LMFDB - Embedded newform 104.2.s.b.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [104,2,Mod(69,104)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(104, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("104.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.s (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:	$0.830444181021$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	104.101
Dual form			104.2.s.b.69.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 1.36603i) q^{2} +(0.633975 - 0.366025i) q^{3} +(-1.73205 + 1.00000i) q^{4} +3.73205 q^{5} +(0.732051 + 0.732051i) q^{6} +(-3.00000 - 1.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.23205 + 2.13397i) q^{9} +O(q^{10})$	\(q+(0.366025 + 1.36603i) q^{2} +(0.633975 - 0.366025i) q^{3} +(-1.73205 + 1.00000i) q^{4} +3.73205 q^{5} +(0.732051 + 0.732051i) q^{6} +(-3.00000 - 1.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.23205 + 2.13397i) q^{9} +(1.36603 + 5.09808i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-0.732051 + 1.26795i) q^{12} +(-2.59808 - 2.50000i) q^{13} +(1.26795 - 4.73205i) q^{14} +(2.36603 - 1.36603i) q^{15} +(2.00000 - 3.46410i) q^{16} +(0.232051 - 0.401924i) q^{17} +(-3.36603 - 0.901924i) q^{18} +(0.633975 - 1.09808i) q^{19} +(-6.46410 + 3.73205i) q^{20} -2.53590 q^{21} +(-2.00000 + 2.00000i) q^{22} +(-4.09808 - 7.09808i) q^{23} +(-2.00000 - 0.535898i) q^{24} +8.92820 q^{25} +(2.46410 - 4.46410i) q^{26} +4.00000i q^{27} +6.92820 q^{28} +(2.59808 - 1.50000i) q^{29} +(2.73205 + 2.73205i) q^{30} +4.73205i q^{31} +(5.46410 + 1.46410i) q^{32} +(1.26795 + 0.732051i) q^{33} +(0.633975 + 0.169873i) q^{34} +(-11.1962 - 6.46410i) q^{35} -4.92820i q^{36} +(2.13397 + 3.69615i) q^{37} +(1.73205 + 0.464102i) q^{38} +(-2.56218 - 0.633975i) q^{39} +(-7.46410 - 7.46410i) q^{40} +(-7.96410 + 4.59808i) q^{41} +(-0.928203 - 3.46410i) q^{42} +(2.19615 + 1.26795i) q^{43} +(-3.46410 - 2.00000i) q^{44} +(-4.59808 + 7.96410i) q^{45} +(8.19615 - 8.19615i) q^{46} +6.73205i q^{47} -2.92820i q^{48} +(2.50000 + 4.33013i) q^{49} +(3.26795 + 12.1962i) q^{50} -0.339746i q^{51} +(7.00000 + 1.73205i) q^{52} -3.92820i q^{53} +(-5.46410 + 1.46410i) q^{54} +(3.73205 + 6.46410i) q^{55} +(2.53590 + 9.46410i) q^{56} -0.928203i q^{57} +(3.00000 + 3.00000i) q^{58} +(0.267949 - 0.464102i) q^{59} +(-2.73205 + 4.73205i) q^{60} +(0.866025 + 0.500000i) q^{61} +(-6.46410 + 1.73205i) q^{62} +(7.39230 - 4.26795i) q^{63} +8.00000i q^{64} +(-9.69615 - 9.33013i) q^{65} +(-0.535898 + 2.00000i) q^{66} +(3.63397 + 6.29423i) q^{67} +0.928203i q^{68} +(-5.19615 - 3.00000i) q^{69} +(4.73205 - 17.6603i) q^{70} +(8.02628 + 4.63397i) q^{71} +(6.73205 - 1.80385i) q^{72} -1.73205i q^{73} +(-4.26795 + 4.26795i) q^{74} +(5.66025 - 3.26795i) q^{75} +2.53590i q^{76} -6.92820i q^{77} +(-0.0717968 - 3.73205i) q^{78} -10.3923 q^{79} +(7.46410 - 12.9282i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(-9.19615 - 9.19615i) q^{82} +1.46410 q^{83} +(4.39230 - 2.53590i) q^{84} +(0.866025 - 1.50000i) q^{85} +(-0.928203 + 3.46410i) q^{86} +(1.09808 - 1.90192i) q^{87} +(1.46410 - 5.46410i) q^{88} +(6.46410 - 3.73205i) q^{89} +(-12.5622 - 3.36603i) q^{90} +(3.46410 + 12.0000i) q^{91} +(14.1962 + 8.19615i) q^{92} +(1.73205 + 3.00000i) q^{93} +(-9.19615 + 2.46410i) q^{94} +(2.36603 - 4.09808i) q^{95} +(4.00000 - 1.07180i) q^{96} +(-5.19615 - 3.00000i) q^{97} +(-5.00000 + 5.00000i) q^{98} -4.92820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{3} + 8 q^{5} - 4 q^{6} - 12 q^{7} - 8 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 6 * q^3 + 8 * q^5 - 4 * q^6 - 12 * q^7 - 8 * q^8 + 2 * q^9	$ 4 q - 2 q^{2} + 6 q^{3} + 8 q^{5} - 4 q^{6} - 12 q^{7} - 8 q^{8} + 2 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{12} + 12 q^{14} + 6 q^{15} + 8 q^{16} - 6 q^{17} - 10 q^{18} + 6 q^{19} - 12 q^{20} - 24 q^{21} - 8 q^{22} - 6 q^{23} - 8 q^{24} + 8 q^{25} - 4 q^{26} + 4 q^{30} + 8 q^{32} + 12 q^{33} + 6 q^{34} - 24 q^{35} + 12 q^{37} + 14 q^{39} - 16 q^{40} - 18 q^{41} + 24 q^{42} - 12 q^{43} - 8 q^{45} + 12 q^{46} + 10 q^{49} + 20 q^{50} + 28 q^{52} - 8 q^{54} + 8 q^{55} + 24 q^{56} + 12 q^{58} + 8 q^{59} - 4 q^{60} - 12 q^{62} - 12 q^{63} - 18 q^{65} - 16 q^{66} + 18 q^{67} + 12 q^{70} - 6 q^{71} + 20 q^{72} - 24 q^{74} - 12 q^{75} - 28 q^{78} + 16 q^{80} - 2 q^{81} - 16 q^{82} - 8 q^{83} - 24 q^{84} + 24 q^{86} - 6 q^{87} - 8 q^{88} + 12 q^{89} - 26 q^{90} + 36 q^{92} - 16 q^{94} + 6 q^{95} + 16 q^{96} - 20 q^{98} + 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^3 + 8 * q^5 - 4 * q^6 - 12 * q^7 - 8 * q^8 + 2 * q^9 + 2 * q^10 + 4 * q^11 + 4 * q^12 + 12 * q^14 + 6 * q^15 + 8 * q^16 - 6 * q^17 - 10 * q^18 + 6 * q^19 - 12 * q^20 - 24 * q^21 - 8 * q^22 - 6 * q^23 - 8 * q^24 + 8 * q^25 - 4 * q^26 + 4 * q^30 + 8 * q^32 + 12 * q^33 + 6 * q^34 - 24 * q^35 + 12 * q^37 + 14 * q^39 - 16 * q^40 - 18 * q^41 + 24 * q^42 - 12 * q^43 - 8 * q^45 + 12 * q^46 + 10 * q^49 + 20 * q^50 + 28 * q^52 - 8 * q^54 + 8 * q^55 + 24 * q^56 + 12 * q^58 + 8 * q^59 - 4 * q^60 - 12 * q^62 - 12 * q^63 - 18 * q^65 - 16 * q^66 + 18 * q^67 + 12 * q^70 - 6 * q^71 + 20 * q^72 - 24 * q^74 - 12 * q^75 - 28 * q^78 + 16 * q^80 - 2 * q^81 - 16 * q^82 - 8 * q^83 - 24 * q^84 + 24 * q^86 - 6 * q^87 - 8 * q^88 + 12 * q^89 - 26 * q^90 + 36 * q^92 - 16 * q^94 + 6 * q^95 + 16 * q^96 - 20 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$3$	0.633975	−	0.366025i	0.366025	−	0.211325i	−0.305695	−	0.952129i	$-0.598889\pi$
$3$	0.633975	−	0.366025i	0.366025	−	0.211325i	0.671721	+	0.740805i	$0.265556\pi$
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	3.73205			1.66902			0.834512	−	0.550990i	$-0.185750\pi$
$5$	3.73205			1.66902			0.834512	+	0.550990i	$0.185750\pi$
$6$	0.732051	+	0.732051i	0.298858	+	0.298858i
$7$	−3.00000	−	1.73205i	−1.13389	−	0.654654i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−3.00000	−	1.73205i	−1.13389	−	0.654654i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	−1.23205	+	2.13397i	−0.410684	+	0.711325i
$10$	1.36603	+	5.09808i	0.431975	+	1.61215i
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	−0.732051	+	1.26795i	−0.211325	+	0.366025i
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$14$	1.26795	−	4.73205i	0.338874	−	1.26469i
$15$	2.36603	−	1.36603i	0.610905	−	0.352706i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	0.232051	−	0.401924i	0.0562806	−	0.0974808i	−0.836512	−	0.547948i	$-0.815409\pi$
$17$	0.232051	−	0.401924i	0.0562806	−	0.0974808i	0.892793	+	0.450467i	$0.148743\pi$
$18$	−3.36603	−	0.901924i	−0.793380	−	0.212585i
$19$	0.633975	−	1.09808i	0.145444	−	0.251916i	−0.784095	−	0.620641i	$-0.786872\pi$
$19$	0.633975	−	1.09808i	0.145444	−	0.251916i	0.929538	+	0.368725i	$0.120206\pi$
$20$	−6.46410	+	3.73205i	−1.44542	+	0.834512i
$21$	−2.53590			−0.553378
$22$	−2.00000	+	2.00000i	−0.426401	+	0.426401i
$23$	−4.09808	−	7.09808i	−0.854508	−	1.48005i	−0.877101	−	0.480306i	$-0.840525\pi$
$23$	−4.09808	−	7.09808i	−0.854508	−	1.48005i	0.0225928	−	0.999745i	$-0.492808\pi$
$24$	−2.00000	−	0.535898i	−0.408248	−	0.109390i
$25$	8.92820			1.78564
$26$	2.46410	−	4.46410i	0.483250	−	0.875482i
$27$			4.00000i			0.769800i
$28$	6.92820			1.30931
$29$	2.59808	−	1.50000i	0.482451	−	0.278543i	−0.238987	−	0.971023i	$-0.576815\pi$
$29$	2.59808	−	1.50000i	0.482451	−	0.278543i	0.721437	+	0.692480i	$0.243482\pi$
