LMFDB - Embedded newform 104.2.s.a.69.2

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:	$1$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			69.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	104.69
Dual form			104.2.s.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{2} +(-0.633975 - 0.366025i) q^{3} -2.00000i q^{4} -3.73205 q^{5} +(1.00000 - 0.267949i) q^{6} +(-3.00000 + 1.73205i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.23205 - 2.13397i) q^{9} +(3.73205 - 3.73205i) 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} -4.00000 q^{16} +(0.232051 + 0.401924i) q^{17} +(3.36603 + 0.901924i) q^{18} +(-0.633975 - 1.09808i) q^{19} +7.46410i q^{20} +2.53590 q^{21} +(-0.732051 - 2.73205i) q^{22} +(-4.09808 + 7.09808i) q^{23} +(-0.535898 - 2.00000i) q^{24} +8.92820 q^{25} +(-0.0980762 + 5.09808i) q^{26} +4.00000i q^{27} +(3.46410 + 6.00000i) q^{28} +(-2.59808 - 1.50000i) q^{29} +(-3.73205 + 1.00000i) q^{30} -4.73205i q^{31} +(4.00000 - 4.00000i) q^{32} +(1.26795 - 0.732051i) q^{33} +(-0.633975 - 0.169873i) q^{34} +(11.1962 - 6.46410i) q^{35} +(-4.26795 + 2.46410i) 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} +(-2.53590 + 2.53590i) q^{42} +(-2.19615 + 1.26795i) q^{43} +(3.46410 + 2.00000i) q^{44} +(4.59808 + 7.96410i) q^{45} +(-3.00000 - 11.1962i) q^{46} -6.73205i q^{47} +(2.53590 + 1.46410i) q^{48} +(2.50000 - 4.33013i) q^{49} +(-8.92820 + 8.92820i) q^{50} -0.339746i q^{51} +(-5.00000 - 5.19615i) q^{52} -3.92820i q^{53} +(-4.00000 - 4.00000i) q^{54} +(3.73205 - 6.46410i) q^{55} +(-9.46410 - 2.53590i) q^{56} +0.928203i q^{57} +(4.09808 - 1.09808i) q^{58} +(-0.267949 - 0.464102i) q^{59} +(2.73205 - 4.73205i) q^{60} +(-0.866025 + 0.500000i) q^{61} +(4.73205 + 4.73205i) 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} +(0.803848 - 0.464102i) q^{68} +(5.19615 - 3.00000i) q^{69} +(-4.73205 + 17.6603i) q^{70} +(8.02628 - 4.63397i) q^{71} +(1.80385 - 6.73205i) q^{72} +1.73205i q^{73} +(-1.56218 - 5.83013i) q^{74} +(-5.66025 - 3.26795i) q^{75} +(-2.19615 + 1.26795i) q^{76} -6.92820i q^{77} +(1.92820 - 3.19615i) q^{78} -10.3923 q^{79} +14.9282 q^{80} +(-2.23205 + 3.86603i) q^{81} +(12.5622 - 3.36603i) q^{82} -1.46410 q^{83} -5.07180i q^{84} +(-0.866025 - 1.50000i) q^{85} +(0.928203 - 3.46410i) q^{86} +(1.09808 + 1.90192i) q^{87} +(-5.46410 + 1.46410i) 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} +(6.73205 + 6.73205i) q^{94} +(2.36603 + 4.09808i) q^{95} +(-4.00000 + 1.07180i) q^{96} +(-5.19615 + 3.00000i) q^{97} +(1.83013 + 6.83013i) q^{98} +4.92820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 6 q^{3} - 8 q^{5} + 4 q^{6} - 12 q^{7} + 8 q^{8} + 2 q^{9} + 8 q^{10} - 4 q^{11} + 4 q^{12} + 12 q^{14} + 6 q^{15} - 16 q^{16} - 6 q^{17} + 10 q^{18} - 6 q^{19} + 24 q^{21} + 4 q^{22} - 6 q^{23}+ \cdots - 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^5 + 4 * q^6 - 12 * q^7 + 8 * q^8 + 2 * q^9 + 8 * q^10 - 4 * q^11 + 4 * q^12 + 12 * q^14 + 6 * q^15 - 16 * q^16 - 6 * q^17 + 10 * q^18 - 6 * q^19 + 24 * q^21 + 4 * q^22 - 6 * q^23 - 16 * q^24 + 8 * q^25 + 10 * q^26 - 8 * q^30 + 16 * q^32 + 12 * q^33 - 6 * q^34 + 24 * q^35 - 24 * q^36 - 12 * q^37 + 14 * q^39 - 16 * q^40 - 18 * q^41 - 24 * q^42 + 12 * q^43 + 8 * q^45 - 12 * q^46 + 24 * q^48 + 10 * q^49 - 8 * q^50 - 20 * q^52 - 16 * q^54 + 8 * q^55 - 24 * q^56 + 6 * q^58 - 8 * q^59 + 4 * q^60 + 12 * q^62 - 12 * q^63 - 18 * q^65 - 16 * q^66 - 18 * q^67 + 24 * q^68 - 12 * q^70 - 6 * q^71 + 28 * q^72 + 18 * q^74 + 12 * q^75 + 12 * q^76 - 20 * q^78 + 32 * q^80 - 2 * q^81 + 26 * q^82 + 8 * q^83 - 24 * q^86 - 6 * q^87 - 8 * q^88 + 12 * q^89 - 26 * q^90 + 36 * q^92 + 20 * q^94 + 6 * q^95 - 16 * q^96 - 10 * q^98 - 8 * q^99

Character values

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

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

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 $

