$982$	−36.5167	−	9.78461i	−1.16529	−	0.312239i
$983$	−22.3301	−	38.6769i	−0.712220	−	1.23360i	−0.964022	−	0.265823i	$-0.914356\pi$
$983$	−22.3301	−	38.6769i	−0.712220	−	1.23360i	0.251801	−	0.967779i	$-0.418977\pi$
$984$	−6.58846	+	24.5885i	−0.210032	+	0.783851i
$985$	4.26795	+	2.46410i	0.135988	+	0.0785128i
$986$	4.85641	+	18.1244i	0.154659	+	0.577197i
$987$	−10.9808	−	3.80385i	−0.349522	−	0.121078i
$988$	−38.7846	−	67.1769i	−1.23390	−	2.13718i
$989$	20.1673	+	11.6436i	0.641283	+	0.370245i
$990$		0			0
$991$	−11.5814	+	6.68653i	−0.367896	+	0.212405i	−0.672539	−	0.740062i	$-0.734796\pi$
$991$	−11.5814	+	6.68653i	−0.367896	+	0.212405i	0.304643	+	0.952467i	$0.401463\pi$
$992$	−8.78461	+	8.78461i	−0.278912	+	0.278912i
$993$			39.3731i			1.24947i
$994$	16.3205	+	11.0526i	0.517655	+	0.350566i
$995$	−18.0000			−0.570638
$996$		−	50.7846i		−	1.60917i
$997$	−22.5622	−	39.0788i	−0.714551	−	1.23764i	−0.963132	−	0.269028i	$-0.913298\pi$
$997$	−22.5622	−	39.0788i	−0.714551	−	1.23764i	0.248581	−	0.968611i	$-0.420036\pi$
$998$	−22.3923	+	22.3923i	−0.708816	+	0.708816i
$999$	5.19615	−	9.00000i	0.164399	−	0.284747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bj.d.131.2	yes	4
4.3	odd	2		1120.2.bz.d.271.2		4
7.3	odd	6		280.2.bj.a.171.2	yes	4
8.3	odd	2		280.2.bj.a.131.1	✓	4
8.5	even	2		1120.2.bz.a.271.1		4
28.3	even	6		1120.2.bz.a.591.1		4
56.3	even	6	inner	280.2.bj.d.171.2	yes	4
56.45	odd	6		1120.2.bz.d.591.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.a.131.1	✓	4	8.3	odd	2
280.2.bj.a.171.2	yes	4	7.3	odd	6
280.2.bj.d.131.2	yes	4	1.1	even	1	trivial
280.2.bj.d.171.2	yes	4	56.3	even	6	inner
1120.2.bz.a.271.1		4	8.5	even	2
1120.2.bz.a.591.1		4	28.3	even	6
1120.2.bz.d.271.2		4	4.3	odd	2
1120.2.bz.d.591.2		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.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.36603 + 0.633975i) q^{6} +(-0.866025 + 2.50000i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.36603 + 0.633975i) q^{6} +(-0.866025 + 2.50000i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.00000 - 1.00000i) q^{10} +(0.732051 + 1.26795i) q^{11} -3.46410 q^{12} +4.73205 q^{13} +(-2.09808 + 3.09808i) q^{14} +1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.09808 + 0.633975i) q^{17} +(-7.09808 - 4.09808i) q^{19} +(1.73205 - 1.00000i) q^{20} +(-0.866025 - 4.50000i) q^{21} +(0.535898 + 2.00000i) q^{22} +(5.13397 + 2.96410i) q^{23} +(-4.73205 - 1.26795i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(6.46410 + 1.73205i) q^{26} -5.19615i q^{27} +(-4.00000 + 3.46410i) q^{28} -10.4641i q^{29} +(-0.633975 + 2.36603i) q^{30} +(1.09808 + 1.90192i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-2.19615 - 1.26795i) q^{33} +(-1.73205 + 0.464102i) q^{34} +(1.73205 + 2.00000i) q^{35} +(1.73205 + 1.00000i) q^{37} +(-8.19615 - 8.19615i) q^{38} +(-7.09808 + 4.09808i) q^{39} +(2.73205 - 0.732051i) q^{40} -5.19615i q^{41} +(0.464102 - 6.46410i) q^{42} +3.92820 q^{43} +2.92820i q^{44} +(5.92820 + 5.92820i) q^{46} +(1.26795 - 2.19615i) q^{47} +(-6.00000 - 3.46410i) q^{48} +(-5.50000 - 4.33013i) q^{49} +(-0.366025 - 