$30$	2.73205	+	2.73205i	0.498802	+	0.498802i
$31$			4.73205i			0.849901i	0.905216	+	0.424951i	$0.139709\pi$
$31$			4.73205i			0.849901i	−0.905216	+	0.424951i	$0.860291\pi$
$32$	5.46410	+	1.46410i	0.965926	+	0.258819i
$33$	1.26795	+	0.732051i	0.220722	+	0.127434i
$34$	0.633975	+	0.169873i	0.108726	+	0.0291330i
$35$	−11.1962	−	6.46410i	−1.89250	−	1.09263i
$36$		−	4.92820i		−	0.821367i
$37$	2.13397	+	3.69615i	0.350823	+	0.607644i	0.986394	−	0.164399i	$-0.0525685\pi$
$37$	2.13397	+	3.69615i	0.350823	+	0.607644i	−0.635571	+	0.772043i	$0.719235\pi$
$38$	1.73205	+	0.464102i	0.280976	+	0.0752872i
$39$	−2.56218	−	0.633975i	−0.410277	−	0.101517i
$40$	−7.46410	−	7.46410i	−1.18018	−	1.18018i
$41$	−7.96410	+	4.59808i	−1.24378	+	0.718099i	−0.969862	−	0.243653i	$-0.921654\pi$
$41$	−7.96410	+	4.59808i	−1.24378	+	0.718099i	−0.273921	+	0.961752i	$0.588321\pi$
$42$	−0.928203	−	3.46410i	−0.143225	−	0.534522i
$43$	2.19615	+	1.26795i	0.334910	+	0.193360i	0.658019	−	0.753001i	$-0.271395\pi$
$43$	2.19615	+	1.26795i	0.334910	+	0.193360i	−0.323109	+	0.946362i	$0.604728\pi$
$44$	−3.46410	−	2.00000i	−0.522233	−	0.301511i
$45$	−4.59808	+	7.96410i	−0.685441	+	1.18722i
$46$	8.19615	−	8.19615i	1.20846	−	1.20846i
$47$			6.73205i			0.981971i	0.871168	+	0.490985i	$0.163363\pi$
$47$			6.73205i			0.981971i	−0.871168	+	0.490985i	$0.836637\pi$
$48$		−	2.92820i		−	0.422650i
$49$	2.50000	+	4.33013i	0.357143	+	0.618590i
$50$	3.26795	+	12.1962i	0.462158	+	1.72480i
$51$		−	0.339746i		−	0.0475740i
$52$	7.00000	+	1.73205i	0.970725	+	0.240192i
$53$		−	3.92820i		−	0.539580i	−0.962919	−	0.269790i	$-0.913046\pi$
$53$		−	3.92820i		−	0.539580i	0.962919	−	0.269790i	$-0.0869543\pi$
$54$	−5.46410	+	1.46410i	−0.743570	+	0.199239i
$55$	3.73205	+	6.46410i	0.503230	+	0.871619i
$56$	2.53590	+	9.46410i	0.338874	+	1.26469i
$57$		−	0.928203i		−	0.122944i
$58$	3.00000	+	3.00000i	0.393919	+	0.393919i
$59$	0.267949	−	0.464102i	0.0348840	−	0.0604209i	−0.848056	−	0.529906i	$-0.822227\pi$
$59$	0.267949	−	0.464102i	0.0348840	−	0.0604209i	0.882940	+	0.469485i	$0.155560\pi$
$60$	−2.73205	+	4.73205i	−0.352706	+	0.610905i
$61$	0.866025	+	0.500000i	0.110883	+	0.0640184i	0.554416	−	0.832240i	$-0.312942\pi$
$61$	0.866025	+	0.500000i	0.110883	+	0.0640184i	−0.443533	+	0.896258i	$0.646275\pi$
$62$	−6.46410	+	1.73205i	−0.820942	+	0.219971i
$63$	7.39230	−	4.26795i	0.931343	−	0.537711i
$64$			8.00000i			1.00000i
$65$	−9.69615	−	9.33013i	−1.20266	−	1.15726i
$66$	−0.535898	+	2.00000i	−0.0659645	+	0.246183i
$67$	3.63397	+	6.29423i	0.443961	+	0.768962i	0.997979	−	0.0635419i	$-0.0202397\pi$
$67$	3.63397	+	6.29423i	0.443961	+	0.768962i	−0.554019	+	0.832504i	$0.686906\pi$
$68$			0.928203i			0.112561i
$69$	−5.19615	−	3.00000i	−0.625543	−	0.361158i
$70$	4.73205	−	17.6603i	0.565588	−	2.11080i
$71$	8.02628	+	4.63397i	0.952544	+	0.549952i	0.893870	−	0.448326i	$-0.147979\pi$
$71$	8.02628	+	4.63397i	0.952544	+	0.549952i	0.0586738	+	0.998277i	$0.481313\pi$
$72$	6.73205	−	1.80385i	0.793380	−	0.212585i
$73$		−	1.73205i		−	0.202721i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$		−	1.73205i		−	0.202721i	0.994850	−	0.101361i	$-0.0323196\pi$
$74$	−4.26795	+	4.26795i	−0.496139	+	0.496139i
$75$	5.66025	−	3.26795i	0.653590	−	0.377350i
$76$			2.53590i			0.290887i
$77$		−	6.92820i		−	0.789542i
$78$	−0.0717968	−	3.73205i	−0.00812938	−	0.422572i
$79$	−10.3923			−1.16923			−0.584613	−	0.811312i	$-0.698754\pi$
$79$	−10.3923			−1.16923			−0.584613	+	0.811312i	$0.698754\pi$
$80$	7.46410	−	12.9282i	0.834512	−	1.44542i
$81$	−2.23205	−	3.86603i	−0.248006	−	0.429558i
$82$	−9.19615	−	9.19615i	−1.01555	−	1.01555i
$83$	1.46410			0.160706			0.0803530	−	0.996766i	$-0.474395\pi$
$83$	1.46410			0.160706			0.0803530	+	0.996766i	$0.474395\pi$
$84$	4.39230	−	2.53590i	0.479240	−	0.276689i
$85$	0.866025	−	1.50000i	0.0939336	−	0.162698i
$86$	−0.928203	+	3.46410i	−0.100091	+	0.373544i
$87$	1.09808	−	1.90192i	0.117726	−	0.203908i
$88$	1.46410	−	5.46410i	0.156074	−	0.582475i
$89$	6.46410	−	3.73205i	0.685193	−	0.395597i	−0.116615	−	0.993177i	$-0.537205\pi$
$89$	6.46410	−	3.73205i	0.685193	−	0.395597i	0.801809	+	0.597581i	$0.203871\pi$
$90$	−12.5622	−	3.36603i	−1.32417	−	0.354810i
$91$	3.46410	+	12.0000i	0.363137	+	1.25794i
$92$	14.1962	+	8.19615i	1.48005	+	0.854508i
$93$	1.73205	+	3.00000i	0.179605	+	0.311086i
$94$	−9.19615	+	2.46410i	−0.948511	+	0.254153i
$95$	2.36603	−	4.09808i	0.242749	−	0.420454i
$96$	4.00000	−	1.07180i	0.408248	−	0.109390i
$97$	−5.19615	−	3.00000i	−0.527589	−	0.304604i	0.212445	−	0.977173i	$-0.431857\pi$
$97$	−5.19615	−	3.00000i	−0.527589	−	0.304604i	−0.740034	+	0.672569i	$0.765191\pi$
$98$	−5.00000	+	5.00000i	−0.505076	+	0.505076i
$99$	−4.92820			−0.495303
$100$	−15.4641	+	8.92820i	−1.54641	+	0.892820i
$101$	−9.99038	+	5.76795i	−0.994080	+	0.573932i	−0.906491	−	0.422224i	$-0.861249\pi$
$101$	−9.99038	+	5.76795i	−0.994080	+	0.573932i	−0.0875887	+	0.996157i	$0.527916\pi$
$102$	0.464102	−	0.124356i	0.0459529	−	0.0123130i
$103$	6.19615			0.610525			0.305263	−	0.952268i	$-0.401256\pi$
$103$	6.19615			0.610525			0.305263	+	0.952268i	$0.401256\pi$
$104$	0.196152	+	10.1962i	0.0192343	+	0.999815i
$105$	−9.46410			−0.923602
$106$	5.36603	−	1.43782i	0.521194	−	0.139654i
$107$	15.2942	−	8.83013i	1.47855	−	0.853641i	0.478843	−	0.877900i	$-0.341056\pi$
$107$	15.2942	−	8.83013i	1.47855	−	0.853641i	0.999706	+	0.0242598i	$0.00772291\pi$
$108$	−4.00000	−	6.92820i	−0.384900	−	0.666667i
$109$	6.00000			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$110$	−7.46410	+	7.46410i	−0.711674	+	0.711674i
$111$	2.70577	+	1.56218i	0.256820	+	0.148275i
$112$	−12.0000	+	6.92820i	−1.13389	+	0.654654i
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	−0.786806	−	0.617200i	$-0.788267\pi$
$113$	1.50000	−	2.59808i	0.141108	−	0.244406i	0.927914	+	0.372794i	$0.121600\pi$
$114$	1.26795	−	0.339746i	0.118754	−	0.0318201i
$115$	−15.2942	−	26.4904i	−1.42619	−	2.47024i
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	8.53590	−	2.46410i	0.789144	−	0.227806i
$118$	0.732051	+	0.196152i	0.0673907	+	0.0180573i
$119$	−1.39230	+	0.803848i	−0.127632	+	0.0736886i
$120$	−7.46410	−	2.00000i	−0.681376	−	0.182574i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−0.366025	+	1.36603i	−0.0331384	+	0.123674i
$123$	−3.36603	+	5.83013i	−0.303504	+	0.525685i
$124$	−4.73205	−	8.19615i	−0.424951	−	0.736036i
$125$	14.6603			1.31125
$126$	8.53590	+	8.53590i	0.760438	+	0.760438i
$127$	−0.169873	−	0.294229i	−0.0150738	−	0.0261086i	0.858390	−	0.512997i	$-0.171465\pi$
$127$	−0.169873	−	0.294229i	−0.0150738	−	0.0261086i	−0.873464	+	0.486889i	$0.838132\pi$
$128$	−10.9282	+	2.92820i	−0.965926	+	0.258819i
$129$	1.85641			0.163447
$130$	9.19615	−	16.6603i	0.806556	−	1.46120i
$131$		−	10.7321i		−	0.937664i	−0.883287	−	0.468832i	$-0.844675\pi$
$131$		−	10.7321i		−	0.937664i	0.883287	−	0.468832i	$-0.155325\pi$
$132$	−2.92820			−0.254867
$133$	−3.80385	+	2.19615i	−0.329835	+	0.190431i
$134$	−7.26795	+	7.26795i	−0.627855	+	0.627855i
$135$			14.9282i			1.28482i
$136$	−1.26795	+	0.339746i	−0.108726	+	0.0291330i
$137$	−11.7679	−	6.79423i	−1.00540	−	0.580470i	−0.0955611	−	0.995424i	$-0.530465\pi$
$137$	−11.7679	−	6.79423i	−1.00540	−	0.580470i	−0.909843	+	0.414953i	$0.863798\pi$
$138$	2.19615	−	8.19615i	0.186949	−	0.697703i
$139$	8.19615	+	4.73205i	0.695189	+	0.401367i	0.805553	−	0.592524i	$-0.201868\pi$