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	−0.633975	−	0.366025i	−0.366025	−	0.211325i	0.305695	−	0.952129i	$-0.401111\pi$
$3$	−0.633975	−	0.366025i	−0.366025	−	0.211325i	−0.671721	+	0.740805i	$0.734444\pi$
$4$		−	2.00000i		−	1.00000i
$5$	−3.73205			−1.66902			−0.834512	−	0.550990i	$-0.814250\pi$
$5$	−3.73205			−1.66902			−0.834512	+	0.550990i	$0.814250\pi$
$6$	1.00000	−	0.267949i	0.408248	−	0.109390i
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.188982	+	0.981981i	$0.560519\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−1.23205	−	2.13397i	−0.410684	−	0.711325i
$10$	3.73205	−	3.73205i	1.18018	−	1.18018i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	−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
$16$	−4.00000			−1.00000
$17$	0.232051	+	0.401924i	0.0562806	+	0.0974808i	0.892793	−	0.450467i	$-0.148743\pi$
$17$	0.232051	+	0.401924i	0.0562806	+	0.0974808i	−0.836512	+	0.547948i	$0.815409\pi$
$18$	3.36603	+	0.901924i	0.793380	+	0.212585i
$19$	−0.633975	−	1.09808i	−0.145444	−	0.251916i	0.784095	−	0.620641i	$-0.213128\pi$
$19$	−0.633975	−	1.09808i	−0.145444	−	0.251916i	−0.929538	+	0.368725i	$0.879794\pi$
$20$			7.46410i			1.66902i
$21$	2.53590			0.553378
$22$	−0.732051	−	2.73205i	−0.156074	−	0.582475i
$23$	−4.09808	+	7.09808i	−0.854508	+	1.48005i	0.0225928	+	0.999745i	$0.492808\pi$
$23$	−4.09808	+	7.09808i	−0.854508	+	1.48005i	−0.877101	+	0.480306i	$0.840525\pi$
$24$	−0.535898	−	2.00000i	−0.109390	−	0.408248i
$25$	8.92820			1.78564
$26$	−0.0980762	+	5.09808i	−0.0192343	+	0.999815i
$27$			4.00000i			0.769800i
$28$	3.46410	+	6.00000i	0.654654	+	1.13389i
$29$	−2.59808	−	1.50000i	−0.482451	−	0.278543i	0.238987	−	0.971023i	$-0.423185\pi$
$29$	−2.59808	−	1.50000i	−0.482451	−	0.278543i	−0.721437	+	0.692480i	$0.756518\pi$
$30$	−3.73205	+	1.00000i	−0.681376	+	0.182574i
$31$		−	4.73205i		−	0.849901i	−0.905216	−	0.424951i	$-0.860291\pi$
$31$		−	4.73205i		−	0.849901i	0.905216	−	0.424951i	$-0.139709\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	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
$36$	−4.26795	+	2.46410i	−0.711325	+	0.410684i
$37$	−2.13397	+	3.69615i	−0.350823	+	0.607644i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	−2.13397	+	3.69615i	−0.350823	+	0.607644i	0.635571	+	0.772043i	$0.280765\pi$
$38$	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	−0.273921	−	0.961752i	$-0.588321\pi$
$41$	−7.96410	−	4.59808i	−1.24378	−	0.718099i	−0.969862	+	0.243653i	$0.921654\pi$
$42$	−2.53590	+	2.53590i	−0.391298	+	0.391298i
$43$	−2.19615	+	1.26795i	−0.334910	+	0.193360i	−0.658019	−	0.753001i	$-0.728605\pi$
$43$	−2.19615	+	1.26795i	−0.334910	+	0.193360i	0.323109	+	0.946362i	$0.395272\pi$
$44$	3.46410	+	2.00000i	0.522233	+	0.301511i
$45$	4.59808	+	7.96410i	0.685441	+	1.18722i
$46$	−3.00000	−	11.1962i	−0.442326	−	1.65078i
$47$		−	6.73205i		−	0.981971i	−0.871168	−	0.490985i	$-0.836637\pi$
$47$		−	6.73205i		−	0.981971i	0.871168	−	0.490985i	$-0.163363\pi$
$48$	2.53590	+	1.46410i	0.366025	+	0.211325i
$49$	2.50000	−	4.33013i	0.357143	−	0.618590i
$50$	−8.92820	+	8.92820i	−1.26264	+	1.26264i
$51$		−	0.339746i		−	0.0475740i
$52$	−5.00000	−	5.19615i	−0.693375	−	0.720577i
$53$		−	3.92820i		−	0.539580i	−0.962919	−	0.269790i	$-0.913046\pi$
$53$		−	3.92820i		−	0.539580i	0.962919	−	0.269790i	$-0.0869543\pi$
$54$	−4.00000	−	4.00000i	−0.544331	−	0.544331i
$55$	3.73205	−	6.46410i	0.503230	−	0.871619i
$56$	−9.46410	−	2.53590i	−1.26469	−	0.338874i
$57$			0.928203i			0.122944i
$58$	4.09808	−	1.09808i	0.538104	−	0.144184i
$59$	−0.267949	−	0.464102i	−0.0348840	−	0.0604209i	0.848056	−	0.529906i	$-0.177773\pi$
$59$	−0.267949	−	0.464102i	−0.0348840	−	0.0604209i	−0.882940	+	0.469485i	$0.844440\pi$
$60$	2.73205	−	4.73205i	0.352706	−	0.610905i
$61$	−0.866025	+	0.500000i	−0.110883	+	0.0640184i	−0.554416	−	0.832240i	$-0.687058\pi$