1.36603i) q^{50} +(1.09808 - 1.90192i) q^{51} +(8.19615 + 4.73205i) q^{52} +(0.169873 - 0.0980762i) q^{53} +(1.90192 - 7.09808i) q^{54} +1.46410 q^{55} +(-6.73205 + 3.26795i) q^{56} +14.1962 q^{57} +(3.83013 - 14.2942i) q^{58} +(4.09808 - 2.36603i) q^{59} +(-1.73205 + 3.00000i) q^{60} +(2.13397 - 3.69615i) q^{61} +(0.803848 + 3.00000i) q^{62} +8.00000i q^{64} +(2.36603 - 4.09808i) q^{65} +(-2.53590 - 2.53590i) q^{66} +(-5.69615 - 9.86603i) q^{67} -2.53590 q^{68} -10.2679 q^{69} +(1.63397 + 3.36603i) q^{70} -5.26795i q^{71} +(-10.0981 + 5.83013i) q^{73} +(2.00000 + 2.00000i) q^{74} +(1.50000 + 0.866025i) q^{75} +(-8.19615 - 14.1962i) q^{76} +(-3.80385 + 0.732051i) q^{77} +(-11.1962 + 3.00000i) q^{78} +(-4.09808 - 2.36603i) q^{79} +4.00000 q^{80} +(4.50000 + 7.79423i) q^{81} +(1.90192 - 7.09808i) q^{82} +14.6603i q^{83} +(3.00000 - 8.66025i) q^{84} +1.26795i q^{85} +(5.36603 + 1.43782i) q^{86} +(9.06218 + 15.6962i) q^{87} +(-1.07180 + 4.00000i) q^{88} +(12.6962 + 7.33013i) q^{89} +(-4.09808 + 11.8301i) q^{91} +(5.92820 + 10.2679i) q^{92} +(-3.29423 - 1.90192i) q^{93} +(2.53590 - 2.53590i) q^{94} +(-7.09808 + 4.09808i) q^{95} +(-6.92820 - 6.92820i) q^{96} +3.46410i q^{97} +(-5.92820 - 7.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 6 q^{3} + 2 q^{5} - 6 q^{6} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 6 * q^3 + 2 * q^5 - 6 * q^6 + 8 * q^8	\( 4 q + 2 q^{2} - 6 q^{3} + 2 q^{5} - 6 q^{6} + 8 q^{8} + 4 q^{10} - 4 q^{11} + 12 q^{13} + 2 q^{14} + 8 q^{16} + 6 q^{17} - 18 q^{19} + 16 q^{22} + 24 q^{23} - 12 q^{24} - 2 q^{25} + 12 q^{26} - 16 q^{28} - 6 q^{30} - 6 q^{31} - 8 q^{32} + 12 q^{33} - 12 q^{38} - 18 q^{39} + 4 q^{40} - 12 q^{42} - 12 q^{43} - 4 q^{46} + 12 q^{47} - 24 q^{48} - 22 q^{49} + 2 q^{50} - 6 q^{51} + 12 q^{52} + 18 q^{53} + 18 q^{54} - 8 q^{55} - 20 q^{56} + 36 q^{57} - 2 q^{58} + 6 q^{59} + 12 q^{61} + 24 q^{62} + 6 q^{65} - 24 q^{66} - 2 q^{67} - 24 q^{68} - 48 q^{69} + 10 q^{70} - 30 q^{73} + 8 q^{74} + 6 q^{75} - 12 q^{76} - 36 q^{77} - 24 q^{78} - 6 q^{79} + 16 q^{80} + 18 q^{81} + 18 q^{82} + 12 q^{84} + 18 q^{86} + 12 q^{87} - 32 q^{88} + 30 q^{89} - 6 q^{91} - 4 q^{92} + 18 q^{93} + 24 q^{94} - 18 q^{95} + 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 6 * q^3 + 2 * q^5 - 6 * q^6 + 8 * q^8 + 4 * q^10 - 4 * q^11 + 12 * q^13 + 2 * q^14 + 8 * q^16 + 6 * q^17 - 18 * q^19 + 16 * q^22 + 24 * q^23 - 12 * q^24 - 2 * q^25 + 12 * q^26 - 16 * q^28 - 6 * q^30 - 6 * q^31 - 8 * q^32 + 12 * q^33 - 12 * q^38 - 18 * q^39 + 4 * q^40 - 12 * q^42 - 12 * q^43 - 4 * q^46 + 12 * q^47 - 24 * q^48 - 22 * q^49 + 2 * q^50 - 6 * q^51 + 12 * q^52 + 18 * q^53 + 18 * q^54 - 8 * q^55 - 20 * q^56 + 36 * q^57 - 2 * q^58 + 6 * q^59 + 12 * q^61 + 24 * q^62 + 6 * q^65 - 24 * q^66 - 2 * q^67 - 24 * q^68 - 48 * q^69 + 10 * q^70 - 30 * q^73 + 8 * q^74 + 6 * q^75 - 12 * q^76 - 36 * q^77 - 24 * q^78 - 6 * q^79 + 16 * q^80 + 18 * q^81 + 18 * q^82 + 12 * q^84 + 18 * q^86 + 12 * q^87 - 32 * q^88 + 30 * q^89 - 6 * q^91 - 4 * q^92 + 18 * q^93 + 24 * q^94 - 18 * q^95 + 4 * q^98

Introduction

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