$139$	8.19615	+	4.73205i	0.695189	+	0.401367i	−0.110364	+	0.993891i	$0.535202\pi$
$140$	25.8564			2.18527
$141$	2.46410	+	4.26795i	0.207515	+	0.359426i
$142$	−3.39230	+	12.6603i	−0.284676	+	1.06242i
$143$	1.73205	−	7.00000i	0.144841	−	0.585369i
$144$	4.92820	+	8.53590i	0.410684	+	0.711325i
$145$	9.69615	−	5.59808i	0.805222	−	0.464895i
$146$	2.36603	−	0.633975i	0.195814	−	0.0524681i
$147$	3.16987	+	1.83013i	0.261447	+	0.150946i
$148$	−7.39230	−	4.26795i	−0.607644	−	0.350823i
$149$	−5.86603	+	10.1603i	−0.480564	+	0.832360i	−0.999751	−	0.0222997i	$-0.992901\pi$
$149$	−5.86603	+	10.1603i	−0.480564	+	0.832360i	0.519188	+	0.854660i	$0.326235\pi$
$150$	6.53590	+	6.53590i	0.533654	+	0.533654i
$151$			2.19615i			0.178720i	0.995999	+	0.0893602i	$0.0284822\pi$
$151$			2.19615i			0.178720i	−0.995999	+	0.0893602i	$0.971518\pi$
$152$	−3.46410	+	0.928203i	−0.280976	+	0.0752872i
$153$	0.571797	+	0.990381i	0.0462270	+	0.0800676i
$154$	9.46410	−	2.53590i	0.762639	−	0.204349i
$155$			17.6603i			1.41851i
$156$	5.07180	−	1.46410i	0.406069	−	0.117222i
$157$			3.92820i			0.313505i	0.987638	+	0.156752i	$0.0501025\pi$
$157$			3.92820i			0.313505i	−0.987638	+	0.156752i	$0.949898\pi$
$158$	−3.80385	−	14.1962i	−0.302618	−	1.12939i
$159$	−1.43782	−	2.49038i	−0.114027	−	0.197500i
$160$	20.3923	+	5.46410i	1.61215	+	0.431975i
$161$			28.3923i			2.23763i
$162$	4.46410	−	4.46410i	0.350733	−	0.350733i
$163$	−8.19615	+	14.1962i	−0.641972	+	1.11193i	0.343020	+	0.939328i	$0.388550\pi$
$163$	−8.19615	+	14.1962i	−0.641972	+	1.11193i	−0.984992	+	0.172600i	$0.944783\pi$
$164$	9.19615	−	15.9282i	0.718099	−	1.24378i
$165$	4.73205	+	2.73205i	0.368390	+	0.212690i
$166$	0.535898	+	2.00000i	0.0415938	+	0.155230i
$167$	−4.26795	+	2.46410i	−0.330264	+	0.190678i	−0.655958	−	0.754797i	$-0.727735\pi$
$167$	−4.26795	+	2.46410i	−0.330264	+	0.190678i	0.325694	+	0.945475i	$0.394402\pi$
$168$	5.07180	+	5.07180i	0.391298	+	0.391298i
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	2.36603	+	0.633975i	0.181466	+	0.0486236i
$171$	1.56218	+	2.70577i	0.119463	+	0.206916i
$172$	−5.07180			−0.386721
$173$	−16.3923	−	9.46410i	−1.24628	−	0.719542i	−0.275918	−	0.961181i	$-0.588982\pi$
$173$	−16.3923	−	9.46410i	−1.24628	−	0.719542i	−0.970366	+	0.241639i	$0.922315\pi$
$174$	3.00000	+	0.803848i	0.227429	+	0.0609395i
$175$	−26.7846	−	15.4641i	−2.02473	−	1.16898i
$176$	8.00000			0.603023
$177$		−	0.392305i		−	0.0294874i
$178$	7.46410	+	7.46410i	0.559458	+	0.559458i
$179$	12.0000	−	6.92820i	0.896922	−	0.517838i	0.0207218	−	0.999785i	$-0.493404\pi$
$179$	12.0000	−	6.92820i	0.896922	−	0.517838i	0.876200	+	0.481947i	$0.160070\pi$
$180$		−	18.3923i		−	1.37088i
$181$		−	18.4641i		−	1.37243i	−0.727401	−	0.686213i	$-0.759272\pi$
$181$		−	18.4641i		−	1.37243i	0.727401	−	0.686213i	$-0.240728\pi$
$182$	−15.1244	+	9.12436i	−1.12109	+	0.676342i
$183$	0.732051			0.0541148
$184$	−6.00000	+	22.3923i	−0.442326	+	1.65078i
$185$	7.96410	+	13.7942i	0.585532	+	1.01417i
$186$	−3.46410	+	3.46410i	−0.254000	+	0.254000i
$187$	0.928203			0.0678769
$188$	−6.73205	−	11.6603i	−0.490985	−	0.850411i
$189$	6.92820	−	12.0000i	0.503953	−	0.872872i
$190$	6.46410	+	1.73205i	0.468955	+	0.125656i
$191$	−1.90192	+	3.29423i	−0.137618	+	0.238362i	−0.926595	−	0.376062i	$-0.877278\pi$
$191$	−1.90192	+	3.29423i	−0.137618	+	0.238362i	0.788976	+	0.614424i	$0.210611\pi$
$192$	2.92820	+	5.07180i	0.211325	+	0.366025i
$193$	11.3038	−	6.52628i	0.813669	−	0.469772i	−0.0345595	−	0.999403i	$-0.511003\pi$
$193$	11.3038	−	6.52628i	0.813669	−	0.469772i	0.848228	+	0.529631i	$0.177670\pi$
$194$	2.19615	−	8.19615i	0.157675	−	0.588449i
$195$	−9.56218	−	2.36603i	−0.684762	−	0.169435i
$196$	−8.66025	−	5.00000i	−0.618590	−	0.357143i
$197$	−6.26795	−	10.8564i	−0.446573	−	0.773487i	0.551587	−	0.834117i	$-0.314022\pi$
$197$	−6.26795	−	10.8564i	−0.446573	−	0.773487i	−0.998160	+	0.0606302i	$0.980689\pi$
$198$	−1.80385	−	6.73205i	−0.128194	−	0.478426i
$199$	7.56218	−	13.0981i	0.536069	−	0.928498i	−0.463042	−	0.886336i	$-0.653242\pi$
$199$	7.56218	−	13.0981i	0.536069	−	0.928498i	0.999111	−	0.0421618i	$-0.0134245\pi$
$200$	−17.8564	−	17.8564i	−1.26264	−	1.26264i
$201$	4.60770	+	2.66025i	0.325002	+	0.187640i
$202$	−11.5359	−	11.5359i	−0.811663	−	0.811663i
$203$	−10.3923			−0.729397
$204$	0.339746	+	0.588457i	0.0237870	+	0.0412002i
$205$	−29.7224	+	17.1603i	−2.07590	+	1.19852i
$206$	2.26795	+	8.46410i	0.158016	+	0.589722i
$207$	20.1962			1.40373
$208$	−13.8564	+	4.00000i	−0.960769	+	0.277350i
$209$	2.53590			0.175412
$210$	−3.46410	−	12.9282i	−0.239046	−	0.892131i
$211$	−24.7583	+	14.2942i	−1.70443	+	0.984055i	−0.763285	+	0.646061i	$0.776415\pi$
$211$	−24.7583	+	14.2942i	−1.70443	+	0.984055i	−0.941148	+	0.337994i	$0.890252\pi$
$212$	3.92820	+	6.80385i	0.269790	+	0.467290i
$213$	6.78461			0.464874
$214$	17.6603	+	17.6603i	1.20723	+	1.20723i
$215$	8.19615	+	4.73205i	0.558973	+	0.322723i
$216$	8.00000	−	8.00000i	0.544331	−	0.544331i
$217$	8.19615	−	14.1962i	0.556391	−	0.963698i
$218$	2.19615	+	8.19615i	0.148742	+	0.555113i
$219$	−0.633975	−	1.09808i	−0.0428400	−	0.0742011i
$220$	−12.9282	−	7.46410i	−0.871619	−	0.503230i
$221$	−1.60770	+	0.464102i	−0.108145	+	0.0312189i
$222$	−1.14359	+	4.26795i	−0.0767530	+	0.286446i
$223$	−22.0981	+	12.7583i	−1.47980	+	0.854361i	−0.999738	−	0.0228756i	$-0.992718\pi$
$223$	−22.0981	+	12.7583i	−1.47980	+	0.854361i	−0.480058	+	0.877237i	$0.659385\pi$
$224$	−13.8564	−	13.8564i	−0.925820	−	0.925820i
$225$	−11.0000	+	19.0526i	−0.733333	+	1.27017i
$226$	4.09808	+	1.09808i	0.272600	+	0.0730429i
$227$	13.0263	−	22.5622i	0.864585	−	1.49750i	−0.00287459	−	0.999996i	$-0.500915\pi$
$227$	13.0263	−	22.5622i	0.864585	−	1.49750i	0.867459	−	0.497508i	$-0.165752\pi$
$228$	0.928203	+	1.60770i	0.0614718	+	0.106472i
$229$	12.9282			0.854320			0.427160	−	0.904176i	$-0.359514\pi$
$229$	12.9282			0.854320			0.427160	+	0.904176i	$0.359514\pi$
$230$	30.5885	−	30.5885i	2.01694	−	2.01694i
$231$	−2.53590	−	4.39230i	−0.166850	−	0.288992i
$232$	−8.19615	−	2.19615i	−0.538104	−	0.144184i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$	6.49038	+	10.7583i	0.424289	+	0.703294i
$235$			25.1244i			1.63893i
$236$			1.07180i			0.0697680i
$237$	−6.58846	+	3.80385i	−0.427966	+	0.247086i
$238$	−1.60770	−	1.60770i	−0.104211	−	0.104211i
$239$		−	18.3923i		−	1.18970i	−0.803837	−	0.594850i	$-0.797212\pi$
$239$		−	18.3923i		−	1.18970i	0.803837	−	0.594850i	$-0.202788\pi$
$240$		−	10.9282i		−	0.705412i
$241$	9.69615	+	5.59808i	0.624584	+	0.360604i	0.778652	−	0.627457i	$-0.215904\pi$
$241$	9.69615	+	5.59808i	0.624584	+	0.360604i	−0.154068	+	0.988060i	$0.549237\pi$
$242$	9.56218	+	2.56218i	0.614680	+	0.164703i
$243$	−13.2224	−	7.63397i	−0.848219	−	0.489720i
$244$	−2.00000			−0.128037
$245$	9.33013	+	16.1603i	0.596080	+	1.03244i
$246$	−9.19615	−	2.46410i	−0.586325	−	0.157105i
$247$	−4.39230	+	1.26795i	−0.279476	+	0.0806777i
$248$	9.46410	−	9.46410i	0.600971	−	0.600971i
$249$	0.928203	−	0.535898i	0.0588225	−	0.0339612i
$250$	5.36603	+	20.0263i	0.339377	+	1.26657i
$251$	−7.09808	−	4.09808i	−0.448027	−	0.258668i	0.258970	−	0.965885i	$-0.416617\pi$
$251$	−7.09808	−	4.09808i	−0.448027	−	0.258668i	−0.706996	+	0.707217i	$0.749950\pi$
$252$	−8.53590	+	14.7846i	−0.537711	+	0.931343i
$253$	8.19615	−	14.1962i	0.515288	−	0.892504i