$61$	−0.866025	+	0.500000i	−0.110883	+	0.0640184i	0.443533	+	0.896258i	$0.353725\pi$
$62$	4.73205	+	4.73205i	0.600971	+	0.600971i
$63$	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	$-0.979760\pi$
$67$	−3.63397	+	6.29423i	−0.443961	+	0.768962i	0.554019	+	0.832504i	$0.313094\pi$
$68$	0.803848	−	0.464102i	0.0974808	−	0.0562806i
$69$	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	0.0586738	−	0.998277i	$-0.481313\pi$
$71$	8.02628	−	4.63397i	0.952544	−	0.549952i	0.893870	+	0.448326i	$0.147979\pi$
$72$	1.80385	−	6.73205i	0.212585	−	0.793380i
$73$			1.73205i			0.202721i	0.994850	+	0.101361i	$0.0323196\pi$
$73$			1.73205i			0.202721i	−0.994850	+	0.101361i	$0.967680\pi$
$74$	−1.56218	−	5.83013i	−0.181599	−	0.677738i
$75$	−5.66025	−	3.26795i	−0.653590	−	0.377350i
$76$	−2.19615	+	1.26795i	−0.251916	+	0.145444i
$77$		−	6.92820i		−	0.789542i
$78$	1.92820	−	3.19615i	0.218326	−	0.361893i
$79$	−10.3923			−1.16923			−0.584613	−	0.811312i	$-0.698754\pi$
$79$	−10.3923			−1.16923			−0.584613	+	0.811312i	$0.698754\pi$
$80$	14.9282			1.66902
$81$	−2.23205	+	3.86603i	−0.248006	+	0.429558i
$82$	12.5622	−	3.36603i	1.38726	−	0.371715i
$83$	−1.46410			−0.160706			−0.0803530	−	0.996766i	$-0.525605\pi$
$83$	−1.46410			−0.160706			−0.0803530	+	0.996766i	$0.525605\pi$
$84$		−	5.07180i		−	0.553378i
$85$	−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
$88$	−5.46410	+	1.46410i	−0.582475	+	0.156074i
$89$	6.46410	+	3.73205i	0.685193	+	0.395597i	0.801809	−	0.597581i	$-0.203871\pi$
$89$	6.46410	+	3.73205i	0.685193	+	0.395597i	−0.116615	+	0.993177i	$0.537205\pi$
$90$	−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
$94$	6.73205	+	6.73205i	0.694358	+	0.694358i
$95$	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	−0.740034	−	0.672569i	$-0.765191\pi$
$97$	−5.19615	+	3.00000i	−0.527589	+	0.304604i	0.212445	+	0.977173i	$0.431857\pi$
$98$	1.83013	+	6.83013i	0.184871	+	0.689947i
$99$	4.92820			0.495303
$100$		−	17.8564i		−	1.78564i
$101$	9.99038	+	5.76795i	0.994080	+	0.573932i	0.906491	−	0.422224i	$-0.138751\pi$
$101$	9.99038	+	5.76795i	0.994080	+	0.573932i	0.0875887	+	0.996157i	$0.472084\pi$
$102$	0.339746	+	0.339746i	0.0336399	+	0.0336399i
$103$	6.19615			0.610525			0.305263	−	0.952268i	$-0.401256\pi$
$103$	6.19615			0.610525			0.305263	+	0.952268i	$0.401256\pi$
$104$	10.1962	+	0.196152i	0.999815	+	0.0192343i
$105$	−9.46410			−0.923602
$106$	3.92820	+	3.92820i	0.381541	+	0.381541i
$107$	−15.2942	−	8.83013i	−1.47855	−	0.853641i	−0.478843	−	0.877900i	$-0.658944\pi$
$107$	−15.2942	−	8.83013i	−1.47855	−	0.853641i	−0.999706	+	0.0242598i	$0.992277\pi$
$108$	8.00000			0.769800
$109$	−6.00000			−0.574696			−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000			−0.574696			−0.287348	+	0.957826i	$0.592774\pi$
$110$	2.73205	+	10.1962i	0.260491	+	0.972165i
$111$	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	0.927914	−	0.372794i	$-0.121600\pi$
$113$	1.50000	+	2.59808i	0.141108	+	0.244406i	−0.786806	+	0.617200i	$0.788267\pi$
$114$	−0.928203	−	0.928203i	−0.0869342	−	0.0869342i
$115$	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
$120$	2.00000	+	7.46410i	0.182574	+	0.681376i
$121$	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
$124$	−9.46410			−0.849901
$125$	−14.6603			−1.31125
$126$	−11.6603	+	3.12436i	−1.03878	+	0.278340i
$127$	−0.169873	+	0.294229i	−0.0150738	+	0.0261086i	−0.873464	−	0.486889i	$-0.838132\pi$
$127$	−0.169873	+	0.294229i	−0.0150738	+	0.0261086i	0.858390	+	0.512997i	$0.171465\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$	1.85641			0.163447
$130$	0.366025	−	19.0263i	0.0321026	−	1.66872i
$131$		−	10.7321i		−	0.937664i	−0.883287	−	0.468832i	$-0.844675\pi$
$131$		−	10.7321i		−	0.937664i	0.883287	−	0.468832i	$-0.155325\pi$
$132$	−1.46410	−	2.53590i	−0.127434	−	0.220722i
$133$	3.80385	+	2.19615i	0.329835	+	0.190431i
$134$	−2.66025	−	9.92820i	−0.229811	−	0.857666i
$135$		−	14.9282i		−	1.28482i
