LMFDB - Embedded newform 280.2.bj.a.131.1

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:	$1$
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			131.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	280.131
Dual form			280.2.bj.a.171.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-1.50000 + 0.866025i) q^{3} +2.00000i q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.36603 + 0.633975i) q^{6} +(0.866025 - 2.50000i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.50000 + 0.866025i) q^{3} +2.00000i 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} +(1.36603 - 0.366025i) q^{10} +(0.732051 + 1.26795i) q^{11} +(-1.73205 - 3.00000i) q^{12} -4.73205 q^{13} +(-3.36603 + 1.63397i) q^{14} -1.73205i q^{15} -4.00000 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} +(-1.26795 + 4.73205i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(4.73205 + 4.73205i) q^{26} -5.19615i q^{27} +(5.00000 + 1.73205i) q^{28} +10.4641i q^{29} +(-1.73205 + 1.73205i) q^{30} +(-1.09808 - 1.90192i) q^{31} +(4.00000 + 4.00000i) 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} +(3.00000 + 11.1962i) q^{38} +(7.09808 - 4.09808i) q^{39} +(0.732051 + 2.73205i) q^{40} -5.19615i q^{41} +(3.63397 - 5.36603i) q^{42} +3.92820 q^{43} +(-2.53590 + 1.46410i) q^{44} +(2.16987 + 8.09808i) 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} -9.46410i q^{52} +(-0.169873 + 0.0980762i) q^{53} +(-5.19615 + 5.19615i) q^{54} -1.46410 q^{55} +(-3.26795 - 6.73205i) q^{56} +14.1962 q^{57} +(10.4641 - 10.4641i) q^{58} +(4.09808 - 2.36603i) q^{59} +3.46410 q^{60} +(-2.13397 + 3.69615i) q^{61} +(-0.803848 + 3.00000i) q^{62} -8.00000i q^{64} +(2.36603 - 4.09808i) q^{65} +(0.928203 + 3.46410i) q^{66} +(-5.69615 - 9.86603i) q^{67} +(-1.26795 - 2.19615i) q^{68} +10.2679 q^{69} +(0.267949 - 3.73205i) q^{70} +5.26795i q^{71} +(-10.0981 + 5.83013i) q^{73} +(0.732051 + 2.73205i) 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} +(2.00000 - 3.46410i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-5.19615 + 5.19615i) q^{82} +14.6603i q^{83} +(-9.00000 + 1.73205i) q^{84} -1.26795i q^{85} +(-3.92820 - 3.92820i) q^{86} +(-9.06218 - 15.6962i) q^{87} +(4.00000 + 1.07180i) 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} +(3.46410 - 0.928203i) q^{94} +(7.09808 - 4.09808i) q^{95} +(-9.46410 - 2.53590i) q^{96} +3.46410i q^{97} +(1.16987 + 9.83013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 6 q^{3} - 2 q^{5} + 6 q^{6} + 8 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 - 6 * q^3 - 2 * q^5 + 6 * q^6 + 8 * q^8	$ 4 q - 4 q^{2} - 6 q^{3} - 2 q^{5} + 6 q^{6} + 8 q^{8} + 2 q^{10} - 4 q^{11} - 12 q^{13} - 10 q^{14} - 16 q^{16} + 6 q^{17} - 18 q^{19} + 16 q^{22} - 24 q^{23} - 12 q^{24} - 2 q^{25} + 12 q^{26} + 20 q^{28} + 6 q^{31} + 16 q^{32} + 12 q^{33} + 12 q^{38} + 18 q^{39} - 4 q^{40} + 18 q^{42} - 12 q^{43} - 24 q^{44} + 26 q^{46} - 12 q^{47} + 24 q^{48} - 22 q^{49} + 2 q^{50} - 6 q^{51} - 18 q^{53} + 8 q^{55} - 20 q^{56} + 36 q^{57} + 28 q^{58} + 6 q^{59} - 12 q^{61} - 24 q^{62} + 6 q^{65} - 24 q^{66} - 2 q^{67} - 12 q^{68} + 48 q^{69} + 8 q^{70} - 30 q^{73} - 4 q^{74} + 6 q^{75} + 12 q^{76} + 36 q^{77} - 24 q^{78} + 6 q^{79} + 8 q^{80} + 18 q^{81} - 36 q^{84} + 12 q^{86} - 12 q^{87} + 16 q^{88} + 30 q^{89} - 6 q^{91} - 4 q^{92} - 18 q^{93} + 18 q^{95} - 24 q^{96} + 22 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 6 * q^3 - 2 * q^5 + 6 * q^6 + 8 * q^8 + 2 * q^10 - 4 * q^11 - 12 * q^13 - 10 * q^14 - 16 * q^16 + 6 * q^17 - 18 * q^19 + 16 * q^22 - 24 * q^23 - 12 * q^24 - 2 * q^25 + 12 * q^26 + 20 * q^28 + 6 * q^31 + 16 * q^32 + 12 * q^33 + 12 * q^38 + 18 * q^39 - 4 * q^40 + 18 * q^42 - 12 * q^43 - 24 * q^44 + 26 * q^46 - 12 * q^47 + 24 * q^48 - 22 * q^49 + 2 * q^50 - 6 * q^51 - 18 * q^53 + 8 * q^55 - 20 * q^56 + 36 * q^57 + 28 * q^58 + 6 * q^59 - 12 * q^61 - 24 * q^62 + 6 * q^65 - 24 * q^66 - 2 * q^67 - 12 * q^68 + 48 * q^69 + 8 * q^70 - 30 * q^73 - 4 * q^74 + 6 * q^75 + 12 * q^76 + 36 * q^77 - 24 * q^78 + 6 * q^79 + 8 * q^80 + 18 * q^81 - 36 * q^84 + 12 * q^86 - 12 * q^87 + 16 * q^88 + 30 * q^89 - 6 * q^91 - 4 * q^92 - 18 * q^93 + 18 * q^95 - 24 * q^96 + 22 * 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 $

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$	−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	$0.5\pi$
$4$			2.00000i			1.00000i
$5$	−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
$10$	1.36603	−	0.366025i	0.431975	−	0.115747i
$11$	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	$0.762492\pi$
$12$	−1.73205	−	3.00000i	−0.500000	−	0.866025i
$13$	−4.73205			−1.31243			−0.656217	−	0.754572i	$-0.727845\pi$
$13$	−4.73205			−1.31243			−0.656217	+	0.754572i	$0.727845\pi$
$14$	−3.36603	+	1.63397i	−0.899608	+	0.436698i
$15$		−	1.73205i		−	0.447214i
$16$	−4.00000			−1.00000
$17$	−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	−0.142188	−	0.989840i	$-0.545414\pi$
$23$	−5.13397	−	2.96410i	−1.07051	−	0.618058i	−0.928320	+	0.371782i	$0.878747\pi$
$24$	−1.26795	+	4.73205i	−0.258819	+	0.965926i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	4.73205	+	4.73205i	0.928032	+	0.928032i
$27$		−	5.19615i		−	1.00000i
$28$	5.00000	+	1.73205i	0.944911	+	0.327327i
$29$			10.4641i			1.94313i	0.236763	+	0.971567i	$0.423914\pi$
$29$			10.4641i			1.94313i	−0.236763	+	0.971567i	$0.576086\pi$
$30$	−1.73205	+	1.73205i	−0.316228	+	0.316228i
$31$	−1.09808	−	1.90192i	−0.197220	−	0.341596i	0.750406	−	0.660977i	$-0.229858\pi$
$31$	−1.09808	−	1.90192i	−0.197220	−	0.341596i	−0.947626	+	0.319382i	$0.896525\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	−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	0.350823	−	0.936442i	$-0.385902\pi$
$37$	−1.73205	−	1.00000i	−0.284747	−	0.164399i	−0.635571	+	0.772043i	$0.719235\pi$
$38$	3.00000	+	11.1962i	0.486664	+	1.81626i
$39$	7.09808	−	4.09808i	1.13660	−	0.656217i
$40$	0.732051	+	2.73205i	0.115747	+	0.431975i
$41$		−	5.19615i		−	0.811503i	−0.913984	−	0.405751i	$-0.867010\pi$
$41$		−	5.19615i		−	0.811503i	0.913984	−	0.405751i	$-0.132990\pi$
$42$	3.63397	−	5.36603i	0.560734	−	0.827996i
$43$	3.92820			0.599045			0.299523	−	0.954089i	$-0.403173\pi$
$43$	3.92820			0.599045			0.299523	+	0.954089i	$0.403173\pi$
$44$	−2.53590	+	1.46410i	−0.382301	+	0.220722i
$45$		0			0
$46$	2.16987	+	8.09808i	0.319930	+	1.19400i