$254$	0.339746	−	0.339746i	0.0213176	−	0.0213176i
$255$		−	1.26795i		−	0.0794021i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−11.4282	−	19.7942i	−0.712872	−	1.23473i	−0.963775	−	0.266718i	$-0.914061\pi$
$257$	−11.4282	−	19.7942i	−0.712872	−	1.23473i	0.250903	−	0.968012i	$-0.419273\pi$
$258$	0.679492	+	2.53590i	0.0423033	+	0.157878i
$259$		−	14.7846i		−	0.918671i
$260$	26.1244	+	6.46410i	1.62016	+	0.400887i
$261$			7.39230i			0.457572i
$262$	14.6603	−	3.92820i	0.905714	−	0.242685i
$263$	−8.19615	−	14.1962i	−0.505396	−	0.875372i	−0.999981	−	0.00624249i	$-0.998013\pi$
$263$	−8.19615	−	14.1962i	−0.505396	−	0.875372i	0.494584	−	0.869130i	$-0.335320\pi$
$264$	−1.07180	−	4.00000i	−0.0659645	−	0.246183i
$265$		−	14.6603i		−	0.900572i
$266$	−4.39230	−	4.39230i	−0.269309	−	0.269309i
$267$	2.73205	−	4.73205i	0.167199	−	0.289597i
$268$	−12.5885	−	7.26795i	−0.768962	−	0.443961i
$269$	8.19615	+	4.73205i	0.499728	+	0.288518i	0.728601	−	0.684938i	$-0.240171\pi$
$269$	8.19615	+	4.73205i	0.499728	+	0.288518i	−0.228873	+	0.973456i	$0.573504\pi$
$270$	−20.3923	+	5.46410i	−1.24104	+	0.332535i
$271$	−15.0000	+	8.66025i	−0.911185	+	0.526073i	−0.880812	−	0.473466i	$-0.843003\pi$
$271$	−15.0000	+	8.66025i	−0.911185	+	0.526073i	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	−0.928203	−	1.60770i	−0.0562806	−	0.0974808i
$273$	6.58846	+	6.33975i	0.398752	+	0.383699i
$274$	4.97372	−	18.5622i	0.300473	−	1.12138i
$275$	8.92820	+	15.4641i	0.538391	+	0.932520i
$276$	12.0000			0.722315
$277$	12.4019	+	7.16025i	0.745159	+	0.430218i	0.823942	−	0.566674i	$-0.191770\pi$
$277$	12.4019	+	7.16025i	0.745159	+	0.430218i	−0.0787828	+	0.996892i	$0.525103\pi$
$278$	−3.46410	+	12.9282i	−0.207763	+	0.775382i
$279$	−10.0981	−	5.83013i	−0.604556	−	0.349041i
$280$	9.46410	+	35.3205i	0.565588	+	2.11080i
$281$			10.6603i			0.635937i	0.948101	+	0.317969i	$0.103001\pi$
$281$			10.6603i			0.635937i	−0.948101	+	0.317969i	$0.896999\pi$
$282$	−4.92820	+	4.92820i	−0.293470	+	0.293470i
$283$	26.6603	−	15.3923i	1.58479	−	0.914978i	0.590641	−	0.806934i	$-0.298875\pi$
$283$	26.6603	−	15.3923i	1.58479	−	0.914978i	0.994146	−	0.108043i	$-0.0344586\pi$
$284$	−18.5359			−1.09990
$285$		−	3.46410i		−	0.205196i
$286$	10.1962	−	0.196152i	0.602911	−	0.0115987i
$287$	31.8564			1.88042
$288$	−9.85641	+	9.85641i	−0.580794	+	0.580794i
$289$	8.39230	+	14.5359i	0.493665	+	0.855053i
$290$	11.1962	+	11.1962i	0.657461	+	0.657461i
$291$	−4.39230			−0.257481
$292$	1.73205	+	3.00000i	0.101361	+	0.175562i
$293$	1.40192	−	2.42820i	0.0819013	−	0.141857i	−0.822165	−	0.569249i	$-0.807234\pi$
$293$	1.40192	−	2.42820i	0.0819013	−	0.141857i	0.904067	+	0.427392i	$0.140567\pi$
$294$	−1.33975	+	5.00000i	−0.0781356	+	0.291606i
$295$	1.00000	−	1.73205i	0.0582223	−	0.100844i
$296$	3.12436	−	11.6603i	0.181599	−	0.677738i
$297$	−6.92820	+	4.00000i	−0.402015	+	0.232104i
$298$	−16.0263	−	4.29423i	−0.928377	−	0.248758i
$299$	−7.09808	+	28.6865i	−0.410492	+	1.65899i
$300$	−6.53590	+	11.3205i	−0.377350	+	0.653590i
$301$	−4.39230	−	7.60770i	−0.253168	−	0.438500i
$302$	−3.00000	+	0.803848i	−0.172631	+	0.0462562i
$303$	−4.22243	+	7.31347i	−0.242572	+	0.420148i
$304$	−2.53590	−	4.39230i	−0.145444	−	0.251916i
$305$	3.23205	+	1.86603i	0.185067	+	0.106848i
$306$	−1.14359	+	1.14359i	−0.0653749	+	0.0653749i
$307$	2.19615			0.125341			0.0626705	−	0.998034i	$-0.480038\pi$
$307$	2.19615			0.125341			0.0626705	+	0.998034i	$0.480038\pi$
$308$	6.92820	+	12.0000i	0.394771	+	0.683763i
$309$	3.92820	−	2.26795i	0.223468	−	0.129019i
$310$	−24.1244	+	6.46410i	−1.37017	+	0.367136i
$311$	−18.5885			−1.05405			−0.527027	−	0.849848i	$-0.676693\pi$
$311$	−18.5885			−1.05405			−0.527027	+	0.849848i	$0.676693\pi$
$312$	3.85641	+	6.39230i	0.218326	+	0.361893i
$313$	−2.53590			−0.143337			−0.0716687	−	0.997428i	$-0.522832\pi$
$313$	−2.53590			−0.143337			−0.0716687	+	0.997428i	$0.522832\pi$
$314$	−5.36603	+	1.43782i	−0.302822	+	0.0811410i
$315$	27.5885	−	15.9282i	1.55443	−	0.897453i
$316$	18.0000	−	10.3923i	1.01258	−	0.584613i
$317$	25.1962			1.41516			0.707578	−	0.706635i	$-0.249788\pi$
$317$	25.1962			1.41516			0.707578	+	0.706635i	$0.249788\pi$
$318$	2.87564	−	2.87564i	0.161258	−	0.161258i
$319$	5.19615	+	3.00000i	0.290929	+	0.167968i
$320$			29.8564i			1.66902i
$321$	6.46410	−	11.1962i	0.360791	−	0.624908i
$322$	−38.7846	+	10.3923i	−2.16138	+	0.579141i
$323$	−0.294229	−	0.509619i	−0.0163713	−	0.0283560i
$324$	7.73205	+	4.46410i	0.429558	+	0.248006i
$325$	−23.1962	−	22.3205i	−1.28669	−	1.23812i
$326$	−22.3923	−	6.00000i	−1.24020	−	0.332309i
$327$	3.80385	−	2.19615i	0.210353	−	0.121448i
$328$	25.1244	+	6.73205i	1.38726	+	0.371715i
$329$	11.6603	−	20.1962i	0.642851	−	1.11345i
$330$	−2.00000	+	7.46410i	−0.110096	+	0.410885i
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	−0.652680	−	0.757634i	$-0.726355\pi$
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	0.982470	+	0.186421i	$0.0596888\pi$
$332$	−2.53590	+	1.46410i	−0.139176	+	0.0803530i
$333$	−10.5167			−0.576309
$334$	−4.92820	−	4.92820i	−0.269659	−	0.269659i
$335$	13.5622	+	23.4904i	0.740981	+	1.28342i
$336$	−5.07180	+	8.78461i	−0.276689	+	0.479240i
$337$	−33.2487			−1.81117			−0.905586	−	0.424162i	$-0.860569\pi$
$337$	−33.2487			−1.81117			−0.905586	+	0.424162i	$0.860569\pi$
$338$	−17.5622	+	5.43782i	−0.955257	+	0.295779i
$339$		−	2.19615i		−	0.119279i
$340$			3.46410i			0.187867i
$341$	−8.19615	+	4.73205i	−0.443847	+	0.256255i
$342$	−3.12436	+	3.12436i	−0.168946	+	0.168946i
$343$			6.92820i			0.374088i
$344$	−1.85641	−	6.92820i	−0.100091	−	0.373544i
$345$	−19.3923	−	11.1962i	−1.04405	−	0.602781i
$346$	6.92820	−	25.8564i	0.372463	−	1.39005i
$347$	−1.09808	−	0.633975i	−0.0589478	−	0.0340335i	0.470236	−	0.882540i	$-0.344169\pi$
$347$	−1.09808	−	0.633975i	−0.0589478	−	0.0340335i	−0.529184	+	0.848507i	$0.677502\pi$
$348$			4.39230i			0.235452i
$349$	2.66025	+	4.60770i	0.142400	+	0.246644i	0.928400	−	0.371582i	$-0.121185\pi$
$349$	2.66025	+	4.60770i	0.142400	+	0.246644i	−0.786000	+	0.618227i	$0.787851\pi$
$350$	11.3205	−	42.2487i	0.605107	−	2.25829i
$351$	10.0000	−	10.3923i	0.533761	−	0.554700i
$352$	2.92820	+	10.9282i	0.156074	+	0.582475i
$353$	−15.8205	+	9.13397i	−0.842041	+	0.486152i	−0.857957	−	0.513721i	$-0.828267\pi$
$353$	−15.8205	+	9.13397i	−0.842041	+	0.486152i	0.0159167	+	0.999873i	$0.494933\pi$
$354$	0.535898	−	0.143594i	0.0284827	−	0.00763191i
$355$	29.9545	+	17.2942i	1.58982	+	0.917882i
$356$	−7.46410	+	12.9282i	−0.395597	+	0.685193i
$357$	−0.588457	+	1.01924i	−0.0311445	+	0.0539438i
$358$	13.8564	+	13.8564i	0.732334	+	0.732334i
$359$		−	13.0718i		−	0.689903i	−0.938621	−	0.344952i	$-0.887895\pi$
$359$		−	13.0718i		−	0.689903i	0.938621	−	0.344952i	$-0.112105\pi$
$360$	25.1244	−	6.73205i	1.32417	−	0.354810i
$361$	8.69615	+	15.0622i	0.457692	+	0.792746i
$362$	25.2224	−	6.75833i	1.32566	−	0.355210i
$363$		−	5.12436i		−	0.268959i
$364$	−18.0000	−	17.3205i	−0.943456	−	0.907841i
$365$		−	6.46410i		−	0.338347i
$366$	0.267949	+	1.00000i	0.0140059	+	0.0522708i
$367$	14.0981	+	24.4186i	0.735914	+	1.27464i	0.954321	+	0.298782i	$0.0965804\pi$
$367$	14.0981	+	24.4186i	0.735914	+	1.27464i	−0.218408	+	0.975858i	$0.570086\pi$
$368$	−32.7846			−1.70902
$369$		−	22.6603i		−	1.17965i
$370$	−15.9282	+	15.9282i	−0.828068	+	0.828068i
$371$	−6.80385	+	11.7846i	−0.353238	+	0.611826i