$136$	−0.339746	+	1.26795i	−0.0291330	+	0.108726i
$137$	−11.7679	+	6.79423i	−1.00540	+	0.580470i	−0.909843	−	0.414953i	$-0.863798\pi$
$137$	−11.7679	+	6.79423i	−1.00540	+	0.580470i	−0.0955611	+	0.995424i	$0.530465\pi$
$138$	−2.19615	+	8.19615i	−0.186949	+	0.697703i
$139$	−8.19615	+	4.73205i	−0.695189	+	0.401367i	−0.805553	−	0.592524i	$-0.798132\pi$
$139$	−8.19615	+	4.73205i	−0.695189	+	0.401367i	0.110364	+	0.993891i	$0.464798\pi$
$140$	−12.9282	−	22.3923i	−1.09263	−	1.89250i
$141$	−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
$146$	−1.73205	−	1.73205i	−0.143346	−	0.143346i
$147$	−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	$-0.00709882\pi$
$149$	5.86603	+	10.1603i	0.480564	+	0.832360i	−0.519188	+	0.854660i	$0.673765\pi$
$150$	8.92820	−	2.39230i	0.728985	−	0.195331i
$151$		−	2.19615i		−	0.178720i	−0.995999	−	0.0893602i	$-0.971518\pi$
$151$		−	2.19615i		−	0.178720i	0.995999	−	0.0893602i	$-0.0284822\pi$
$152$	0.928203	−	3.46410i	0.0752872	−	0.280976i
$153$	0.571797	−	0.990381i	0.0462270	−	0.0800676i
$154$	6.92820	+	6.92820i	0.558291	+	0.558291i
$155$			17.6603i			1.41851i
$156$	1.26795	+	5.12436i	0.101517	+	0.410277i
$157$			3.92820i			0.313505i	0.987638	+	0.156752i	$0.0501025\pi$
$157$			3.92820i			0.313505i	−0.987638	+	0.156752i	$0.949898\pi$
$158$	10.3923	−	10.3923i	0.826767	−	0.826767i
$159$	−1.43782	+	2.49038i	−0.114027	+	0.197500i
$160$	−14.9282	+	14.9282i	−1.18018	+	1.18018i
$161$		−	28.3923i		−	2.23763i
$162$	−1.63397	−	6.09808i	−0.128377	−	0.479110i
$163$	8.19615	+	14.1962i	0.641972	+	1.11193i	0.984992	+	0.172600i	$0.0552169\pi$
$163$	8.19615	+	14.1962i	0.641972	+	1.11193i	−0.343020	+	0.939328i	$0.611450\pi$
$164$	−9.19615	+	15.9282i	−0.718099	+	1.24378i
$165$	−4.73205	+	2.73205i	−0.368390	+	0.212690i
$166$	1.46410	−	1.46410i	0.113636	−	0.113636i
$167$	−4.26795	−	2.46410i	−0.330264	−	0.190678i	0.325694	−	0.945475i	$-0.394402\pi$
$167$	−4.26795	−	2.46410i	−0.330264	−	0.190678i	−0.655958	+	0.754797i	$0.727735\pi$
$168$	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
$172$	2.53590	+	4.39230i	0.193360	+	0.334910i
$173$	16.3923	−	9.46410i	1.24628	−	0.719542i	0.275918	−	0.961181i	$-0.411018\pi$
$173$	16.3923	−	9.46410i	1.24628	−	0.719542i	0.970366	+	0.241639i	$0.0776850\pi$
$174$	−3.00000	−	0.803848i	−0.227429	−	0.0609395i
$175$	−26.7846	+	15.4641i	−2.02473	+	1.16898i
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$			0.392305i			0.0294874i
$178$	−10.1962	+	2.73205i	−0.764234	+	0.204776i
$179$	−12.0000	−	6.92820i	−0.896922	−	0.517838i	−0.0207218	−	0.999785i	$-0.506596\pi$
$179$	−12.0000	−	6.92820i	−0.896922	−	0.517838i	−0.876200	+	0.481947i	$0.839930\pi$
$180$	15.9282	−	9.19615i	1.18722	−	0.685441i
$181$		−	18.4641i		−	1.37243i	−0.727401	−	0.686213i	$-0.759272\pi$
$181$		−	18.4641i		−	1.37243i	0.727401	−	0.686213i	$-0.240728\pi$
$182$	−8.53590	−	15.4641i	−0.632723	−	1.14628i
$183$	0.732051			0.0541148
$184$	−22.3923	+	6.00000i	−1.65078	+	0.442326i
$185$	7.96410	−	13.7942i	0.585532	−	1.01417i
$186$	−1.26795	−	4.73205i	−0.0929705	−	0.346971i
$187$	−0.928203			−0.0678769
$188$	−13.4641			−0.981971
$189$	−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	0.788976	−	0.614424i	$-0.210611\pi$
$191$	−1.90192	−	3.29423i	−0.137618	−	0.238362i	−0.926595	+	0.376062i	$0.877278\pi$
$192$	2.92820	−	5.07180i	0.211325	−	0.366025i
$193$	11.3038	+	6.52628i	0.813669	+	0.469772i	0.848228	−	0.529631i	$-0.177670\pi$
$193$	11.3038	+	6.52628i	0.813669	+	0.469772i	−0.0345595	+	0.999403i	$0.511003\pi$
$194$	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	$-0.685978\pi$
$197$	6.26795	−	10.8564i	0.446573	−	0.773487i	0.998160	+	0.0606302i	$0.0193110\pi$
$198$	−4.92820	+	4.92820i	−0.350232	+	0.350232i
$199$	7.56218	+	13.0981i	0.536069	+	0.928498i	0.999111	+	0.0421618i	$0.0134245\pi$
$199$	7.56218	+	13.0981i	0.536069	+	0.928498i	−0.463042	+	0.886336i	$0.653242\pi$