$47$	−1.26795	+	2.19615i	−0.184949	+	0.320342i	−0.943559	−	0.331203i	$-0.892545\pi$
$47$	−1.26795	+	2.19615i	−0.184949	+	0.320342i	0.758610	+	0.651545i	$0.225879\pi$
$48$	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
$52$		−	9.46410i		−	1.31243i
$53$	−0.169873	+	0.0980762i	−0.0233338	+	0.0134718i	−0.511622	−	0.859211i	$-0.670955\pi$
$53$	−0.169873	+	0.0980762i	−0.0233338	+	0.0134718i	0.488288	+	0.872683i	$0.337622\pi$
$54$	−5.19615	+	5.19615i	−0.707107	+	0.707107i
$55$	−1.46410			−0.197419
$56$	−3.26795	−	6.73205i	−0.436698	−	0.899608i
$57$	14.1962			1.88033
$58$	10.4641	−	10.4641i	1.37400	−	1.37400i
$59$	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	$0.233664\pi$
$60$	3.46410			0.447214
$61$	−2.13397	+	3.69615i	−0.273227	+	0.473244i	−0.969686	−	0.244353i	$-0.921424\pi$
$61$	−2.13397	+	3.69615i	−0.273227	+	0.473244i	0.696459	+	0.717597i	$0.254758\pi$
$62$	−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
$66$	0.928203	+	3.46410i	0.114254	+	0.426401i
$67$	−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	$-0.411659\pi$
$68$	−1.26795	−	2.19615i	−0.153761	−	0.266323i
$69$	10.2679			1.23612
$70$	0.267949	−	3.73205i	0.0320261	−	0.446065i
$71$			5.26795i			0.625191i	0.949886	+	0.312595i	$0.101198\pi$
$71$			5.26795i			0.625191i	−0.949886	+	0.312595i	$0.898802\pi$
$72$		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	$0.572382\pi$
$74$	0.732051	+	2.73205i	0.0850992	+	0.317594i
$75$	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	0.712494	−	0.701678i	$-0.247566\pi$
$79$	4.09808	+	2.36603i	0.461070	+	0.266199i	−0.251424	+	0.967877i	$0.580899\pi$
$80$	2.00000	−	3.46410i	0.223607	−	0.387298i
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	−5.19615	+	5.19615i	−0.573819	+	0.573819i
$83$			14.6603i			1.60917i	0.593836	+	0.804586i	$0.297613\pi$
$83$			14.6603i			1.60917i	−0.593836	+	0.804586i	$0.702387\pi$
$84$	−9.00000	+	1.73205i	−0.981981	+	0.188982i
$85$		−	1.26795i		−	0.137528i
$86$	−3.92820	−	3.92820i	−0.423589	−	0.423589i
$87$	−9.06218	−	15.6962i	−0.971567	−	1.68280i
$88$	4.00000	+	1.07180i	0.426401	+	0.114254i
$89$	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
$94$	3.46410	−	0.928203i	0.357295	−	0.0957369i
$95$	7.09808	−	4.09808i	0.728247	−	0.420454i
$96$	−9.46410	−	2.53590i	−0.965926	−	0.258819i
$97$			3.46410i			0.351726i	0.984415	+	0.175863i	$0.0562716\pi$
$97$			3.46410i			0.351726i	−0.984415	+	0.175863i	$0.943728\pi$
$98$	1.16987	+	9.83013i	0.118175	+	0.992993i
$99$		0			0
$100$	1.73205	−	1.00000i	0.173205	−	0.100000i
$101$	−5.59808	−	9.69615i	−0.557029	−	0.964803i	−0.997743	−	0.0671552i	$-0.978608\pi$
$101$	−5.59808	−	9.69615i	−0.557029	−	0.964803i	0.440713	−	0.897648i	$-0.354726\pi$
$102$	−3.00000	+	0.803848i	−0.297044	+	0.0795928i
$103$	−1.33013	+	2.30385i	−0.131061	+	0.227005i	−0.924086	−	0.382185i	$-0.875172\pi$
$103$	−1.33013	+	2.30385i	−0.131061	+	0.227005i	0.793025	+	0.609190i	$0.208505\pi$
$104$	−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	$0.276538\pi$
$108$	10.3923			1.00000
$109$	15.0622	−	8.69615i	1.44269	−	0.832940i	0.444666	−	0.895696i	$-0.353322\pi$
$109$	15.0622	−	8.69615i	1.44269	−	0.832940i	0.998029	+	0.0627561i	$0.0199890\pi$
$110$	1.46410	+	1.46410i	0.139597	+	0.139597i
$111$	3.46410			0.328798
$112$	−3.46410	+	10.0000i	−0.327327	+	0.944911i
$113$	−3.26795			−0.307423			−0.153711	−	0.988116i	$-0.549123\pi$
$113$	−3.26795			−0.307423			−0.153711	+	0.988116i	$0.549123\pi$
$114$	−14.1962	−	14.1962i	−1.32959	−	1.32959i
$115$	5.13397	−	2.96410i	0.478746	−	0.276404i
$116$	−20.9282			−1.94313
$117$		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
$122$	5.83013	−	1.56218i	0.527835	−	0.141433i
$123$	4.50000	+	7.79423i	0.405751	+	0.702782i
$124$	3.80385	−	2.19615i	0.341596	−	0.197220i
$125$	1.00000			0.0894427
$126$		0			0
$127$			15.4641i			1.37222i	0.727499	+	0.686109i	$0.240683\pi$
$127$			15.4641i			1.37222i	−0.727499	+	0.686109i	$0.759317\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$	−5.89230	+	3.40192i	−0.518789	+	0.299523i
$130$	−6.46410	+	1.73205i	−0.566939	+	0.151911i
$131$	−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
$136$	−0.928203	+	3.46410i	−0.0795928	+	0.297044i
$137$	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	$0.655761\pi$
$138$	−10.2679	−	10.2679i	−0.874066	−	0.874066i
$139$			9.46410i			0.802735i	0.915917	+	0.401367i	$0.131465\pi$
$139$			9.46410i			0.802735i	−0.915917	+	0.401367i	$0.868535\pi$
$140$	−4.00000	+	3.46410i	−0.338062	+	0.292770i
$141$		−	4.39230i		−	0.369899i
$142$	5.26795	−	5.26795i	0.442076	−	0.442076i
$143$	−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	0.410036	−	0.912070i	$-0.365516\pi$
$149$	−2.13397	−	1.23205i	−0.174822	−	0.100934i	−0.584858	+	0.811136i	$0.698850\pi$
$150$	−0.633975	−	2.36603i	−0.0517638	−	0.193185i
$151$	5.02628	−	2.90192i	0.409033	−	0.236155i	−0.281341	−	0.959608i	$-0.590779\pi$
$151$	5.02628	−	2.90192i	0.409033	−	0.236155i	0.690374	+	0.723453i	$0.257446\pi$
$152$	−22.3923	+	6.00000i	−1.81626	+	0.486664i
$153$		0			0
$154$	−4.53590	−	3.07180i	−0.365513	−	0.247532i
$155$	2.19615			0.176399
$156$	8.19615	+	14.1962i	0.656217	+	1.13660i
$157$	−1.26795	−	2.19615i	−0.101193	−	0.175272i	0.810983	−	0.585069i	$-0.198933\pi$
$157$	−1.26795	−	2.19615i	−0.101193	−	0.175272i	−0.912177	+	0.409797i	$0.865599\pi$
$158$	−1.73205	−	6.46410i	−0.137795	−	0.514256i
$159$	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	$0.0385779\pi$
$164$	10.3923			0.811503
$165$	2.19615	−	1.26795i	0.170970	−	0.0987097i
$166$	14.6603	−	14.6603i	1.13786	−	1.13786i
$167$	−3.33975			−0.258437			−0.129219	−	0.991616i	$-0.541247\pi$
$167$	−3.33975			−0.258437			−0.129219	+	0.991616i	$0.541247\pi$
$168$	10.7321	+	7.26795i	0.827996	+	0.560734i
$169$	9.39230			0.722485
$170$	−1.26795	+	1.26795i	−0.0972473	+	0.0972473i
$171$		0			0
$172$			7.85641i			0.599045i
$173$	−0.803848	+	1.39230i	−0.0611154	+	0.105855i	−0.894964	−	0.446138i	$-0.852799\pi$
$173$	−0.803848	+	1.39230i	−0.0611154	+	0.105855i	0.833849	+	0.551993i	$0.186132\pi$
$174$	−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
$178$	−5.36603	−	20.0263i	−0.402201	−	1.50103i
$179$	−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	$-0.520504\pi$
$181$	−1.73205			−0.128742			−0.0643712	+	0.997926i	$0.520504\pi$
$182$	15.9282	−	7.73205i	1.18068	−	0.573138i