$372$	−6.00000	−	3.46410i	−0.311086	−	0.179605i
$373$	22.3301	+	12.8923i	1.15621	+	0.667538i	0.950393	−	0.311052i	$-0.100681\pi$
$373$	22.3301	+	12.8923i	1.15621	+	0.667538i	0.205817	+	0.978590i	$0.434015\pi$
$374$	0.339746	+	1.26795i	0.0175678	+	0.0655641i
$375$	9.29423	−	5.36603i	0.479952	−	0.277100i
$376$	13.4641	−	13.4641i	0.694358	−	0.694358i
$377$	−10.5000	−	2.59808i	−0.540778	−	0.133808i
$378$	18.9282	+	5.07180i	0.973562	+	0.260865i
$379$	−11.0263	−	19.0981i	−0.566382	−	0.981002i	−0.996920	−	0.0784297i	$-0.975009\pi$
$379$	−11.0263	−	19.0981i	−0.566382	−	0.981002i	0.430538	−	0.902573i	$-0.358324\pi$
$380$			9.46410i			0.485498i
$381$	−0.215390	−	0.124356i	−0.0110348	−	0.00637093i
$382$	−5.19615	−	1.39230i	−0.265858	−	0.0712365i
$383$	17.3205	+	10.0000i	0.885037	+	0.510976i	0.872316	−	0.488943i	$-0.162617\pi$
$383$	17.3205	+	10.0000i	0.885037	+	0.510976i	0.0127209	+	0.999919i	$0.495951\pi$
$384$	−5.85641	+	5.85641i	−0.298858	+	0.298858i
$385$		−	25.8564i		−	1.31776i
$386$	13.0526	+	13.0526i	0.664358	+	0.664358i
$387$	−5.41154	+	3.12436i	−0.275084	+	0.158820i
$388$	12.0000			0.609208
$389$			18.7128i			0.948777i	0.880316	+	0.474389i	$0.157331\pi$
$389$			18.7128i			0.948777i	−0.880316	+	0.474389i	$0.842669\pi$
$390$	−0.267949	−	13.9282i	−0.0135681	−	0.705282i
$391$	−3.80385			−0.192369
$392$	3.66025	−	13.6603i	0.184871	−	0.689947i
$393$	−3.92820	−	6.80385i	−0.198152	−	0.343209i
$394$	12.5359	−	12.5359i	0.631549	−	0.631549i
$395$	−38.7846			−1.95147
$396$	8.53590	−	4.92820i	0.428945	−	0.247652i
$397$	−12.1244	+	21.0000i	−0.608504	+	1.05396i	0.382983	+	0.923755i	$0.374897\pi$
$397$	−12.1244	+	21.0000i	−0.608504	+	1.05396i	−0.991487	+	0.130204i	$0.958437\pi$
$398$	20.6603	+	5.53590i	1.03560	+	0.277490i
$399$	−1.60770	+	2.78461i	−0.0804854	+	0.139405i
$400$	17.8564	−	30.9282i	0.892820	−	1.54641i
$401$	8.42820	−	4.86603i	0.420884	−	0.242998i	−0.274571	−	0.961567i	$-0.588536\pi$
$401$	8.42820	−	4.86603i	0.420884	−	0.242998i	0.695456	+	0.718569i	$0.255203\pi$
$402$	−1.94744	+	7.26795i	−0.0971295	+	0.362492i
$403$	11.8301	−	12.2942i	0.589301	−	0.612419i
$404$	11.5359	−	19.9808i	0.573932	−	0.994080i
$405$	−8.33013	−	14.4282i	−0.413927	−	0.716943i
$406$	−3.80385	−	14.1962i	−0.188782	−	0.704543i
$407$	−4.26795	+	7.39230i	−0.211554	+	0.366423i
$408$	−0.679492	+	0.679492i	−0.0336399	+	0.0336399i
$409$	0.696152	+	0.401924i	0.0344225	+	0.0198739i	0.517113	−	0.855917i	$-0.327007\pi$
$409$	0.696152	+	0.401924i	0.0344225	+	0.0198739i	−0.482690	+	0.875791i	$0.660340\pi$
$410$	−34.3205	−	34.3205i	−1.69497	−	1.69497i
$411$	−9.94744			−0.490671
$412$	−10.7321	+	6.19615i	−0.528730	+	0.305263i
$413$	−1.60770	+	0.928203i	−0.0791095	+	0.0456739i
$414$	7.39230	+	27.5885i	0.363312	+	1.35590i
$415$	5.46410			0.268222
$416$	−10.5359	−	17.4641i	−0.516565	−	0.856248i
$417$	6.92820			0.339276
$418$	0.928203	+	3.46410i	0.0453999	+	0.169435i
$419$	−16.9019	+	9.75833i	−0.825713	+	0.476726i	−0.852383	−	0.522919i	$-0.824843\pi$
$419$	−16.9019	+	9.75833i	−0.825713	+	0.476726i	0.0266696	+	0.999644i	$0.491510\pi$
$420$	16.3923	−	9.46410i	0.799863	−	0.461801i
$421$	−30.1244			−1.46817			−0.734086	−	0.679057i	$-0.762389\pi$
$421$	−30.1244			−1.46817			−0.734086	+	0.679057i	$0.762389\pi$
$422$	−28.5885	−	28.5885i	−1.39166	−	1.39166i
$423$	−14.3660	−	8.29423i	−0.698500	−	0.403279i
$424$	−7.85641	+	7.85641i	−0.381541	+	0.381541i
$425$	2.07180	−	3.58846i	0.100497	−	0.174066i
$426$	2.48334	+	9.26795i	0.120318	+	0.449034i
$427$	−1.73205	−	3.00000i	−0.0838198	−	0.145180i
$428$	−17.6603	+	30.5885i	−0.853641	+	1.47855i
$429$	−1.46410	−	5.07180i	−0.0706875	−	0.244869i
$430$	−3.46410	+	12.9282i	−0.167054	+	0.623453i
$431$	15.4641	−	8.92820i	0.744880	−	0.430056i	−0.0789612	−	0.996878i	$-0.525160\pi$
$431$	15.4641	−	8.92820i	0.744880	−	0.430056i	0.823841	+	0.566821i	$0.191827\pi$
$432$	13.8564	+	8.00000i	0.666667	+	0.384900i
$433$	−10.5000	+	18.1865i	−0.504598	+	0.873989i	0.495388	+	0.868672i	$0.335026\pi$
$433$	−10.5000	+	18.1865i	−0.504598	+	0.873989i	−0.999986	+	0.00531724i	$0.998307\pi$
$434$	22.3923	+	6.00000i	1.07487	+	0.288009i
$435$	4.09808	−	7.09808i	0.196488	−	0.340327i
$436$	−10.3923	+	6.00000i	−0.497701	+	0.287348i
$437$	−10.3923			−0.497131
$438$	1.26795	−	1.26795i	0.0605850	−	0.0605850i
$439$	−7.80385	−	13.5167i	−0.372457	−	0.645115i	0.617486	−	0.786582i	$-0.288151\pi$
$439$	−7.80385	−	13.5167i	−0.372457	−	0.645115i	−0.989943	+	0.141467i	$0.954818\pi$
$440$	5.46410	−	20.3923i	0.260491	−	0.972165i
$441$	−12.3205			−0.586691
$442$	−1.22243	−	2.02628i	−0.0581452	−	0.0963803i
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	−6.24871			−0.296551
$445$	24.1244	−	13.9282i	1.14360	−	0.660260i
$446$	−25.5167	−	25.5167i	−1.20825	−	1.20825i
$447$			8.58846i			0.406220i
$448$	13.8564	−	24.0000i	0.654654	−	1.13389i
$449$	18.4641	+	10.6603i	0.871375	+	0.503088i	0.867805	−	0.496905i	$-0.165530\pi$
$449$	18.4641	+	10.6603i	0.871375	+	0.503088i	0.00356996	+	0.999994i	$0.498864\pi$
$450$	−30.0526	−	8.05256i	−1.41669	−	0.379601i
$451$	−15.9282	−	9.19615i	−0.750030	−	0.433030i
$452$			6.00000i			0.282216i
$453$	0.803848	+	1.39230i	0.0377681	+	0.0654162i
$454$	35.5885	+	9.53590i	1.67025	+	0.447542i
$455$	12.9282	+	44.7846i	0.606084	+	2.09953i
$456$	−1.85641	+	1.85641i	−0.0869342	+	0.0869342i
$457$	6.69615	−	3.86603i	0.313233	−	0.180845i	−0.335139	−	0.942169i	$-0.608783\pi$
$457$	6.69615	−	3.86603i	0.313233	−	0.180845i	0.648372	+	0.761324i	$0.275450\pi$
$458$	4.73205	+	17.6603i	0.221114	+	0.825209i
$459$	1.60770	+	0.928203i	0.0750408	+	0.0433248i
$460$	52.9808	+	30.5885i	2.47024	+	1.42619i
$461$	−14.3301	+	24.8205i	−0.667421	+	1.15601i	0.311202	+	0.950344i	$0.399268\pi$
$461$	−14.3301	+	24.8205i	−0.667421	+	1.15601i	−0.978623	+	0.205663i	$0.934065\pi$
$462$	5.07180	−	5.07180i	0.235961	−	0.235961i
$463$		−	16.3923i		−	0.761815i	−0.924613	−	0.380908i	$-0.875612\pi$
$463$		−	16.3923i		−	0.761815i	0.924613	−	0.380908i	$-0.124388\pi$
$464$		−	12.0000i		−	0.557086i
$465$	6.46410	+	11.1962i	0.299766	+	0.519209i
$466$		0			0
$467$			20.5359i			0.950288i	0.879908	+	0.475144i	$0.157604\pi$
$467$			20.5359i			0.950288i	−0.879908	+	0.475144i	$0.842396\pi$
$468$	−12.3205	+	12.8038i	−0.569516	+	0.591858i
$469$		−	25.1769i		−	1.16256i
$470$	−34.3205	+	9.19615i	−1.58309	+	0.424187i
$471$	1.43782	+	2.49038i	0.0662513	+	0.114751i
$472$	−1.46410	+	0.392305i	−0.0673907	+	0.0180573i
$473$			5.07180i			0.233201i
$474$	−7.60770	−	7.60770i	−0.349433	−	0.349433i
$475$	5.66025	−	9.80385i	0.259710	−	0.449831i
$476$	1.60770	−	2.78461i	0.0736886	−	0.127632i
$477$	8.38269	+	4.83975i	0.383817	+	0.221597i
$478$	25.1244	−	6.73205i	1.14916	−	0.307917i
$479$	−25.3468	+	14.6340i	−1.15812	+	0.668643i	−0.950854	−	0.309640i	$-0.899791\pi$
$479$	−25.3468	+	14.6340i	−1.15812	+	0.668643i	−0.207271	+	0.978284i	$0.566458\pi$
$480$	14.9282	−	4.00000i	0.681376	−	0.182574i
$481$	3.69615	−	14.9378i	0.168530	−	0.681106i
$482$	−4.09808	+	15.2942i	−0.186662	+	0.696633i
$483$	10.3923	+	18.0000i	0.472866	+	0.819028i
$484$			14.0000i			0.636364i
$485$	−19.3923	−	11.1962i	−0.880559	−	0.508391i
$486$	5.58846	−	20.8564i	0.253498	−	0.946066i
$487$	20.1962	+	11.6603i	0.915175	+	0.528377i	0.882093	−	0.471076i	$-0.156134\pi$
$487$	20.1962	+	11.6603i	0.915175	+	0.528377i	0.0330824	+	0.999453i	$0.489468\pi$
$488$	−0.732051	−	2.73205i	−0.0331384	−	0.123674i