$200$	17.8564	+	17.8564i	1.26264	+	1.26264i
$201$	4.60770	−	2.66025i	0.325002	−	0.187640i
$202$	−15.7583	+	4.22243i	−1.10875	+	0.297089i
$203$	10.3923			0.729397
$204$	−0.679492			−0.0475740
$205$	29.7224	+	17.1603i	2.07590	+	1.19852i
$206$	−6.19615	+	6.19615i	−0.431706	+	0.431706i
$207$	20.1962			1.40373
$208$	−10.3923	+	10.0000i	−0.720577	+	0.693375i
$209$	2.53590			0.175412
$210$	9.46410	−	9.46410i	0.653085	−	0.653085i
$211$	24.7583	+	14.2942i	1.70443	+	0.984055i	0.941148	+	0.337994i	$0.109748\pi$
$211$	24.7583	+	14.2942i	1.70443	+	0.984055i	0.763285	+	0.646061i	$0.223585\pi$
$212$	−7.85641			−0.539580
$213$	−6.78461			−0.464874
$214$	24.1244	−	6.46410i	1.64911	−	0.441877i
$215$	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
$218$	6.00000	−	6.00000i	0.406371	−	0.406371i
$219$	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	−0.480058	−	0.877237i	$-0.659385\pi$
$223$	−22.0981	−	12.7583i	−1.47980	−	0.854361i	−0.999738	+	0.0228756i	$0.992718\pi$
$224$	−5.07180	+	18.9282i	−0.338874	+	1.26469i
$225$	−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	−0.867459	−	0.497508i	$-0.834248\pi$
$227$	−13.0263	−	22.5622i	−0.864585	−	1.49750i	0.00287459	−	0.999996i	$-0.499085\pi$
$228$	1.85641			0.122944
$229$	−12.9282			−0.854320			−0.427160	−	0.904176i	$-0.640486\pi$
$229$	−12.9282			−0.854320			−0.427160	+	0.904176i	$0.640486\pi$
$230$	11.1962	+	41.7846i	0.738252	+	2.75520i
$231$	−2.53590	+	4.39230i	−0.166850	+	0.288992i
$232$	−2.19615	−	8.19615i	−0.144184	−	0.538104i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$	11.0000	−	6.07180i	0.719092	−	0.396926i
$235$			25.1244i			1.63893i
$236$	−0.928203	+	0.535898i	−0.0604209	+	0.0348840i
$237$	6.58846	+	3.80385i	0.427966	+	0.247086i
$238$	2.19615	−	0.588457i	0.142355	−	0.0381440i
$239$			18.3923i			1.18970i	0.803837	+	0.594850i	$0.202788\pi$
$239$			18.3923i			1.18970i	−0.803837	+	0.594850i	$0.797212\pi$
$240$	−9.46410	−	5.46410i	−0.610905	−	0.352706i
$241$	9.69615	−	5.59808i	0.624584	−	0.360604i	−0.154068	−	0.988060i	$-0.549237\pi$
$241$	9.69615	−	5.59808i	0.624584	−	0.360604i	0.778652	+	0.627457i	$0.215904\pi$
$242$	−9.56218	−	2.56218i	−0.614680	−	0.164703i
$243$	13.2224	−	7.63397i	0.848219	−	0.489720i
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$	−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
$250$	14.6603	−	14.6603i	0.927196	−	0.927196i
$251$	7.09808	−	4.09808i	0.448027	−	0.258668i	−0.258970	−	0.965885i	$-0.583383\pi$
$251$	7.09808	−	4.09808i	0.448027	−	0.258668i	0.706996	+	0.707217i	$0.250050\pi$
$252$	8.53590	−	14.7846i	0.537711	−	0.931343i
$253$	−8.19615	−	14.1962i	−0.515288	−	0.892504i
$254$	−0.124356	−	0.464102i	−0.00780277	−	0.0291203i
$255$			1.26795i			0.0794021i
$256$	16.0000			1.00000
$257$	−11.4282	+	19.7942i	−0.712872	+	1.23473i	0.250903	+	0.968012i	$0.419273\pi$
$257$	−11.4282	+	19.7942i	−0.712872	+	1.23473i	−0.963775	+	0.266718i	$0.914061\pi$
$258$	−1.85641	+	1.85641i	−0.115575	+	0.115575i
$259$		−	14.7846i		−	0.918671i
$260$	18.6603	+	19.3923i	1.15726	+	1.20266i
$261$			7.39230i			0.457572i
$262$	10.7321	+	10.7321i	0.663028	+	0.663028i
$263$	−8.19615	+	14.1962i	−0.505396	+	0.875372i	0.494584	+	0.869130i	$0.335320\pi$
$263$	−8.19615	+	14.1962i	−0.505396	+	0.875372i	−0.999981	+	0.00624249i	$0.998013\pi$
$264$	4.00000	+	1.07180i	0.246183	+	0.0659645i
$265$			14.6603i			0.900572i
$266$	−6.00000	+	1.60770i	−0.367884	+	0.0985741i
$267$	−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	$-0.759829\pi$
$269$	−8.19615	+	4.73205i	−0.499728	+	0.288518i	0.228873	+	0.973456i	$0.426496\pi$
$270$	14.9282	+	14.9282i	0.908502	+	0.908502i
$271$	−15.0000	−	8.66025i	−0.911185	−	0.526073i	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−15.0000	−	8.66025i	−0.911185	−	0.526073i	−0.880812	+	0.473466i	$0.843003\pi$
$272$	−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
$276$	−6.00000	−	10.3923i	−0.361158	−	0.625543i