$183$		−	7.39230i		−	0.546455i
$184$	−16.1962	+	4.33975i	−1.19400	+	0.319930i
$185$	1.73205	−	1.00000i	0.127343	−	0.0735215i
$186$	−1.39230	−	5.19615i	−0.102089	−	0.381000i
$187$	−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	$-0.989204\pi$
$191$	−21.1244	−	12.1962i	−1.52850	−	0.882483i	−0.529080	−	0.848572i	$-0.677463\pi$
$192$	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	$0.999523\pi$
$194$	3.46410	−	3.46410i	0.248708	−	0.248708i
$195$			8.19615i			0.586939i
$196$	8.66025	−	11.0000i	0.618590	−	0.785714i
$197$		−	4.92820i		−	0.351120i	−0.984469	−	0.175560i	$-0.943826\pi$
$197$		−	4.92820i		−	0.351120i	0.984469	−	0.175560i	$-0.0561736\pi$
$198$		0			0
$199$	9.00000	+	15.5885i	0.637993	+	1.10504i	0.985873	+	0.167497i	$0.0535685\pi$
$199$	9.00000	+	15.5885i	0.637993	+	1.10504i	−0.347879	+	0.937539i	$0.613098\pi$
$200$	−2.73205	−	0.732051i	−0.193185	−	0.0517638i
$201$	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
$206$	3.63397	−	0.973721i	0.253191	−	0.0678423i
$207$		0			0
$208$	18.9282			1.31243
$209$		−	12.0000i		−	0.830057i
$210$	2.83013	+	5.83013i	0.195297	+	0.402317i
$211$	−18.5885			−1.27968			−0.639841	−	0.768507i	$-0.721000\pi$
$211$	−18.5885			−1.27968			−0.639841	+	0.768507i	$0.721000\pi$
$212$	−0.196152	−	0.339746i	−0.0134718	−	0.0233338i
$213$	−4.56218	−	7.90192i	−0.312595	−	0.541431i
$214$	9.56218	−	2.56218i	0.653657	−	0.175147i
$215$	−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
$220$		−	2.92820i		−	0.197419i
$221$	5.19615	−	3.00000i	0.349531	−	0.201802i
$222$	−3.46410	−	3.46410i	−0.232495	−	0.232495i
$223$	13.8564			0.927894			0.463947	−	0.885863i	$-0.346433\pi$
$223$	13.8564			0.927894			0.463947	+	0.885863i	$0.346433\pi$
$224$	13.4641	−	6.53590i	0.899608	−	0.436698i
$225$		0			0
$226$	3.26795	+	3.26795i	0.217381	+	0.217381i
$227$	−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	$0.387165\pi$
$228$			28.3923i			1.88033i
$229$	7.73205	−	13.3923i	0.510948	−	0.884988i	−0.488971	−	0.872300i	$-0.662628\pi$
$229$	7.73205	−	13.3923i	0.510948	−	0.884988i	0.999919	−	0.0126885i	$-0.00403898\pi$
$230$	−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
$236$	4.73205	+	8.19615i	0.308030	+	0.533524i
$237$	−8.19615			−0.532397
$238$	2.66025	−	3.92820i	0.172439	−	0.254628i
$239$			1.80385i			0.116681i	0.998297	+	0.0583406i	$0.0185809\pi$
$239$			1.80385i			0.116681i	−0.998297	+	0.0583406i	$0.981419\pi$
$240$			6.92820i			0.447214i
$241$	−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	$0.414763\pi$
$242$	−12.0981	+	3.24167i	−0.777694	+	0.208382i
$243$		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
$248$	−6.00000	−	1.60770i	−0.381000	−	0.102089i
$249$	−12.6962	−	21.9904i	−0.804586	−	1.39358i
$250$	−1.00000	−	1.00000i	−0.0632456	−	0.0632456i
$251$		−	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
$254$	15.4641	−	15.4641i	0.970304	−	0.970304i
$255$	1.09808	+	1.90192i	0.0687642	+	0.119103i
$256$	16.0000			1.00000
$257$	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
$262$	4.39230	+	16.3923i	0.271357	+	1.01272i
$263$	−13.9186	+	8.03590i	−0.858257	+	0.495515i	−0.863428	−	0.504472i	$-0.831687\pi$
$263$	−13.9186	+	8.03590i	−0.858257	+	0.495515i	0.00517143	+	0.999987i	$0.498354\pi$
$264$	−6.92820	+	1.85641i	−0.426401	+	0.114254i
$265$		−	0.196152i		−	0.0120495i
$266$	30.5885	+	2.19615i	1.87550	+	0.134655i
$267$	−25.3923			−1.55398
$268$	19.7321	−	11.3923i	1.20533	−	0.695896i
$269$	4.33013	+	7.50000i	0.264013	+	0.457283i	0.967304	−	0.253618i	$-0.0816206\pi$
$269$	4.33013	+	7.50000i	0.264013	+	0.457283i	−0.703292	+	0.710901i	$0.748287\pi$
$270$	−1.90192	−	7.09808i	−0.115747	−	0.431975i
$271$	−7.09808	+	12.2942i	−0.431177	+	0.746821i	−0.996975	−	0.0777230i	$-0.975235\pi$
$271$	−7.09808	+	12.2942i	−0.431177	+	0.746821i	0.565798	+	0.824544i	$0.308568\pi$
$272$	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
$276$			20.5359i			1.23612i
$277$	−1.90192	+	1.09808i	−0.114276	+	0.0659770i	−0.556048	−	0.831150i	$-0.687683\pi$
$277$	−1.90192	+	1.09808i	−0.114276	+	0.0659770i	0.441773	+	0.897127i	$0.354350\pi$
$278$	9.46410	−	9.46410i	0.567619	−	0.567619i
$279$		0			0
$280$	7.46410	+	0.535898i	0.446065	+	0.0320261i
$281$	21.8564			1.30384			0.651922	−	0.758286i	$-0.273963\pi$
$281$	21.8564			1.30384			0.651922	+	0.758286i	$0.273963\pi$
$282$	−4.39230	+	4.39230i	−0.261558	+	0.261558i
$283$	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	$0.300502\pi$
$284$	−10.5359			−0.625191
$285$	−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
$290$	3.83013	+	14.2942i	0.224913	+	0.839386i
$291$	−3.00000	−	5.19615i	−0.175863	−	0.304604i
$292$	−11.6603	−	20.1962i	−0.682365	−	1.18189i
$293$	13.8564			0.809500			0.404750	−	0.914427i	$-0.367359\pi$
$293$	13.8564			0.809500			0.404750	+	0.914427i	$0.367359\pi$
$294$	−10.2679	−	13.7321i	−0.598839	−	0.800869i
$295$			4.73205i			0.275511i
$296$	−5.46410	+	1.46410i	−0.317594	+	0.0850992i
$297$	6.58846	−	3.80385i	0.382301	−	0.220722i
$298$	0.901924	+	3.36603i	0.0522470	+	0.194989i
$299$	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
$304$	28.3923	+	16.3923i	1.62841	+	0.940163i
$305$	−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	$0.944083\pi$
$308$	1.46410	+	7.60770i	0.0834249	+	0.433489i
$309$		−	4.60770i		−	0.262123i
$310$	−2.19615	−	2.19615i	−0.124733	−	0.124733i
$311$	1.90192	+	3.29423i	0.107848	+	0.186799i	0.914898	−	0.403684i	$-0.132271\pi$
$311$	1.90192	+	3.29423i	0.107848	+	0.186799i	−0.807050	+	0.590483i	$0.798937\pi$
$312$	6.00000	−	22.3923i	0.339683	−	1.26771i
$313$	−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	0.708168	−	0.706044i	$-0.249522\pi$
$317$	8.02628	+	4.63397i	0.450801	+	0.260270i	−0.257368	+	0.966314i	$0.582855\pi$
$318$	−0.464102	+	0.124356i	−0.0260255	+	0.00697352i
$319$	−13.2679	+	7.66025i	−0.742863	+	0.428892i
$320$	6.92820	+	4.00000i	0.387298	+	0.223607i
$321$		−	12.1244i		−	0.676716i
$322$	22.1244	+	1.58846i	1.23294	+	0.0885213i
$323$	10.3923			0.578243
$324$	−15.5885	+	9.00000i	−0.866025	+	0.500000i
$325$	2.36603	+	4.09808i	0.131243	+	0.227320i
$326$	−13.6603	+	3.66025i	−0.756571	+	0.202723i
$327$	−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	$-0.0481256\pi$
$332$	−29.3205			−1.60917
$333$		0			0
$334$	3.33975	+	3.33975i	0.182743	+	0.182743i
$335$	11.3923			0.622428