$489$			12.0000i			0.542659i
$490$	−18.6603	+	18.6603i	−0.842984	+	0.842984i
$491$	−6.58846	+	3.80385i	−0.297333	+	0.171665i	−0.641244	−	0.767337i	$-0.721581\pi$
$491$	−6.58846	+	3.80385i	−0.297333	+	0.171665i	0.343911	+	0.939002i	$0.388248\pi$
$492$		−	13.4641i		−	0.607009i
$493$		−	1.39230i		−	0.0627063i
$494$	−3.33975	−	5.53590i	−0.150262	−	0.249072i
$495$	−18.3923			−0.826673
$496$	16.3923	+	9.46410i	0.736036	+	0.424951i
$497$	−16.0526	−	27.8038i	−0.720056	−	1.24717i
$498$	1.07180	+	1.07180i	0.0480284	+	0.0480284i
$499$	8.87564			0.397328			0.198664	−	0.980068i	$-0.436340\pi$
$499$	8.87564			0.397328			0.198664	+	0.980068i	$0.436340\pi$
$500$	−25.3923	+	14.6603i	−1.13558	+	0.655626i
$501$	−1.80385	+	3.12436i	−0.0805900	+	0.139586i
$502$	3.00000	−	11.1962i	0.133897	−	0.499709i
$503$	−4.39230	+	7.60770i	−0.195843	+	0.339210i	−0.947177	−	0.320712i	$-0.896078\pi$
$503$	−4.39230	+	7.60770i	−0.195843	+	0.339210i	0.751333	+	0.659923i	$0.229411\pi$
$504$	−23.3205	−	6.24871i	−1.03878	−	0.278340i
$505$	−37.2846	+	21.5263i	−1.65914	+	0.957907i
$506$	22.3923	+	6.00000i	0.995459	+	0.266733i
$507$	5.07180	+	8.05256i	0.225246	+	0.357627i
$508$	0.588457	+	0.339746i	0.0261086	+	0.0150738i
$509$	3.93782	+	6.82051i	0.174541	+	0.302314i	0.940002	−	0.341168i	$-0.110823\pi$
$509$	3.93782	+	6.82051i	0.174541	+	0.302314i	−0.765461	+	0.643482i	$0.777489\pi$
$510$	1.73205	−	0.464102i	0.0766965	−	0.0205508i
$511$	−3.00000	+	5.19615i	−0.132712	+	0.229864i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	4.39230	+	2.53590i	0.193925	+	0.111963i
$514$	22.8564	−	22.8564i	1.00815	−	1.00815i
$515$	23.1244			1.01898
$516$	−3.21539	+	1.85641i	−0.141550	+	0.0817237i
$517$	−11.6603	+	6.73205i	−0.512817	+	0.296075i
$518$	20.1962	−	5.41154i	0.887368	−	0.237770i
$519$	−13.8564			−0.608229
$520$	0.732051	+	38.0526i	0.0321026	+	1.66872i
$521$	9.24871			0.405193			0.202597	−	0.979262i	$-0.435062\pi$
$521$	9.24871			0.405193			0.202597	+	0.979262i	$0.435062\pi$
$522$	−10.0981	+	2.70577i	−0.441981	+	0.118428i
$523$	−0.803848	+	0.464102i	−0.0351498	+	0.0202937i	−0.517472	−	0.855700i	$-0.673127\pi$
$523$	−0.803848	+	0.464102i	−0.0351498	+	0.0202937i	0.482322	+	0.875994i	$0.339793\pi$
$524$	10.7321	+	18.5885i	0.468832	+	0.812041i
$525$	−22.6410			−0.988135
$526$	16.3923	−	16.3923i	0.714738	−	0.714738i
$527$	1.90192	+	1.09808i	0.0828491	+	0.0478330i
$528$	5.07180	−	2.92820i	0.220722	−	0.127434i
$529$	−22.0885	+	38.2583i	−0.960368	+	1.66341i
$530$	20.0263	−	5.36603i	0.869886	−	0.233085i
$531$	0.660254	+	1.14359i	0.0286526	+	0.0496277i
$532$	4.39230	−	7.60770i	0.190431	−	0.329835i
$533$	32.1865	+	7.96410i	1.39415	+	0.344964i
$534$	7.46410	+	2.00000i	0.323003	+	0.0865485i
$535$	57.0788	−	32.9545i	2.46773	−	1.42475i
$536$	5.32051	−	19.8564i	0.229811	−	0.857666i
$537$	5.07180	−	8.78461i	0.218864	−	0.379084i
$538$	−3.46410	+	12.9282i	−0.149348	+	0.557374i
$539$	−5.00000	+	8.66025i	−0.215365	+	0.373024i
$540$	−14.9282	−	25.8564i	−0.642408	−	1.11268i
$541$	35.4449			1.52389			0.761947	−	0.647640i	$-0.224244\pi$
$541$	35.4449			1.52389			0.761947	+	0.647640i	$0.224244\pi$
$542$	−17.3205	−	17.3205i	−0.743980	−	0.743980i
$543$	−6.75833	−	11.7058i	−0.290028	−	0.502343i
$544$	1.85641	−	1.85641i	0.0795928	−	0.0795928i
$545$	22.3923			0.959181
$546$	−6.24871	+	11.3205i	−0.267420	+	0.484473i
$547$		−	18.5885i		−	0.794785i	−0.917649	−	0.397393i	$-0.869915\pi$
$547$		−	18.5885i		−	0.794785i	0.917649	−	0.397393i	$-0.130085\pi$
$548$	27.1769			1.16094
$549$	−2.13397	+	1.23205i	−0.0910758	+	0.0525826i
$550$	−17.8564	+	17.8564i	−0.761400	+	0.761400i
$551$		−	3.80385i		−	0.162049i
$552$	4.39230	+	16.3923i	0.186949	+	0.697703i
$553$	31.1769	+	18.0000i	1.32578	+	0.765438i
$554$	−5.24167	+	19.5622i	−0.222697	+	0.831117i
$555$	10.0981	+	5.83013i	0.428639	+	0.247475i
$556$	−18.9282			−0.802735
$557$	−2.40192	−	4.16025i	−0.101773	−	0.176276i	0.810642	−	0.585542i	$-0.199118\pi$
$557$	−2.40192	−	4.16025i	−0.101773	−	0.176276i	−0.912415	+	0.409266i	$0.865785\pi$
$558$	4.26795	−	15.9282i	0.180677	−	0.674295i
$559$	−2.53590	−	8.78461i	−0.107257	−	0.371549i
$560$	−44.7846	+	25.8564i	−1.89250	+	1.09263i
$561$	0.588457	−	0.339746i	0.0248447	−	0.0143441i
$562$	−14.5622	+	3.90192i	−0.614268	+	0.164593i
$563$	13.9808	+	8.07180i	0.589219	+	0.340186i	0.764789	−	0.644281i	$-0.222843\pi$
$563$	13.9808	+	8.07180i	0.589219	+	0.340186i	−0.175570	+	0.984467i	$0.556177\pi$
$564$	−8.53590	−	4.92820i	−0.359426	−	0.207515i
$565$	5.59808	−	9.69615i	0.235513	−	0.407920i
$566$	30.7846	+	30.7846i	1.29397	+	1.29397i
$567$			15.4641i			0.649431i
$568$	−6.78461	−	25.3205i	−0.284676	−	1.06242i
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	0.999994	+	0.00354413i	$0.00112814\pi$
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	−0.496928	+	0.867792i	$0.665539\pi$
$570$	4.73205	−	1.26795i	0.198204	−	0.0531085i
$571$			2.39230i			0.100115i	0.998746	+	0.0500574i	$0.0159404\pi$
$571$			2.39230i			0.100115i	−0.998746	+	0.0500574i	$0.984060\pi$
$572$	4.00000	+	13.8564i	0.167248	+	0.579365i
$573$			2.78461i			0.116329i
$574$	11.6603	+	43.5167i	0.486690	+	1.81635i
$575$	−36.5885	−	63.3731i	−1.52584	−	2.64284i
$576$	−17.0718	−	9.85641i	−0.711325	−	0.410684i
$577$		−	34.2679i		−	1.42659i	−0.700862	−	0.713297i	$-0.747201\pi$
$577$		−	34.2679i		−	1.42659i	0.700862	−	0.713297i	$-0.252799\pi$
$578$	−16.7846	+	16.7846i	−0.698148	+	0.698148i
$579$	4.77757	−	8.27499i	0.198549	−	0.343897i
$580$	−11.1962	+	19.3923i	−0.464895	+	0.805222i
$581$	−4.39230	−	2.53590i	−0.182224	−	0.105207i
$582$	−1.60770	−	6.00000i	−0.0666411	−	0.248708i
$583$	6.80385	−	3.92820i	0.281787	−	0.162690i
$584$	−3.46410	+	3.46410i	−0.143346	+	0.143346i
$585$	31.8564	−	9.19615i	1.31710	−	0.380214i
$586$	3.83013	+	1.02628i	0.158221	+	0.0423952i
$587$	−22.5885	−	39.1244i	−0.932325	−	1.61483i	−0.779335	−	0.626607i	$-0.784443\pi$
$587$	−22.5885	−	39.1244i	−0.932325	−	1.61483i	−0.152990	−	0.988228i	$-0.548890\pi$
$588$	−7.32051			−0.301893
$589$	5.19615	+	3.00000i	0.214104	+	0.123613i
$590$	2.73205	+	0.732051i	0.112477	+	0.0301381i
$591$	−7.94744	−	4.58846i	−0.326914	−	0.188744i
$592$	17.0718			0.701647
$593$			1.58846i			0.0652301i	0.999468	+	0.0326151i	$0.0103835\pi$
$593$			1.58846i			0.0652301i	−0.999468	+	0.0326151i	$0.989616\pi$
$594$	−8.00000	−	8.00000i	−0.328244	−	0.328244i
$595$	−5.19615	+	3.00000i	−0.213021	+	0.122988i
$596$		−	23.4641i		−	0.961127i
$597$		−	11.0718i		−	0.453138i
$598$	−41.7846	+	0.803848i	−1.70870	+	0.0328718i
$599$	−13.2679			−0.542114			−0.271057	−	0.962563i	$-0.587373\pi$
$599$	−13.2679			−0.542114			−0.271057	+	0.962563i	$0.587373\pi$
$600$	−17.8564	−	4.78461i	−0.728985	−	0.195331i
$601$	−13.0359	−	22.5788i	−0.531745	−	0.921010i	−0.999313	−	0.0370529i	$-0.988203\pi$
$601$	−13.0359	−	22.5788i	−0.531745	−	0.921010i	0.467568	−	0.883957i	$-0.345130\pi$
$602$	8.78461	−	8.78461i	0.358034	−	0.358034i
$603$	−17.9090			−0.729309
$604$	−2.19615	−	3.80385i	−0.0893602	−	0.154776i
$605$	13.0622	−	22.6244i	0.531053	−	0.919811i
$606$	−11.5359	−	3.09103i	−0.468614	−	0.125565i
$607$	−1.29423	+	2.24167i	−0.0525311	+	0.0909866i	−0.891095	−	0.453816i	$-0.850062\pi$
$607$	−1.29423	+	2.24167i	−0.0525311	+	0.0909866i	0.838564	+	0.544803i	$0.183396\pi$
$608$	5.07180	−	5.07180i	0.205689	−	0.205689i
$609$	−6.58846	+	3.80385i	−0.266978	+	0.154140i