$277$	−12.4019	+	7.16025i	−0.745159	+	0.430218i	−0.823942	−	0.566674i	$-0.808230\pi$
$277$	−12.4019	+	7.16025i	−0.745159	+	0.430218i	0.0787828	+	0.996892i	$0.474897\pi$
$278$	3.46410	−	12.9282i	0.207763	−	0.775382i
$279$	−10.0981	+	5.83013i	−0.604556	+	0.349041i
$280$	35.3205	+	9.46410i	2.11080	+	0.565588i
$281$		−	10.6603i		−	0.635937i	−0.948101	−	0.317969i	$-0.896999\pi$
$281$		−	10.6603i		−	0.635937i	0.948101	−	0.317969i	$-0.103001\pi$
$282$	−1.80385	−	6.73205i	−0.107418	−	0.400888i
$283$	−26.6603	−	15.3923i	−1.58479	−	0.914978i	−0.994146	−	0.108043i	$-0.965541\pi$
$283$	−26.6603	−	15.3923i	−1.58479	−	0.914978i	−0.590641	−	0.806934i	$-0.701125\pi$
$284$	−9.26795	−	16.0526i	−0.549952	−	0.952544i
$285$		−	3.46410i		−	0.205196i
$286$	−8.73205	−	5.26795i	−0.516337	−	0.311500i
$287$	31.8564			1.88042
$288$	−13.4641	−	3.60770i	−0.793380	−	0.212585i
$289$	8.39230	−	14.5359i	0.493665	−	0.855053i
$290$	−15.2942	+	4.09808i	−0.898108	+	0.240647i
$291$	4.39230			0.257481
$292$	3.46410			0.202721
$293$	−1.40192	−	2.42820i	−0.0819013	−	0.141857i	0.822165	−	0.569249i	$-0.192766\pi$
$293$	−1.40192	−	2.42820i	−0.0819013	−	0.141857i	−0.904067	+	0.427392i	$0.859433\pi$
$294$	1.33975	−	5.00000i	0.0781356	−	0.291606i
$295$	1.00000	+	1.73205i	0.0582223	+	0.100844i
$296$	−11.6603	+	3.12436i	−0.677738	+	0.181599i
$297$	−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
$302$	2.19615	+	2.19615i	0.126374	+	0.126374i
$303$	−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
$306$	0.418584	+	1.56218i	0.0239289	+	0.0893038i
$307$	−2.19615			−0.125341			−0.0626705	−	0.998034i	$-0.519962\pi$
$307$	−2.19615			−0.125341			−0.0626705	+	0.998034i	$0.519962\pi$
$308$	−13.8564			−0.789542
$309$	−3.92820	−	2.26795i	−0.223468	−	0.129019i
$310$	−17.6603	−	17.6603i	−1.00304	−	1.00304i
$311$	−18.5885			−1.05405			−0.527027	−	0.849848i	$-0.676693\pi$
$311$	−18.5885			−1.05405			−0.527027	+	0.849848i	$0.676693\pi$
$312$	−6.39230	−	3.85641i	−0.361893	−	0.218326i
$313$	−2.53590			−0.143337			−0.0716687	−	0.997428i	$-0.522832\pi$
$313$	−2.53590			−0.143337			−0.0716687	+	0.997428i	$0.522832\pi$
$314$	−3.92820	−	3.92820i	−0.221681	−	0.221681i
$315$	−27.5885	−	15.9282i	−1.55443	−	0.897453i
$316$			20.7846i			1.16923i
$317$	−25.1962			−1.41516			−0.707578	−	0.706635i	$-0.750212\pi$
$317$	−25.1962			−1.41516			−0.707578	+	0.706635i	$0.750212\pi$
$318$	−1.05256	−	3.92820i	−0.0590246	−	0.220283i
$319$	5.19615	−	3.00000i	0.290929	−	0.167968i
$320$		−	29.8564i		−	1.66902i
$321$	6.46410	+	11.1962i	0.360791	+	0.624908i
$322$	28.3923	+	28.3923i	1.58224	+	1.58224i
$323$	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
$328$	−6.73205	−	25.1244i	−0.371715	−	1.38726i
$329$	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	$-0.273645\pi$
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	−0.982470	+	0.186421i	$0.940311\pi$
$332$			2.92820i			0.160706i
$333$	10.5167			0.576309
$334$	6.73205	−	1.80385i	0.368361	−	0.0987021i
$335$	13.5622	−	23.4904i	0.740981	−	1.28342i
$336$	−10.1436			−0.553378
$337$	−33.2487			−1.81117			−0.905586	−	0.424162i	$-0.860569\pi$
$337$	−33.2487			−1.81117			−0.905586	+	0.424162i	$0.860569\pi$
$338$	12.4904	+	13.4904i	0.679387	+	0.733780i
$339$		−	2.19615i		−	0.119279i
$340$	−3.00000	+	1.73205i	−0.162698	+	0.0939336i
$341$	8.19615	+	4.73205i	0.443847	+	0.256255i
$342$	−1.14359	−	4.26795i	−0.0618385	−	0.230784i
$343$		−	6.92820i		−	0.374088i
$344$	−6.92820	−	1.85641i	−0.373544	−	0.100091i
$345$	−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	$-0.655831\pi$
$347$	1.09808	−	0.633975i	0.0589478	−	0.0340335i	0.529184	+	0.848507i	$0.322498\pi$
$348$	3.80385	−	2.19615i	0.203908	−	0.117726i
$349$	−2.66025	+	4.60770i	−0.142400	+	0.246644i	−0.928400	−	0.371582i	$-0.878815\pi$
$349$	−2.66025	+	4.60770i	−0.142400	+	0.246644i	0.786000	+	0.618227i	$0.212149\pi$