$336$	−3.46410	−	18.0000i	−0.188982	−	0.981981i
$337$	−28.9808			−1.57868			−0.789341	−	0.613955i	$-0.789578\pi$
$337$	−28.9808			−1.57868			−0.789341	+	0.613955i	$0.789578\pi$
$338$	−9.39230	−	9.39230i	−0.510874	−	0.510874i
$339$	4.90192	−	2.83013i	0.266236	−	0.153711i
$340$	2.53590			0.137528
$341$	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
$346$	2.19615	−	0.588457i	0.118066	−	0.0316357i
$347$	−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	$0.986553\pi$
$348$	31.3923	−	18.1244i	1.68280	−	0.971567i
$349$	−34.5167			−1.84763			−0.923817	−	0.382834i	$-0.874948\pi$
$349$	−34.5167			−1.84763			−0.923817	+	0.382834i	$0.874948\pi$
$350$	3.09808	+	2.09808i	0.165599	+	0.112147i
$351$			24.5885i			1.31243i
$352$	−2.14359	+	8.00000i	−0.114254	+	0.426401i
$353$	−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	$0.957983\pi$
$354$	11.1962	−	3.00000i	0.595069	−	0.159448i
$355$	−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	−0.290372	−	0.956914i	$-0.593779\pi$
$359$	−23.9545	−	13.8301i	−1.26427	−	0.729926i	−0.973898	+	0.226988i	$0.927112\pi$
$360$		0			0
$361$	24.0885	+	41.7224i	1.26781	+	2.19592i
$362$	1.73205	+	1.73205i	0.0910346	+	0.0910346i
$363$			15.3397i			0.805128i
$364$	−23.6603	−	8.19615i	−1.24013	−	0.429595i
$365$		−	11.6603i		−	0.610326i
$366$	−7.39230	+	7.39230i	−0.386402	+	0.386402i
$367$	−9.86603	−	17.0885i	−0.515002	−	0.892010i	−0.999848	−	0.0174107i	$-0.994458\pi$
$367$	−9.86603	−	17.0885i	−0.515002	−	0.892010i	0.484846	−	0.874599i	$-0.338876\pi$
$368$	20.5359	+	11.8564i	1.07051	+	0.618058i
$369$		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	0.479045	−	0.877790i	$-0.340983\pi$
$373$	−0.803848	−	0.464102i	−0.0416216	−	0.0240303i	−0.520666	+	0.853760i	$0.674316\pi$
$374$	0.679492	+	2.53590i	0.0351357	+	0.131128i
$375$	−1.50000	+	0.866025i	−0.0774597	+	0.0447214i
$376$	1.85641	+	6.92820i	0.0957369	+	0.357295i
$377$		−	49.5167i		−	2.55024i
$378$	8.49038	+	17.4904i	0.436698	+	0.899608i
$379$	−26.4449			−1.35838			−0.679191	−	0.733962i	$-0.737669\pi$
$379$	−26.4449			−1.35838			−0.679191	+	0.733962i	$0.737669\pi$
$380$	8.19615	+	14.1962i	0.420454	+	0.728247i
$381$	−13.3923	−	23.1962i	−0.686109	−	1.18837i
$382$	8.92820	+	33.3205i	0.456807	+	1.70483i
$383$	8.59808	−	14.8923i	0.439341	−	0.760961i	−0.558298	−	0.829641i	$-0.688545\pi$
$383$	8.59808	−	14.8923i	0.439341	−	0.760961i	0.997639	+	0.0686795i	$0.0218786\pi$
$384$	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
$388$	−6.92820			−0.351726
$389$	21.7128	−	12.5359i	1.10088	−	0.635595i	0.164430	−	0.986389i	$-0.447421\pi$
$389$	21.7128	−	12.5359i	1.10088	−	0.635595i	0.936453	+	0.350793i	$0.114088\pi$
$390$	8.19615	−	8.19615i	0.415028	−	0.415028i
$391$	7.51666			0.380134
$392$	−19.6603	+	2.33975i	−0.992993	+	0.118175i
$393$	20.7846			1.04844
$394$	−4.92820	+	4.92820i	−0.248279	+	0.248279i
$395$	−4.09808	+	2.36603i	−0.206197	+	0.119048i
$396$		0			0
$397$	13.3923	−	23.1962i	0.672141	−	1.16418i	−0.305155	−	0.952303i	$-0.598708\pi$
$397$	13.3923	−	23.1962i	0.672141	−	1.16418i	0.977296	−	0.211879i	$-0.0679583\pi$
$398$	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	$0.234449\pi$
$402$	−7.22243	−	26.9545i	−0.360222	−	1.34437i
$403$	5.19615	+	9.00000i	0.258839	+	0.448322i
$404$	19.3923	−	11.1962i	0.964803	−	0.557029i
$405$	−9.00000			−0.447214
$406$	−17.0981	−	35.2224i	−0.848563	−	1.74806i
$407$		−	2.92820i		−	0.145146i
$408$	−1.60770	−	6.00000i	−0.0795928	−	0.297044i
$409$	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	$0.162686\pi$
$410$	−1.90192	−	7.09808i	−0.0939293	−	0.350549i
$411$	−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
$416$	−18.9282	−	18.9282i	−0.928032	−	0.928032i
$417$	−8.19615	−	14.1962i	−0.401367	−	0.695189i
$418$	−12.0000	+	12.0000i	−0.586939	+	0.586939i
$419$			11.3205i			0.553043i	0.961008	+	0.276522i	$0.0891817\pi$
$419$			11.3205i			0.553043i	−0.961008	+	0.276522i	$0.910818\pi$
$420$	3.00000	−	8.66025i	0.146385	−	0.422577i
$421$			21.2487i			1.03560i	0.855502	+	0.517799i	$0.173249\pi$
$421$			21.2487i			1.03560i	−0.855502	+	0.517799i	$0.826751\pi$
$422$	18.5885	+	18.5885i	0.904872	+	0.904872i
$423$		0			0
$424$	−0.143594	+	0.535898i	−0.00697352	+	0.0260255i
$425$	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
$430$	5.36603	−	1.43782i	0.258773	−	0.0693379i
$431$	−6.92820	+	4.00000i	−0.333720	+	0.192673i	−0.657491	−	0.753462i	$-0.728382\pi$
$431$	−6.92820	+	4.00000i	−0.333720	+	0.192673i	0.323772	+	0.946135i	$0.395049\pi$
$432$			20.7846i			1.00000i
$433$		−	28.9808i		−	1.39273i	−0.717689	−	0.696363i	$-0.754800\pi$
$433$		−	28.9808i		−	1.39273i	0.717689	−	0.696363i	$-0.245200\pi$
$434$	6.80385	+	4.60770i	0.326595	+	0.221176i
$435$	18.1244			0.868996
$436$	17.3923	+	30.1244i	0.832940	+	1.44269i
$437$	24.2942	+	42.0788i	1.16215	+	2.01290i
$438$	−27.5885	+	7.39230i	−1.31823	+	0.353218i
$439$	6.92820	−	12.0000i	0.330665	−	0.572729i	−0.651977	−	0.758238i	$-0.726060\pi$
$439$	6.92820	−	12.0000i	0.330665	−	0.572729i	0.982642	+	0.185510i	$0.0593936\pi$
$440$	−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	$0.219845\pi$
$444$			6.92820i			0.328798i
$445$	−12.6962	+	7.33013i	−0.601855	+	0.347481i
$446$	−13.8564	−	13.8564i	−0.656120	−	0.656120i
$447$	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
$452$		−	6.53590i		−	0.307423i
$453$	−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	$0.767184\pi$
$458$	−21.1244	+	5.66025i	−0.987076	+	0.264486i
$459$	3.29423	+	5.70577i	0.153761	+	0.266323i
$460$	5.92820	+	10.2679i	0.276404	+	0.478746i
$461$	10.1436			0.472434			0.236217	−	0.971700i	$-0.424092\pi$
$461$	10.1436			0.472434			0.236217	+	0.971700i	$0.424092\pi$
$462$	9.46410	+	0.679492i	0.440310	+	0.0316128i
$463$		−	19.3923i		−	0.901237i	−0.892717	−	0.450618i	$-0.851204\pi$
$463$		−	19.3923i		−	0.901237i	0.892717	−	0.450618i	$-0.148796\pi$
$464$		−	41.8564i		−	1.94313i
$465$	−3.29423	+	1.90192i	−0.152766	+	0.0881996i
$466$	−7.19615	+	1.92820i	−0.333355	+	0.0893223i
$467$	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
$472$	3.46410	−	12.9282i	0.159448	−	0.595069i
$473$	2.87564	+	4.98076i	0.132222	+	0.229016i
$474$	8.19615	+	8.19615i	0.376462	+	0.376462i
$475$			8.19615i			0.376065i
$476$	−6.58846	+	1.26795i	−0.301981	+	0.0581164i
$477$		0			0
$478$	1.80385	−	1.80385i	0.0825061	−	0.0825061i