$610$	−1.36603	+	5.09808i	−0.0553088	+	0.206415i
$611$	16.8301	−	17.4904i	0.680874	−	0.707585i
$612$	−1.98076	−	1.14359i	−0.0800676	−	0.0462270i
$613$	20.2583	+	35.0885i	0.818226	+	1.41721i	0.906988	+	0.421157i	$0.138376\pi$
$613$	20.2583	+	35.0885i	0.818226	+	1.41721i	−0.0887617	+	0.996053i	$0.528291\pi$
$614$	0.803848	+	3.00000i	0.0324406	+	0.121070i
$615$	−12.5622	+	21.7583i	−0.506556	+	0.877381i
$616$	−13.8564	+	13.8564i	−0.558291	+	0.558291i
$617$	15.3564	+	8.86603i	0.618226	+	0.356933i	0.776178	−	0.630514i	$-0.217156\pi$
$617$	15.3564	+	8.86603i	0.618226	+	0.356933i	−0.157952	+	0.987447i	$0.550489\pi$
$618$	4.53590	+	4.53590i	0.182461	+	0.182461i
$619$	−24.2487			−0.974638			−0.487319	−	0.873224i	$-0.662025\pi$
$619$	−24.2487			−0.974638			−0.487319	+	0.873224i	$0.662025\pi$
$620$	−17.6603	−	30.5885i	−0.709253	−	1.22846i
$621$	28.3923	−	16.3923i	1.13934	−	0.657801i
$622$	−6.80385	−	25.3923i	−0.272809	−	1.01814i
$623$	−25.8564			−1.03592
$624$	−7.32051	+	7.60770i	−0.293055	+	0.304552i
$625$	10.0718			0.402872
$626$	−0.928203	−	3.46410i	−0.0370985	−	0.138453i
$627$	1.60770	−	0.928203i	0.0642052	−	0.0370689i
$628$	−3.92820	−	6.80385i	−0.156752	−	0.271503i
$629$	1.98076			0.0789782
$630$	31.8564	+	31.8564i	1.26919	+	1.26919i
$631$	−14.7846	−	8.53590i	−0.588566	−	0.339809i	0.175964	−	0.984397i	$-0.443696\pi$
$631$	−14.7846	−	8.53590i	−0.588566	−	0.339809i	−0.764530	+	0.644588i	$0.777029\pi$
$632$	20.7846	+	20.7846i	0.826767	+	0.826767i
$633$	−10.4641	+	18.1244i	−0.415911	+	0.720378i
$634$	9.22243	+	34.4186i	0.366270	+	1.36694i
$635$	−0.633975	−	1.09808i	−0.0251585	−	0.0435758i
$636$	4.98076	+	2.87564i	0.197500	+	0.114027i
$637$	4.33013	−	17.5000i	0.171566	−	0.693375i
$638$	−2.19615	+	8.19615i	−0.0869465	+	0.324489i
$639$	−19.7776	+	11.4186i	−0.782389	+	0.451712i
$640$	−40.7846	+	10.9282i	−1.61215	+	0.431975i
$641$	7.03590	−	12.1865i	0.277901	−	0.481339i	−0.692962	−	0.720974i	$-0.743695\pi$
$641$	7.03590	−	12.1865i	0.277901	−	0.481339i	0.970863	+	0.239635i	$0.0770279\pi$
$642$	17.6603	+	4.73205i	0.696995	+	0.186759i
$643$	−19.3923	+	33.5885i	−0.764758	+	1.32460i	0.175617	+	0.984459i	$0.443808\pi$
$643$	−19.3923	+	33.5885i	−0.764758	+	1.32460i	−0.940375	+	0.340141i	$0.889525\pi$
$644$	−28.3923	−	49.1769i	−1.11881	−	1.93784i
$645$	6.92820			0.272798
$646$	0.588457	−	0.588457i	0.0231525	−	0.0231525i
$647$	−14.8301	−	25.6865i	−0.583032	−	1.00984i	−0.995118	−	0.0986965i	$-0.968533\pi$
$647$	−14.8301	−	25.6865i	−0.583032	−	1.00984i	0.412085	−	0.911145i	$-0.364801\pi$
$648$	−3.26795	+	12.1962i	−0.128377	+	0.479110i
$649$	1.07180			0.0420717
$650$	22.0000	−	39.8564i	0.862911	−	1.56330i
$651$		−	12.0000i		−	0.470317i
$652$		−	32.7846i		−	1.28394i
$653$	−31.1769	+	18.0000i	−1.22005	+	0.704394i	−0.964928	−	0.262515i	$-0.915448\pi$
$653$	−31.1769	+	18.0000i	−1.22005	+	0.704394i	−0.255119	+	0.966910i	$0.582115\pi$
$654$	4.39230	+	4.39230i	0.171753	+	0.171753i
$655$		−	40.0526i		−	1.56498i
$656$			36.7846i			1.43620i
$657$	3.69615	+	2.13397i	0.144201	+	0.0832543i
$658$	31.8564	+	8.53590i	1.24189	+	0.332764i
$659$	26.7846	+	15.4641i	1.04338	+	0.602396i	0.920789	−	0.390061i	$-0.127546\pi$
$659$	26.7846	+	15.4641i	1.04338	+	0.602396i	0.122591	+	0.992457i	$0.460880\pi$
$660$	−10.9282			−0.425380
$661$	6.06218	+	10.5000i	0.235791	+	0.408403i	0.959502	−	0.281701i	$-0.0908985\pi$
$661$	6.06218	+	10.5000i	0.235791	+	0.408403i	−0.723711	+	0.690103i	$0.757565\pi$
$662$	16.3923	+	4.39230i	0.637105	+	0.170712i
$663$	−0.849365	+	0.882686i	−0.0329866	+	0.0342807i
$664$	−2.92820	−	2.92820i	−0.113636	−	0.113636i
$665$	−14.1962	+	8.19615i	−0.550503	+	0.317833i
$666$	−3.84936	−	14.3660i	−0.149160	−	0.556672i
$667$	−21.2942	−	12.2942i	−0.824516	−	0.476034i
$668$	4.92820	−	8.53590i	0.190678	−	0.330264i
$669$	−9.33975	+	16.1769i	−0.361095	+	0.625436i
$670$	−27.1244	+	27.1244i	−1.04791	+	1.04791i
$671$			2.00000i			0.0772091i
$672$	−13.8564	−	3.71281i	−0.534522	−	0.143225i
$673$	5.50000	+	9.52628i	0.212009	+	0.367211i	0.952343	−	0.305028i	$-0.0986659\pi$
$673$	5.50000	+	9.52628i	0.212009	+	0.367211i	−0.740334	+	0.672239i	$0.765333\pi$
$674$	−12.1699	−	45.4186i	−0.468766	−	1.74946i
$675$			35.7128i			1.37459i
$676$	−13.8564	−	22.0000i	−0.532939	−	0.846154i
$677$			7.85641i			0.301946i	0.988538	+	0.150973i	$0.0482407\pi$
$677$			7.85641i			0.301946i	−0.988538	+	0.150973i	$0.951759\pi$
$678$	3.00000	−	0.803848i	0.115214	−	0.0308716i
$679$	10.3923	+	18.0000i	0.398820	+	0.690777i
$680$	−4.73205	+	1.26795i	−0.181466	+	0.0486236i
$681$		−	19.0718i		−	0.730833i
$682$	−9.46410	−	9.46410i	−0.362399	−	0.362399i
$683$	5.63397	−	9.75833i	0.215578	−	0.373392i	−0.737873	−	0.674939i	$-0.764170\pi$
$683$	5.63397	−	9.75833i	0.215578	−	0.373392i	0.953451	+	0.301547i	$0.0975031\pi$
$684$	−5.41154	−	3.12436i	−0.206916	−	0.119463i
$685$	−43.9186	−	25.3564i	−1.67804	−	0.968818i
$686$	−9.46410	+	2.53590i	−0.361341	+	0.0968211i
$687$	8.19615	−	4.73205i	0.312703	−	0.180539i
$688$	8.78461	−	5.07180i	0.334910	−	0.193360i
$689$	−9.82051	+	10.2058i	−0.374132	+	0.388809i
$690$	8.19615	−	30.5885i	0.312022	−	1.16448i
$691$	9.00000	+	15.5885i	0.342376	+	0.593013i	0.984873	−	0.173275i	$-0.0554350\pi$
$691$	9.00000	+	15.5885i	0.342376	+	0.593013i	−0.642497	+	0.766288i	$0.722102\pi$
$692$	37.8564			1.43908
$693$	14.7846	+	8.53590i	0.561621	+	0.324252i
$694$	0.464102	−	1.73205i	0.0176171	−	0.0657477i
$695$	30.5885	+	17.6603i	1.16029	+	0.669892i
$696$	−6.00000	+	1.60770i	−0.227429	+	0.0609395i
$697$			4.26795i			0.161660i
$698$	−5.32051	+	5.32051i	−0.201384	+	0.201384i
$699$		0			0
$700$	61.8564			2.33795
$701$		−	8.78461i		−	0.331790i	−0.986143	−	0.165895i	$-0.946949\pi$
$701$		−	8.78461i		−	0.331790i	0.986143	−	0.165895i	$-0.0530513\pi$
$702$	17.8564	+	9.85641i	0.673947	+	0.372006i
$703$	5.41154			0.204100
$704$	−13.8564	+	8.00000i	−0.522233	+	0.301511i
$705$	9.19615	+	15.9282i	0.346347	+	0.599891i
$706$	−18.2679	−	18.2679i	−0.687523	−	0.687523i
$707$	39.9615			1.50291
$708$	0.392305	+	0.679492i	0.0147437	+	0.0255369i
$709$	20.5981	−	35.6769i	0.773577	−	1.33987i	−0.162014	−	0.986788i	$-0.551799\pi$
$709$	20.5981	−	35.6769i	0.773577	−	1.33987i	0.935591	−	0.353086i	$-0.114868\pi$
$710$	−12.6603	+	47.2487i	−0.475131	+	1.77321i
$711$	12.8038	−	22.1769i	0.480182	−	0.831699i
$712$	−20.3923	−	5.46410i	−0.764234	−	0.204776i
$713$	33.5885	−	19.3923i	1.25790	−	0.726248i
$714$	−1.60770	−	0.430781i	−0.0601665	−	0.0161216i
$715$	6.46410	−	26.1244i	0.241744	−	0.976996i
$716$	−13.8564	+	24.0000i	−0.517838	+	0.896922i
$717$	−6.73205	−	11.6603i	−0.251413	−	0.435460i
$718$	17.8564	−	4.78461i	0.666395	−	0.178560i
$719$	16.8564	−	29.1962i	0.628638	−	1.08883i	−0.359187	−	0.933265i	$-0.616946\pi$
$719$	16.8564	−	29.1962i	0.628638	−	1.08883i	0.987825	−	0.155567i	$-0.0497206\pi$
$720$	18.3923	+	31.8564i	0.685441	+	1.18722i
$721$	−18.5885	−	10.7321i	−0.692270	−	0.399682i
$722$	−17.3923	+	17.3923i	−0.647275	+	0.647275i
$723$	8.19615			0.304818
$724$	18.4641	+	31.9808i	0.686213	+	1.18856i
$725$	23.1962	−	13.3923i	0.861483	−	0.497378i
$726$	7.00000	−	1.87564i	0.259794	−	0.0696117i
$727$	−13.6077			−0.504681			−0.252341	−	0.967638i	$-0.581200\pi$
$727$	−13.6077			−0.504681			−0.252341	+	0.967638i	$0.581200\pi$
$728$	17.0718	−	30.9282i	0.632723	−	1.14628i
$729$	2.21539			0.0820515
$730$	8.83013	−	2.36603i	0.326818	−	0.0875705i