$350$	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	0.0159167	−	0.999873i	$-0.494933\pi$
$353$	−15.8205	−	9.13397i	−0.842041	−	0.486152i	−0.857957	+	0.513721i	$0.828267\pi$
$354$	−0.392305	−	0.392305i	−0.0208508	−	0.0208508i
$355$	−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
$358$	18.9282	−	5.07180i	1.00039	−	0.268053i
$359$			13.0718i			0.689903i	0.938621	+	0.344952i	$0.112105\pi$
$359$			13.0718i			0.689903i	−0.938621	+	0.344952i	$0.887895\pi$
$360$	−6.73205	+	25.1244i	−0.354810	+	1.32417i
$361$	8.69615	−	15.0622i	0.457692	−	0.792746i
$362$	18.4641	+	18.4641i	0.970452	+	0.970452i
$363$		−	5.12436i		−	0.268959i
$364$	24.0000	+	6.92820i	1.25794	+	0.363137i
$365$		−	6.46410i		−	0.338347i
$366$	−0.732051	+	0.732051i	−0.0382649	+	0.0382649i
$367$	14.0981	−	24.4186i	0.735914	−	1.27464i	−0.218408	−	0.975858i	$-0.570086\pi$
$367$	14.0981	−	24.4186i	0.735914	−	1.27464i	0.954321	−	0.298782i	$-0.0965804\pi$
$368$	16.3923	−	28.3923i	0.854508	−	1.48005i
$369$			22.6603i			1.17965i
$370$	5.83013	+	21.7583i	0.303094	+	1.13116i
$371$	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	$-0.899319\pi$
$373$	−22.3301	+	12.8923i	−1.15621	+	0.667538i	−0.205817	+	0.978590i	$0.565985\pi$
$374$	0.928203	−	0.928203i	0.0479962	−	0.0479962i
$375$	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	−0.430538	−	0.902573i	$-0.641676\pi$
$379$	11.0263	−	19.0981i	0.566382	−	0.981002i	0.996920	−	0.0784297i	$-0.0249906\pi$
$380$	8.19615	−	4.73205i	0.420454	−	0.242749i
$381$	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	0.0127209	−	0.999919i	$-0.495951\pi$
$383$	17.3205	−	10.0000i	0.885037	−	0.510976i	0.872316	+	0.488943i	$0.162617\pi$
$384$	2.14359	+	8.00000i	0.109390	+	0.408248i
$385$			25.8564i			1.31776i
$386$	−17.8301	+	4.77757i	−0.907530	+	0.243172i
$387$	5.41154	+	3.12436i	0.275084	+	0.158820i
$388$	6.00000	+	10.3923i	0.304604	+	0.527589i
$389$			18.7128i			0.948777i	0.880316	+	0.474389i	$0.157331\pi$
$389$			18.7128i			0.948777i	−0.880316	+	0.474389i	$0.842669\pi$
$390$	−7.19615	+	11.9282i	−0.364391	+	0.604008i
$391$	−3.80385			−0.192369
$392$	13.6603	−	3.66025i	0.689947	−	0.184871i
$393$	−3.92820	+	6.80385i	−0.198152	+	0.343209i
$394$	4.58846	+	17.1244i	0.231163	+	0.862713i
$395$	38.7846			1.95147
$396$		−	9.85641i		−	0.495303i
$397$	12.1244	+	21.0000i	0.608504	+	1.05396i	0.991487	+	0.130204i	$0.0415634\pi$
$397$	12.1244	+	21.0000i	0.608504	+	1.05396i	−0.382983	+	0.923755i	$0.625103\pi$
$398$	−20.6603	−	5.53590i	−1.03560	−	0.277490i
$399$	−1.60770	−	2.78461i	−0.0804854	−	0.139405i
$400$	−35.7128			−1.78564
$401$	8.42820	+	4.86603i	0.420884	+	0.242998i	0.695456	−	0.718569i	$-0.255203\pi$
$401$	8.42820	+	4.86603i	0.420884	+	0.242998i	−0.274571	+	0.961567i	$0.588536\pi$
$402$	−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
$406$	−10.3923	+	10.3923i	−0.515761	+	0.515761i
$407$	−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	−0.482690	−	0.875791i	$-0.660340\pi$
$409$	0.696152	−	0.401924i	0.0344225	−	0.0198739i	0.517113	+	0.855917i	$0.327007\pi$
$410$	−46.8827	+	12.5622i	−2.31537	+	0.620402i
$411$	9.94744			0.490671
$412$		−	12.3923i		−	0.610525i
$413$	1.60770	+	0.928203i	0.0791095	+	0.0456739i
$414$	−20.1962	+	20.1962i	−0.992587	+	0.992587i
$415$	5.46410			0.268222
$416$	0.392305	−	20.3923i	0.0192343	−	0.999815i
$417$	6.92820			0.339276
$418$	−2.53590	+	2.53590i	−0.124035	+	0.124035i
$419$	16.9019	+	9.75833i	0.825713	+	0.476726i	0.852383	−	0.522919i	$-0.175157\pi$
$419$	16.9019	+	9.75833i	0.825713	+	0.476726i	−0.0266696	+	0.999644i	$0.508490\pi$
$420$			18.9282i			0.923602i
$421$	30.1244			1.46817			0.734086	−	0.679057i	$-0.237611\pi$
$421$	30.1244			1.46817			0.734086	+	0.679057i	$0.237611\pi$
$422$	−39.0526	+	10.4641i	−1.90105	+	0.509384i
$423$	−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
$426$	6.78461	−	6.78461i	0.328715	−	0.328715i