$479$	2.83013	+	4.90192i	0.129312	+	0.223975i	0.923410	−	0.383815i	$-0.125390\pi$
$479$	2.83013	+	4.90192i	0.129312	+	0.223975i	−0.794098	+	0.607789i	$0.792057\pi$
$480$	6.92820	−	6.92820i	0.316228	−	0.316228i
$481$	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	0.0725939	−	0.997362i	$-0.476872\pi$
$487$	21.4641	−	12.3923i	0.972631	−	0.561549i	0.900037	+	0.435813i	$0.143539\pi$
$488$	3.12436	+	11.6603i	0.141433	+	0.527835i
$489$			17.3205i			0.783260i
$490$	−9.09808	−	3.90192i	−0.411009	−	0.176271i
$491$	−26.7321			−1.20640			−0.603200	−	0.797590i	$-0.706108\pi$
$491$	−26.7321			−1.20640			−0.603200	+	0.797590i	$0.706108\pi$
$492$	−15.5885	+	9.00000i	−0.702782	+	0.405751i
$493$	−6.63397	−	11.4904i	−0.298779	−	0.517501i
$494$	−14.1962	−	52.9808i	−0.638715	−	2.38372i
$495$		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	$0.999556\pi$
$500$			2.00000i			0.0894427i
$501$	5.00962	−	2.89230i	0.223813	−	0.129219i
$502$	−15.8038	+	15.8038i	−0.705360	+	0.705360i
$503$	2.66025			0.118615			0.0593074	−	0.998240i	$-0.481111\pi$
$503$	2.66025			0.118615			0.0593074	+	0.998240i	$0.481111\pi$
$504$		0			0
$505$	11.1962			0.498222
$506$	−8.67949	+	8.67949i	−0.385850	+	0.385850i
$507$	−14.0885	+	8.13397i	−0.625690	+	0.361242i
$508$	−30.9282			−1.37222
$509$	−14.2583	+	24.6962i	−0.631989	+	1.09464i	0.355155	+	0.934807i	$0.384428\pi$
$509$	−14.2583	+	24.6962i	−0.631989	+	1.09464i	−0.987145	+	0.159830i	$0.948905\pi$
$510$	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
$514$	−2.19615	−	8.19615i	−0.0968681	−	0.361517i
$515$	−1.33013	−	2.30385i	−0.0586124	−	0.101520i
$516$	−6.80385	−	11.7846i	−0.299523	−	0.518789i
$517$	−3.71281			−0.163289
$518$	7.46410	+	0.535898i	0.327954	+	0.0235460i
$519$		−	2.78461i		−	0.122231i
$520$	−3.46410	−	12.9282i	−0.151911	−	0.566939i
$521$	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
$528$	8.78461	+	5.07180i	0.382301	+	0.220722i
$529$	6.07180	+	10.5167i	0.263991	+	0.457246i
$530$	−0.196152	+	0.196152i	−0.00852032	+	0.00852032i
$531$		0			0
$532$	−28.3923	−	32.7846i	−1.23096	−	1.42139i
$533$			24.5885i			1.06504i
$534$	25.3923	+	25.3923i	1.09883	+	1.09883i
$535$	−3.50000	−	6.06218i	−0.151318	−	0.262091i
$536$	−31.1244	−	8.33975i	−1.34437	−	0.360222i
$537$	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	$0.0921140\pi$
$541$	39.1865	+	22.6244i	1.68476	+	0.972697i	0.726341	+	0.687335i	$0.241219\pi$
$542$	19.3923	−	5.19615i	0.832971	−	0.223194i
$543$	2.59808	−	1.50000i	0.111494	−	0.0643712i
$544$	−6.92820	−	1.85641i	−0.297044	−	0.0795928i
$545$			17.3923i			0.745004i
$546$	−17.1962	+	25.3923i	−0.735927	+	1.08669i
$547$	1.00000			0.0427569			0.0213785	−	0.999771i	$-0.493195\pi$
$547$	1.00000			0.0427569			0.0213785	+	0.999771i	$0.493195\pi$
$548$	−21.4641	+	12.3923i	−0.916901	+	0.529373i
$549$		0			0
$550$	−2.00000	+	0.535898i	−0.0852803	+	0.0228508i
$551$	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
$556$	−18.9282			−0.802735
$557$	−36.1244	+	20.8564i	−1.53064	+	0.883714i	−0.531306	+	0.847180i	$0.678298\pi$
$557$	−36.1244	+	20.8564i	−1.53064	+	0.883714i	−0.999332	+	0.0365341i	$0.988368\pi$
$558$		0			0
$559$	−18.5885			−0.786208
$560$	−6.92820	−	8.00000i	−0.292770	−	0.338062i
$561$	3.21539			0.135754
$562$	−21.8564	−	21.8564i	−0.921957	−	0.921957i
$563$	−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	$0.446488\pi$
$564$	8.78461			0.369899
$565$	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	$0.210413\pi$
$570$	19.3923	−	5.19615i	0.812254	−	0.217643i
$571$	−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	$0.850582\pi$
$572$	12.0000	−	6.92820i	0.501745	−	0.289683i
$573$	42.2487			1.76497
$574$	8.49038	+	17.4904i	0.354382	+	0.730034i
$575$			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	$0.217694\pi$
$578$	21.0263	−	5.63397i	0.874578	−	0.234342i
$579$	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
$584$	−8.53590	+	31.8564i	−0.353218	+	1.31823i
$585$		0			0
$586$	−13.8564	−	13.8564i	−0.572403	−	0.572403i
$587$			9.46410i			0.390625i	0.980741	+	0.195313i	$0.0625722\pi$
$587$			9.46410i			0.390625i	−0.980741	+	0.195313i	$0.937428\pi$
$588$	−3.46410	+	24.0000i	−0.142857	+	0.989743i
$589$			18.0000i			0.741677i
$590$	4.73205	−	4.73205i	0.194815	−	0.194815i
$591$	4.26795	+	7.39230i	0.175560	+	0.304079i
$592$	6.92820	+	4.00000i	0.284747	+	0.164399i
$593$	−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
$598$	−10.2679	−	38.3205i	−0.419888	−	1.56704i
$599$	−13.2679	+	7.66025i	−0.542114	+	0.312989i	−0.745935	−	0.666019i	$-0.767997\pi$
$599$	−13.2679	+	7.66025i	−0.542114	+	0.312989i	0.203821	+	0.979008i	$0.434664\pi$
$600$	4.73205	−	1.26795i	0.193185	−	0.0517638i
$601$		−	1.60770i		−	0.0655793i	−0.999462	−	0.0327896i	$-0.989561\pi$
$601$		−	1.60770i		−	0.0655793i	0.999462	−	0.0327896i	$-0.0104391\pi$
$602$	−13.2224	+	6.41858i	−0.538906	+	0.261602i
$603$		0			0
$604$	5.80385	+	10.0526i	0.236155	+	0.409033i
$605$	4.42820	+	7.66987i	0.180032	+	0.311825i
$606$	−7.09808	−	26.4904i	−0.288340	−	1.07610i
$607$	15.5263	−	26.8923i	0.630192	−	1.09152i	−0.357320	−	0.933982i	$-0.616309\pi$
$607$	15.5263	−	26.8923i	0.630192	−	1.09152i	0.987512	−	0.157543i	$-0.0503573\pi$
$608$	−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	−0.871920	−	0.489648i	$-0.837125\pi$
$613$	−21.8827	+	12.6340i	−0.883833	+	0.510281i	−0.0119129	+	0.999929i	$0.503792\pi$
$614$	6.12436	−	6.12436i	0.247159	−	0.247159i
$615$	−9.00000			−0.362915
$616$	6.14359	−	9.07180i	0.247532	−	0.365513i
$617$	28.9282			1.16461			0.582303	−	0.812972i	$-0.302152\pi$
$617$	28.9282			1.16461			0.582303	+	0.812972i	$0.302152\pi$
$618$	−4.60770	+	4.60770i	−0.185349	+	0.185349i
$619$	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	$0.284475\pi$
$620$			4.39230i			0.176399i
$621$	−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
$626$	6.33975	+	23.6603i	0.253387	+	0.945654i
$627$	10.3923	+	18.0000i	0.415029	+	0.718851i
$628$	4.39230	−	2.53590i	0.175272	−	0.101193i
$629$	2.53590			0.101113
$630$		0			0
$631$		−	21.4641i		−	0.854472i	−0.904140	−	0.427236i	$-0.859487\pi$
$631$		−	21.4641i		−	0.854472i	0.904140	−	0.427236i	$-0.140513\pi$
$632$	12.9282	−	3.46410i	0.514256	−	0.137795i
$633$	27.8827	−	16.0981i	1.10824	−	0.639841i
$634$	−3.39230	−	12.6603i	−0.134726	−	0.502803i
$635$	−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