$731$	1.01924	−	0.588457i	0.0376979	−	0.0217649i
$732$	−1.26795	+	0.732051i	−0.0468648	+	0.0270574i
$733$	4.94744			0.182738			0.0913690	−	0.995817i	$-0.470876\pi$
$733$	4.94744			0.182738			0.0913690	+	0.995817i	$0.470876\pi$
$734$	−28.1962	+	28.1962i	−1.04074	+	1.04074i
$735$	11.8301	+	6.83013i	0.436361	+	0.251933i
$736$	−12.0000	−	44.7846i	−0.442326	−	1.65078i
$737$	−7.26795	+	12.5885i	−0.267718	+	0.463702i
$738$	30.9545	−	8.29423i	1.13945	−	0.305315i
$739$	9.46410	+	16.3923i	0.348143	+	0.603001i	0.985920	−	0.167220i	$-0.0534792\pi$
$739$	9.46410	+	16.3923i	0.348143	+	0.603001i	−0.637777	+	0.770221i	$0.720146\pi$
$740$	−27.5885	−	15.9282i	−1.01417	−	0.585532i
$741$	−2.32051	+	2.41154i	−0.0852460	+	0.0885902i
$742$	−18.5885	−	4.98076i	−0.682404	−	0.182850i
$743$	4.73205	−	2.73205i	0.173602	−	0.100229i	−0.410681	−	0.911779i	$-0.634709\pi$
$743$	4.73205	−	2.73205i	0.173602	−	0.100229i	0.584283	+	0.811550i	$0.301376\pi$
$744$	2.53590	−	9.46410i	0.0929705	−	0.346971i
$745$	−21.8923	+	37.9186i	−0.802072	+	1.38923i
$746$	−9.43782	+	35.2224i	−0.345543	+	1.28958i
$747$	−1.80385	+	3.12436i	−0.0659993	+	0.114314i
$748$	−1.60770	+	0.928203i	−0.0587832	+	0.0339385i
$749$	−61.1769			−2.23536
$750$	10.7321	+	10.7321i	0.391879	+	0.391879i
$751$	18.1962	+	31.5167i	0.663987	+	1.15006i	0.979559	+	0.201158i	$0.0644703\pi$
$751$	18.1962	+	31.5167i	0.663987	+	1.15006i	−0.315572	+	0.948902i	$0.602196\pi$
$752$	23.3205	+	13.4641i	0.850411	+	0.490985i
$753$	−6.00000			−0.218652
$754$	−0.294229	−	15.2942i	−0.0107152	−	0.556983i
$755$			8.19615i			0.298289i
$756$			27.7128i			1.00791i
$757$	−18.3397	+	10.5885i	−0.666569	+	0.384844i	−0.794776	−	0.606904i	$-0.792411\pi$
$757$	−18.3397	+	10.5885i	−0.666569	+	0.384844i	0.128206	+	0.991748i	$0.459078\pi$
$758$	22.0526	−	22.0526i	0.800985	−	0.800985i
$759$		−	12.0000i		−	0.435572i
$760$	−12.9282	+	3.46410i	−0.468955	+	0.125656i
$761$	−10.8564	−	6.26795i	−0.393544	−	0.227213i	0.290150	−	0.956981i	$-0.406295\pi$
$761$	−10.8564	−	6.26795i	−0.393544	−	0.227213i	−0.683695	+	0.729768i	$0.739628\pi$
$762$	0.0910347	−	0.339746i	0.00329784	−	0.0123077i
$763$	−18.0000	−	10.3923i	−0.651644	−	0.376227i
$764$		−	7.60770i		−	0.275237i
$765$	2.13397	+	3.69615i	0.0771540	+	0.133635i
$766$	−7.32051	+	27.3205i	−0.264501	+	0.987130i

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:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(0.633975 - 0.366025i) q^{3} +(-1.73205 + 1.00000i) q^{4} +3.73205 q^{5} +(0.732051 + 0.732051i) q^{6} +(-3.00000 - 1.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.23205 + 2.13397i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 1.36603i) q^{2} +(0.633975 - 0.366025i) q^{3} +(-1.73205 + 1.00000i) q^{4} +3.73205 q^{5} +(0.732051 + 0.732051i) q^{6} +(-3.00000 - 1.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.23205 + 2.13397i) q^{9} +(1.36603 + 5.09808i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-0.732051 + 1.26795i) q^{12} +(-2.59808 - 2.50000i) q^{13} +(1.26795 - 4.73205i) q^{14} +(2.36603 - 1.36603i) q^{15} +(2.00000 - 3.46410i) q^{16} +(0.232051 - 0.401924i) q^{17} +(-3.36603 - 0.901924i) q^{18} +(0.633975 - 1.09808i) q^{19} +(-6.46410 + 3.73205i) q^{20} -2.53590 q^{21} +(-2.00000 + 2.00000i) q^{22} +(-4.09808 - 7.09808i) q^{23} +(-2.00000 - 0.535898i) q^{24} +8.92820 q^{25} +(2.46410 - 4.46410i) q^{26} +4.00000i q^{27} +6.92820 q^{28} +(2.59808 - 1.50000i) q^{29} +(2.73205 + 2.73205i) q^{30} +4.73205i q^{31} +(5.46410 + 1.46410i) q^{32} +(1.26795 + 0.732051i) q^{33} +(0.633975 + 0.169873i) q^{34} +(-11.1962 - 6.46410i) q^{35} -4.92820i q^{36} +(2.13397 + 3.69615i) q^{37} +(1.73205 + 0.464102i) q^{38} +(-2.56218 - 0.633975i) q^{39} +(-7.46410 - 7.46410i) q^{40} +(-7.96410 + 4.59808i) q^{41} +(-0.928203 - 3.46410i) q^{42} +(2.19615 + 1.26795i) q^{43} +(-3.46410 - 2.00000i) q^{44} +(-4.59808 + 7.96410i) q^{45} +(8.19615 - 8.19615i) q^{46} +6.73205i q^{47} -2.92820i q^{48} +(2.50000 + 4.33013i) q^{49} +(3.26795 + 12.1962i) q^{50} -0.339746i q^{51} +(7.00000 + 1.73205i) q^{52} -3.92820i q^{53} +(-5.46410 + 1.46410i) q^{54} +(3.73205 + 6.46410i) q^{55} +(2.53590 + 9.46410i) q^{56} -0.928203i q^{57} +(3.00000 + 3.00000i) q^{58} +(0.267949 - 0.464102i) q^{59} +(-2.73205 + 4.73205i) q^{60} +(0.866025 + 0.500000i) q^{61} +(-6.46410 + 1.73205i) q^{62} +(7.39230 - 4.26795i) q^{63} +8.00000i q^{64} +(-9.69615 - 9.33013i) q^{65} +(-0.535898 + 2.00000i) q^{66} +(3.63397 + 6.29423i) q^{67} +0.928203i q^{68} +(-5.19615 - 3.00000i) q^{69} +(4.73205 - 17.6603i) q^{70} +(8.02628 + 4.63397i) q^{71} +(6.73205 - 1.80385i) q^{72} -1.73205i q^{73} +(-4.26795 + 4.26795i) q^{74} +(5.66025 - 3.26795i) q^{75} +2.53590i q^{76} -6.92820i q^{77} +(-0.0717968 - 3.73205i) q^{78} -10.3923 q^{79} +(7.46410 - 12.9282i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(-9.19615 - 9.19615i) q^{82} +1.46410 q^{83} +(4.39230 - 2.53590i) q^{84} +(0.866025 - 1.50000i) q^{85} +(-0.928203 + 3.46410i) q^{86} +(1.09808 - 1.90192i) q^{87} +(1.46410 - 5.46410i) q^{88} +(6.46410 - 3.73205i) q^{89} +(-12.5622 - 3.36603i) q^{90} +(3.46410 + 12.0000i) q^{91} +(14.1962 + 8.19615i) q^{92} +(1.73205 + 3.00000i) q^{93} +(-9.19615 + 2.46410i) q^{94} +(2.36603 - 4.09808i) q^{95} +(4.00000 - 1.07180i) q^{96} +(-5.19615 - 3.00000i) q^{97} +(-5.00000 + 5.00000i) q^{98} -4.92820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{3} + 8 q^{5} - 4 q^{6} - 12 q^{7} - 8 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 6 * q^3 + 8 * q^5 - 4 * q^6 - 12 * q^7 - 8 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} + 6 q^{3} + 8 q^{5} - 4 q^{6} - 12 q^{7} - 8 q^{8} + 2 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{12} + 12 q^{14} + 6 q^{15} + 8 q^{16} - 6 q^{17} - 10 q^{18} + 6 q^{19} - 12 q^{20} - 24 q^{21} - 8 q^{22} - 6 q^{23} - 8 q^{24} + 8 q^{25} - 4 q^{26} + 4 q^{30} + 8 q^{32} + 12 q^{33} + 6 q^{34} - 24 q^{35} + 12 q^{37} + 14 q^{39} - 16 q^{40} - 18 q^{41} + 24 q^{42} - 12 q^{43} - 8 q^{45} + 12 q^{46} + 10 q^{49} + 20 q^{50} + 28 q^{52} - 8 q^{54} + 8 q^{55} + 24 q^{56} + 12 q^{58} + 8 q^{59} - 4 q^{60} - 12 q^{62} - 12 q^{63} - 18 q^{65} - 16 q^{66} + 18 q^{67} + 12 q^{70} - 6 q^{71} + 20 q^{72} - 24 q^{74} - 12 q^{75} - 28 q^{78} + 16 q^{80} - 2 q^{81} - 16 q^{82} - 8 q^{83} - 24 q^{84} + 24 q^{86} - 6 q^{87} - 8 q^{88} + 12 q^{89} - 26 q^{90} + 36 q^{92} - 16 q^{94} + 6 q^{95} + 16 q^{96} - 20 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^3 + 8 * q^5 - 4 * q^6 - 12 * q^7 - 8 * q^8 + 2 * q^9 + 2 * q^10 + 4 * q^11 + 4 * q^12 + 12 * q^14 + 6 * q^15 + 8 * q^16 - 6 * q^17 - 10 * q^18 + 6 * q^19 - 12 * q^20 - 24 * q^21 - 8 * q^22 - 6 * q^23 - 8 * q^24 + 8 * q^25 - 4 * q^26 + 4 * q^30 + 8 * q^32 + 12 * q^33 + 6 * q^34 - 24 * q^35 + 12 * q^37 + 14 * q^39 - 16 * q^40 - 18 * q^41 + 24 * q^42 - 12 * q^43 - 8 * q^45 + 12 * q^46 + 10 * q^49 + 20 * q^50 + 28 * q^52 - 8 * q^54 + 8 * q^55 + 24 * q^56 + 12 * q^58 + 8 * q^59 - 4 * q^60 - 12 * q^62 - 12 * q^63 - 18 * q^65 - 16 * q^66 + 18 * q^67 + 12 * q^70 - 6 * q^71 + 20 * q^72 - 24 * q^74 - 12 * q^75 - 28 * q^78 + 16 * q^80 - 2 * q^81 - 16 * q^82 - 8 * q^83 - 24 * q^84 + 24 * q^86 - 6 * q^87 - 8 * q^88 + 12 * q^89 - 26 * q^90 + 36 * q^92 - 16 * q^94 + 6 * q^95 + 16 * q^96 - 20 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more