$640$	−2.92820	−	10.9282i	−0.115747	−	0.431975i
$641$	−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	$-0.404958\pi$
$642$	−12.1244	+	12.1244i	−0.478510	+	0.478510i
$643$			19.6077i			0.773252i	0.922237	+	0.386626i	$0.126360\pi$
$643$			19.6077i			0.773252i	−0.922237	+	0.386626i	$0.873640\pi$
$644$	−20.5359	−	23.7128i	−0.809228	−	0.934416i
$645$		−	6.80385i		−	0.267901i
$646$	−10.3923	−	10.3923i	−0.408880	−	0.408880i
$647$	−13.7942	−	23.8923i	−0.542307	−	0.939303i	−0.998771	−	0.0495615i	$-0.984218\pi$
$647$	−13.7942	−	23.8923i	−0.542307	−	0.939303i	0.456464	−	0.889742i	$-0.349116\pi$
$648$	24.5885	+	6.58846i	0.965926	+	0.258819i
$649$	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	0.785870	−	0.618392i	$-0.212216\pi$
$653$	16.4378	+	9.49038i	0.643262	+	0.371387i	−0.142608	+	0.989779i	$0.545549\pi$
$654$	41.1506	−	11.0263i	1.60912	−	0.431162i
$655$	10.3923	−	6.00000i	0.406061	−	0.234439i
$656$			20.7846i			0.811503i
$657$		0			0
$658$	0.679492	−	9.46410i	0.0264894	−	0.368949i
$659$	−17.8038			−0.693539			−0.346770	−	0.937950i	$-0.612721\pi$
$659$	−17.8038			−0.693539			−0.346770	+	0.937950i	$0.612721\pi$
$660$	2.53590	+	4.39230i	0.0987097	+	0.170970i
$661$	1.79423	+	3.10770i	0.0697874	+	0.120875i	0.898808	−	0.438343i	$-0.144435\pi$
$661$	1.79423	+	3.10770i	0.0697874	+	0.120875i	−0.829020	+	0.559219i	$0.811101\pi$
$662$	−31.0526	+	8.32051i	−1.20689	+	0.323386i
$663$	−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
$668$		−	6.67949i		−	0.258437i
$669$	−20.7846	+	12.0000i	−0.803579	+	0.463947i
$670$	−11.3923	−	11.3923i	−0.440123	−	0.440123i
$671$	−6.24871			−0.241229
$672$	−14.5359	+	21.4641i	−0.560734	+	0.827996i
$673$	38.7846			1.49504			0.747518	−	0.664241i	$-0.231245\pi$
$673$	38.7846			1.49504			0.747518	+	0.664241i	$0.231245\pi$
$674$	28.9808	+	28.9808i	1.11630	+	1.11630i
$675$	−4.50000	+	2.59808i	−0.173205	+	0.100000i
$676$			18.7846i			0.722485i
$677$	18.2942	−	31.6865i	0.703104	−	1.21781i	−0.264267	−	0.964450i	$-0.585130\pi$
$677$	18.2942	−	31.6865i	0.703104	−	1.21781i	0.967371	−	0.253363i	$-0.0815367\pi$
$678$	−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
$682$	−4.39230	+	1.17691i	−0.168190	+	0.0450664i
$683$	−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
$686$	25.5885	+	5.58846i	0.976972	+	0.213368i
$687$			26.7846i			1.02190i
$688$	−15.7128			−0.599045
$689$	0.803848	−	0.464102i	0.0306242	−	0.0176809i
$690$	14.0263	−	3.75833i	0.533971	−	0.143077i
$691$	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
$696$	−49.5167	−	13.2679i	−1.87692	−	0.502920i
$697$	3.29423	+	5.70577i	0.124778	+	0.216122i
$698$	34.5167	+	34.5167i	1.30647	+	1.30647i
$699$			9.12436i			0.345115i
$700$	−1.00000	−	5.19615i	−0.0377964	−	0.196396i
$701$		−	33.7846i		−	1.27603i	−0.770025	−	0.638014i	$-0.779756\pi$
$701$		−	33.7846i		−	1.27603i	0.770025	−	0.638014i	$-0.220244\pi$
$702$	24.5885	−	24.5885i	0.928032	−	0.928032i
$703$	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	0.00973296	−	0.999953i	$-0.496902\pi$
$709$	−22.6699	−	13.0885i	−0.851385	−	0.491547i	−0.861118	+	0.508405i	$0.830235\pi$
$710$	1.92820	+	7.19615i	0.0723642	+	0.270067i
$711$		0			0
$712$	40.0526	−	10.7321i	1.50103	−	0.402201i
$713$			13.0192i			0.487574i
$714$	−0.588457	+	8.19615i	−0.0220225	+	0.306733i
$715$	6.92820			0.259100
$716$	31.5167	−	18.1962i	1.17783	−	0.680022i
$717$	−1.56218	−	2.70577i	−0.0583406	−	0.101049i
$718$	10.1244	+	37.7846i	0.377838	+	1.41011i
$719$	−21.4641	+	37.1769i	−0.800476	+	1.38646i	0.118827	+	0.992915i	$0.462087\pi$
$719$	−21.4641	+	37.1769i	−0.800476	+	1.38646i	−0.919303	+	0.393550i	$0.871247\pi$
$720$		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
$724$		−	3.46410i		−	0.128742i
$725$	9.06218	−	5.23205i	0.336561	−	0.194313i
$726$	15.3397	−	15.3397i	0.569311	−	0.569311i
$727$	−25.0526			−0.929148			−0.464574	−	0.885534i	$-0.653793\pi$
$727$	−25.0526			−0.929148			−0.464574	+	0.885534i	$0.653793\pi$
$728$	15.4641	+	31.8564i	0.573138	+	1.18068i
$729$	−27.0000			−1.00000
$730$	−11.6603	+	11.6603i	−0.431565	+	0.431565i
$731$	−4.31347	+	2.49038i	−0.159539	+	0.0921101i
$732$	14.7846			0.546455
$733$	5.19615	−	9.00000i	0.191924	−	0.332423i	−0.753964	−	0.656916i	$-0.771861\pi$
$733$	5.19615	−	9.00000i	0.191924	−	0.332423i	0.945888	+	0.324494i	$0.105194\pi$
$734$	−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	$0.866223\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$	−67.1769			−2.46781
$742$	0.411543	−	0.607695i	0.0151082	−	0.0223092i
$743$		−	9.39230i		−	0.344570i	−0.985047	−	0.172285i	$-0.944885\pi$
$743$		−	9.39230i		−	0.344570i	0.985047	−	0.172285i	$-0.0551150\pi$
$744$	10.3923	−	2.78461i	0.381000	−	0.102089i
$745$	2.13397	−	1.23205i	0.0781828	−	0.0451388i
$746$	0.339746	+	1.26795i	0.0124390	+	0.0464229i
$747$		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	−0.490926	−	0.871201i	$-0.663341\pi$
$751$	−40.8564	−	23.5885i	−1.49087	−	0.860755i	−0.999945	+	0.0104462i	$0.996675\pi$
$752$	5.07180	−	8.78461i	0.184949	−	0.320342i
$753$	13.6865	+	23.7058i	0.498765	+	0.863886i
$754$	−49.5167	+	49.5167i	−1.80329	+	1.80329i
$755$			5.80385i			0.211224i
$756$	9.00000	−	25.9808i	0.327327	−	0.944911i
$757$		−	18.1962i		−	0.661350i	−0.943745	−	0.330675i	$-0.892724\pi$
$757$		−	18.1962i		−	0.661350i	0.943745	−	0.330675i	$-0.107276\pi$
$758$	26.4449	+	26.4449i	0.960521	+	0.960521i
$759$	7.51666	+	13.0192i	0.272837	+	0.472568i
$760$	6.00000	−	22.3923i	0.217643	−	0.812254i
$761$	−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
$766$	−23.4904	+	6.29423i	−0.848742	+	0.227420i
$767$	−19.3923	+	11.1962i	−0.700216	+	0.404270i
$768$	−24.0000	+	13.8564i	−0.866025	+	0.500000i
$769$		−	10.3923i		−	0.374756i	−0.982288	−	0.187378i	$-0.940001\pi$
$769$		−	10.3923i		−	0.374756i	0.982288	−	0.187378i	$-0.0599989\pi$
$770$	4.92820	−	2.39230i	0.177600	−	0.0862127i
$771$	−10.3923			−0.374270
$772$	24.0000	−	13.8564i	0.863779	−	0.498703i
$773$	24.2942	+	42.0788i	0.873803	+	1.51347i	0.858033	+	0.513595i	$0.171687\pi$
$773$	24.2942	+	42.0788i	0.873803	+	1.51347i	0.0157699	+	0.999876i	$0.494980\pi$
$774$		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
$780$	−16.3923			−0.586939
$781$	−6.67949	+	3.85641i	−0.239011	+	0.137993i
$782$	−7.51666	−	7.51666i	−0.268795	−	0.268795i
$783$	54.3731			1.94313
$784$	22.0000	+	17.3205i	0.785714	+	0.618590i
$785$	2.53590			0.0905101
$786$	−20.7846	−	20.7846i	−0.741362	−	0.741362i
$787$	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	$0.127272\pi$
$788$	9.85641			0.351120
$789$	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
$794$	−36.5885	+	9.80385i	−1.29848	+	0.347926i
$795$	0.169873	+	0.294229i	0.00602477	+	0.0104352i
$796$	−31.1769	+	18.0000i	−1.10504	+	0.637993i
$797$	5.32051			0.188462			0.0942310	−	0.995550i	$-0.469961\pi$
$797$	5.32051			0.188462			0.0942310	+	0.995550i	$0.469961\pi$
$798$	−47.7846	+	23.1962i	−1.69156	+	0.821135i
$799$		−	3.21539i		−	0.113752i
$800$	1.46410	−	5.46410i	0.0517638	−	0.193185i
$801$		0			0
$802$	11.5622	−	3.09808i	0.408275	−	0.109397i
$803$	−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
$808$	−30.5885	−	8.19615i	−1.07610	−	0.288340i
$809$	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	$0.728959\pi$
$810$	9.00000	+	9.00000i	0.316228	+	0.316228i
$811$			17.6603i			0.620135i	0.950714	+	0.310068i	$0.100352\pi$
$811$			17.6603i			0.620135i	−0.950714	+	0.310068i	$0.899648\pi$
$812$	−18.1244	+	52.3205i	−0.636040	+	1.83609i
$813$		−	24.5885i		−	0.862355i
$814$	−2.92820	+	2.92820i	−0.102633	+	0.102633i
$815$	5.00000	+	8.66025i	0.175142	+	0.303355i
$816$	−4.39230	+	7.60770i	−0.153761	+	0.266323i
$817$	−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	0.529920	−	0.848048i	$-0.322222\pi$
$821$	1.73205	+	1.00000i	0.0604490	+	0.0349002i	−0.469471	+	0.882948i	$0.655555\pi$
$822$	7.85641	+	29.3205i	0.274024	+	1.02267i
$823$	−20.3827	+	11.7679i	−0.710496	+	0.410205i	−0.811245	−	0.584707i	$-0.801209\pi$
$823$	−20.3827	+	11.7679i	−0.710496	+	0.410205i	0.100749	+	0.994912i	$0.467876\pi$
$824$	1.94744	+	7.26795i	0.0678423	+	0.253191i
$825$			2.53590i			0.0882886i
$826$	−9.92820	+	14.6603i	−0.345446	+	0.510095i
$827$	−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	0.703134	−	0.711057i	$-0.251783\pi$
$829$	−7.60770	−	13.1769i	−0.264226	−	0.457653i	−0.967361	+	0.253404i	$0.918450\pi$
$830$	5.36603	+	20.0263i	0.186257	+	0.695122i
$831$	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
$836$	24.0000			0.830057
$837$	−9.88269	+	5.70577i	−0.341596	+	0.197220i
$838$	11.3205	−	11.3205i	0.391060	−	0.391060i
$839$	−44.5359			−1.53755			−0.768775	−	0.639519i	$-0.779133\pi$
$839$	−44.5359			−1.53755			−0.768775	+	0.639519i	$0.779133\pi$
$840$	−11.6603	+	5.66025i	−0.402317	+	0.195297i
$841$	−80.4974			−2.77577
$842$	21.2487	−	21.2487i	0.732279	−	0.732279i
$843$	−32.7846	+	18.9282i	−1.12916	+	0.651922i
$844$		−	37.1769i		−	1.27968i
$845$	−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
$850$	−0.464102	−	1.73205i	−0.0159186	−	0.0594089i
$851$	5.92820	+	10.2679i	0.203216	+	0.351981i
$852$	15.8038	−	9.12436i	0.541431	−	0.312595i
$853$	−1.51666			−0.0519295			−0.0259647	−	0.999663i	$-0.508266\pi$
$853$	−1.51666			−0.0519295			−0.0259647	+	0.999663i	$0.508266\pi$
$854$	1.14359	−	15.9282i	0.0391330	−	0.545052i
$855$		0			0
$856$	5.12436	+	19.1244i	0.175147	+	0.653657i
$857$	−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	$0.386384\pi$
$858$	−4.39230	−	16.3923i	−0.149951	−	0.559624i
$859$	−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	0.155540	−	0.987830i	$-0.450288\pi$
$863$	−18.2776	−	10.5526i	−0.622176	−	0.359213i	−0.777716	+	0.628616i	$0.783622\pi$
$864$	20.7846	−	20.7846i	0.707107	−	0.707107i
$865$	−0.803848	−	1.39230i	−0.0273316	−	0.0473398i
$866$	−28.9808	+	28.9808i	−0.984806	+	0.984806i
$867$		−	26.6603i		−	0.905430i
$868$	−2.19615	−	11.4115i	−0.0745423	−	0.387333i
$869$			6.92820i			0.235023i
$870$	−18.1244	−	18.1244i	−0.614473	−	0.614473i
$871$	26.9545	+	46.6865i	0.913318	+	1.58191i
$872$	12.7321	−	47.5167i	0.431162	−	1.60912i
$873$		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	−0.275243	−	0.961375i	$-0.588758\pi$
$877$	−36.8827	−	21.2942i	−1.24544	−	0.719055i	−0.970196	+	0.242320i	$0.922092\pi$
$878$	−18.9282	+	5.07180i	−0.638796	+	0.171165i
$879$	−20.7846	+	12.0000i	−0.701047	+	0.404750i
$880$	5.85641			0.197419
$881$		−	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	$0.518564\pi$
$884$	6.00000	+	10.3923i	0.201802	+	0.349531i
$885$	−4.09808	−	7.09808i	−0.137755	−	0.238599i
$886$	9.56218	−	2.56218i	0.321248	−	0.0860780i
$887$	−20.1340	+	34.8731i	−0.676033	+	1.17092i	0.300133	+	0.953897i	$0.402969\pi$
$887$	−20.1340	+	34.8731i	−0.676033	+	1.17092i	−0.976166	+	0.217026i	$0.930364\pi$
$888$	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
$892$			27.7128i			0.927894i
$893$	18.0000	−	10.3923i	0.602347	−	0.347765i
$894$	−4.26795	−	4.26795i	−0.142742	−	0.142742i
$895$	18.1962			0.608230
$896$	13.0718	+	26.9282i	0.436698	+	0.899608i
$897$	−48.5885			−1.62232
$898$	−19.5359	−	19.5359i	−0.651921	−	0.651921i
$899$	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
$906$	13.7321	−	3.67949i	0.456217	−	0.122243i
$907$	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	$0.641278\pi$
$908$	−5.07180	−	8.78461i	−0.168313	−	0.291528i
$909$		0			0
$910$	−1.26795	+	17.6603i	−0.0420321	+	0.585432i
$911$		−	1.71281i		−	0.0567480i	−0.999597	−	0.0283740i	$-0.990967\pi$
$911$		−	1.71281i		−	0.0567480i	0.999597	−	0.0283740i	$-0.00903294\pi$
$912$	−56.7846			−1.88033
$913$	−18.5885	+	10.7321i	−0.615188	+	0.355179i
$914$	55.5167	−	14.8756i	1.83633	−	0.492043i
$915$	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	0.890643	−	0.454704i	$-0.150255\pi$
$919$	28.5622	+	16.4904i	0.942179	+	0.543967i	0.0515365	+	0.998671i	$0.483588\pi$
$920$	4.33975	−	16.1962i	0.143077	−	0.533971i
$921$	−5.30385	−	9.18653i	−0.174768	−	0.302707i
$922$	−10.1436	−	10.1436i	−0.334061	−	0.334061i
$923$		−	24.9282i		−	0.820522i
$924$	−8.78461	−	10.1436i	−0.288992	−	0.333700i
$925$			2.00000i			0.0657596i
$926$	−19.3923	+	19.3923i	−0.637271	+	0.637271i
$927$		0			0
$928$	−41.8564	+	41.8564i	−1.37400	+	1.37400i
$929$	−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
$934$	−10.3468	−	38.6147i	−0.338557	−	1.26351i
$935$	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	$0.927326\pi$
$938$	35.2942	+	23.9019i	1.15240	+	0.780425i
$939$	30.0000			0.979013
$940$	4.39230	−	2.53590i	0.143261	−	0.0827119i
$941$	−12.4641	−	21.5885i	−0.406318	−	0.703764i	0.588156	−	0.808748i	$-0.299854\pi$
$941$	−12.4641	−	21.5885i	−0.406318	−	0.703764i	−0.994474	+	0.104984i	$0.966521\pi$
$942$	−1.60770	−	6.00000i	−0.0523815	−	0.195491i
$943$	−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	$0.0926816\pi$
$948$		−	16.3923i		−	0.532397i
$949$	47.7846	−	27.5885i	1.55115	−	0.895559i
$950$	8.19615	−	8.19615i	0.265918	−	0.265918i
$951$	−16.0526			−0.520540
$952$	7.85641	+	5.32051i	0.254628	+	0.172439i
$953$	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
$956$	−3.60770			−0.116681
$957$	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
$962$	−3.46410	−	12.9282i	−0.111687	−	0.416822i
$963$		0			0
$964$	−7.85641	−	13.6077i	−0.253038	−	0.438274i
$965$	13.8564			0.446054
$966$	−34.5622	+	16.7776i	−1.11202	+	0.539809i
$967$		−	34.1769i		−	1.09906i	−0.835475	−	0.549528i	$-0.814808\pi$
$967$		−	34.1769i		−	1.09906i	0.835475	−	0.549528i	$-0.185192\pi$
$968$	−6.48334	−	24.1962i	−0.208382	−	0.777694i
$969$	−15.5885	+	9.00000i	−0.500773	+	0.289122i
$970$	1.26795	+	4.73205i	0.0407114	+	0.151937i
$971$	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
$976$	8.53590	−	14.7846i	0.273227	−	0.473244i
$977$	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	$0.599819\pi$
$978$	17.3205	−	17.3205i	0.553849	−	0.553849i
$979$			21.4641i			0.685996i
$980$	5.19615	+	13.0000i	0.165985	+	0.415270i
$981$		0			0
$982$	26.7321	+	26.7321i	0.853054	+	0.853054i
$983$	22.3301	+	38.6769i	0.712220	+	1.23360i	0.964022	+	0.265823i	$0.0856437\pi$
$983$	22.3301	+	38.6769i	0.712220	+	1.23360i	−0.251801	+	0.967779i	$0.581023\pi$
$984$	24.5885	+	6.58846i	0.783851	+	0.210032i
$985$	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	−0.304643	−	0.952467i	$-0.598537\pi$
$991$	11.5814	−	6.68653i	0.367896	−	0.212405i	0.672539	+	0.740062i	$0.265204\pi$
$992$	3.21539	−	12.0000i	0.102089	−	0.381000i
$993$			39.3731i			1.24947i
$994$	−8.60770	−	17.7321i	−0.273020	−	0.562426i
$995$	−18.0000			−0.570638
$996$	43.9808	−	25.3923i	1.39358	−	0.804586i
$997$	22.5622	+	39.0788i	0.714551	+	1.23764i	0.963132	+	0.269028i	$0.0867025\pi$
$997$	22.5622	+	39.0788i	0.714551	+	1.23764i	−0.248581	+	0.968611i	$0.579964\pi$
$998$	30.5885	−	8.19615i	0.968261	−	0.259445i
$999$	−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.a.131.1	✓	4
4.3	odd	2		1120.2.bz.a.271.1		4
7.3	odd	6		280.2.bj.d.171.2	yes	4
8.3	odd	2		280.2.bj.d.131.2	yes	4
8.5	even	2		1120.2.bz.d.271.2		4
28.3	even	6		1120.2.bz.d.591.2		4
56.3	even	6	inner	280.2.bj.a.171.2	yes	4
56.45	odd	6		1120.2.bz.a.591.1		4

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.50000 + 0.866025i) q^{3} +2.00000i q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.36603 + 0.633975i) q^{6} +(0.866025 - 2.50000i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.50000 + 0.866025i) q^{3} +2.00000i 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} +(1.36603 - 0.366025i) q^{10} +(0.732051 + 1.26795i) q^{11} +(-1.73205 - 3.00000i) q^{12} -4.73205 q^{13} +(-3.36603 + 1.63397i) q^{14} -1.73205i q^{15} -4.00000 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} +(-1.26795 + 4.73205i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(4.73205 + 4.73205i) q^{26} -5.19615i q^{27} +(5.00000 + 1.73205i) q^{28} +10.4641i q^{29} +(-1.73205 + 1.73205i) q^{30} +(-1.09808 - 1.90192i) q^{31} +(4.00000 + 4.00000i) 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} +(3.00000 + 11.1962i) q^{38} +(7.09808 - 4.09808i) q^{39} +(0.732051 + 2.73205i) q^{40} -5.19615i q^{41} +(3.63397 - 5.36603i) q^{42} +3.92820 q^{43} +(-2.53590 + 1.46410i) q^{44} +(2.16987 + 8.09808i) 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} -9.46410i q^{52} +(-0.169873 + 0.0980762i) q^{53} +(-5.19615 + 5.19615i) q^{54} -1.46410 q^{55} +(-3.26795 - 6.73205i) q^{56} +14.1962 q^{57} +(10.4641 - 10.4641i) q^{58} +(4.09808 - 2.36603i) q^{59} +3.46410 q^{60} +(-2.13397 + 3.69615i) q^{61} +(-0.803848 + 3.00000i) q^{62} -8.00000i q^{64} +(2.36603 - 4.09808i) q^{65} +(0.928203 + 3.46410i) q^{66} +(-5.69615 - 9.86603i) q^{67} +(-1.26795 - 2.19615i) q^{68} +10.2679 q^{69} +(0.267949 - 3.73205i) q^{70} +5.26795i q^{71} +(-10.0981 + 5.83013i) q^{73} +(0.732051 + 2.73205i) 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} +(2.00000 - 3.46410i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-5.19615 + 5.19615i) q^{82} +14.6603i q^{83} +(-9.00000 + 1.73205i) q^{84} -1.26795i q^{85} +(-3.92820 - 3.92820i) q^{86} +(-9.06218 - 15.6962i) q^{87} +(4.00000 + 1.07180i) 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} +(3.46410 - 0.928203i) q^{94} +(7.09808 - 4.09808i) q^{95} +(-9.46410 - 2.53590i) q^{96} +3.46410i q^{97} +(1.16987 + 9.83013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 6 q^{3} - 2 q^{5} + 6 q^{6} + 8 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 - 6 * q^3 - 2 * q^5 + 6 * q^6 + 8 * q^8	\( 4 q - 4 q^{2} - 6 q^{3} - 2 q^{5} + 6 q^{6} + 8 q^{8} + 2 q^{10} - 4 q^{11} - 12 q^{13} - 10 q^{14} - 16 q^{16} + 6 q^{17} - 18 q^{19} + 16 q^{22} - 24 q^{23} - 12 q^{24} - 2 q^{25} + 12 q^{26} + 20 q^{28} + 6 q^{31} + 16 q^{32} + 12 q^{33} + 12 q^{38} + 18 q^{39} - 4 q^{40} + 18 q^{42} - 12 q^{43} - 24 q^{44} + 26 q^{46} - 12 q^{47} + 24 q^{48} - 22 q^{49} + 2 q^{50} - 6 q^{51} - 18 q^{53} + 8 q^{55} - 20 q^{56} + 36 q^{57} + 28 q^{58} + 6 q^{59} - 12 q^{61} - 24 q^{62} + 6 q^{65} - 24 q^{66} - 2 q^{67} - 12 q^{68} + 48 q^{69} + 8 q^{70} - 30 q^{73} - 4 q^{74} + 6 q^{75} + 12 q^{76} + 36 q^{77} - 24 q^{78} + 6 q^{79} + 8 q^{80} + 18 q^{81} - 36 q^{84} + 12 q^{86} - 12 q^{87} + 16 q^{88} + 30 q^{89} - 6 q^{91} - 4 q^{92} - 18 q^{93} + 18 q^{95} - 24 q^{96} + 22 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 6 * q^3 - 2 * q^5 + 6 * q^6 + 8 * q^8 + 2 * q^10 - 4 * q^11 - 12 * q^13 - 10 * q^14 - 16 * q^16 + 6 * q^17 - 18 * q^19 + 16 * q^22 - 24 * q^23 - 12 * q^24 - 2 * q^25 + 12 * q^26 + 20 * q^28 + 6 * q^31 + 16 * q^32 + 12 * q^33 + 12 * q^38 + 18 * q^39 - 4 * q^40 + 18 * q^42 - 12 * q^43 - 24 * q^44 + 26 * q^46 - 12 * q^47 + 24 * q^48 - 22 * q^49 + 2 * q^50 - 6 * q^51 - 18 * q^53 + 8 * q^55 - 20 * q^56 + 36 * q^57 + 28 * q^58 + 6 * q^59 - 12 * q^61 - 24 * q^62 + 6 * q^65 - 24 * q^66 - 2 * q^67 - 12 * q^68 + 48 * q^69 + 8 * q^70 - 30 * q^73 - 4 * q^74 + 6 * q^75 + 12 * q^76 + 36 * q^77 - 24 * q^78 + 6 * q^79 + 8 * q^80 + 18 * q^81 - 36 * q^84 + 12 * q^86 - 12 * q^87 + 16 * q^88 + 30 * q^89 - 6 * q^91 - 4 * q^92 - 18 * q^93 + 18 * q^95 - 24 * q^96 + 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more