$427$	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	0.823841	−	0.566821i	$-0.191827\pi$
$431$	15.4641	+	8.92820i	0.744880	+	0.430056i	−0.0789612	+	0.996878i	$0.525160\pi$
$432$		−	16.0000i		−	0.769800i
$433$	−10.5000	−	18.1865i	−0.504598	−	0.873989i	−0.999986	−	0.00531724i	$-0.998307\pi$
$433$	−10.5000	−	18.1865i	−0.504598	−	0.873989i	0.495388	−	0.868672i	$-0.335026\pi$
$434$	−22.3923	−	6.00000i	−1.07487	−	0.288009i
$435$	−4.09808	−	7.09808i	−0.196488	−	0.340327i
$436$			12.0000i			0.574696i
$437$	10.3923			0.497131
$438$	0.464102	+	1.73205i	0.0221756	+	0.0827606i
$439$	−7.80385	+	13.5167i	−0.372457	+	0.645115i	−0.989943	−	0.141467i	$-0.954818\pi$
$439$	−7.80385	+	13.5167i	−0.372457	+	0.645115i	0.617486	+	0.786582i	$0.288151\pi$
$440$	20.3923	−	5.46410i	0.972165	−	0.260491i
$441$	−12.3205			−0.586691
$442$	−2.07180	+	1.14359i	−0.0985453	+	0.0543952i
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	−3.12436	−	5.41154i	−0.148275	−	0.256820i
$445$	−24.1244	−	13.9282i	−1.14360	−	0.660260i
$446$	34.8564	−	9.33975i	1.65050	−	0.442250i
$447$		−	8.58846i		−	0.406220i
$448$	−13.8564	−	24.0000i	−0.654654	−	1.13389i
$449$	18.4641	−	10.6603i	0.871375	−	0.503088i	0.00356996	−	0.999994i	$-0.498864\pi$
$449$	18.4641	−	10.6603i	0.871375	−	0.503088i	0.867805	+	0.496905i	$0.165530\pi$
$450$	30.0526	+	8.05256i	1.41669	+	0.379601i
$451$	15.9282	−	9.19615i	0.750030	−	0.433030i
$452$	5.19615	−	3.00000i	0.244406	−	0.141108i
$453$	−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	0.648372	−	0.761324i	$-0.275450\pi$
$457$	6.69615	+	3.86603i	0.313233	+	0.180845i	−0.335139	+	0.942169i	$0.608783\pi$
$458$	12.9282	−	12.9282i	0.604095	−	0.604095i
$459$	−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	0.978623	+	0.205663i	$0.0659350\pi$
$461$	14.3301	+	24.8205i	0.667421	+	1.15601i	−0.311202	+	0.950344i	$0.600732\pi$
$462$	−1.85641	−	6.92820i	−0.0863678	−	0.322329i
$463$			16.3923i			0.761815i	0.924613	+	0.380908i	$0.124388\pi$
$463$			16.3923i			0.761815i	−0.924613	+	0.380908i	$0.875612\pi$
$464$	10.3923	+	6.00000i	0.482451	+	0.278543i
$465$	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	$0.842396\pi$
$468$	−4.92820	+	17.0718i	−0.227806	+	0.789144i
$469$		−	25.1769i		−	1.16256i
$470$	−25.1244	−	25.1244i	−1.15890	−	1.15890i
$471$	1.43782	−	2.49038i	0.0662513	−	0.114751i
$472$	0.392305	−	1.46410i	0.0180573	−	0.0673907i
$473$		−	5.07180i		−	0.233201i
$474$	−10.3923	+	2.78461i	−0.477334	+	0.127901i
$475$	−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
$478$	−18.3923	−	18.3923i	−0.841244	−	0.841244i
$479$	−25.3468	−	14.6340i	−1.15812	−	0.668643i	−0.207271	−	0.978284i	$-0.566458\pi$
$479$	−25.3468	−	14.6340i	−1.15812	−	0.668643i	−0.950854	+	0.309640i	$0.899791\pi$
$480$	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
$484$	12.1244	−	7.00000i	0.551107	−	0.318182i
$485$	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	0.0330824	−	0.999453i	$-0.489468\pi$
$487$	20.1962	−	11.6603i	0.915175	−	0.528377i	0.882093	+	0.471076i	$0.156134\pi$
$488$	−2.73205	−	0.732051i	−0.123674	−	0.0331384i
$489$		−	12.0000i		−	0.542659i
$490$	−6.83013	−	25.4904i	−0.308554	−	1.15154i
$491$	6.58846	+	3.80385i	0.297333	+	0.171665i	0.641244	−	0.767337i	$-0.278419\pi$
$491$	6.58846	+	3.80385i	0.297333	+	0.171665i	−0.343911	+	0.939002i	$0.611752\pi$
$492$	11.6603	−	6.73205i	0.525685	−	0.303504i
$493$		−	1.39230i		−	0.0627063i
$494$	5.66025	−	3.12436i	0.254667	−	0.140571i
$495$	−18.3923			−0.826673
$496$			18.9282i			0.849901i
$497$	−16.0526	+	27.8038i	−0.720056	+	1.24717i
$498$	−1.46410	+	0.392305i	−0.0656080	+	0.0175796i
$499$	−8.87564			−0.397328			−0.198664	−	0.980068i	$-0.563660\pi$
$499$	−8.87564			−0.397328			−0.198664	+	0.980068i	$0.563660\pi$
$500$			29.3205i			1.31125i
$501$	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	0.751333	−	0.659923i	$-0.229411\pi$
$503$	−4.39230	−	7.60770i	−0.195843	−	0.339210i	−0.947177	+	0.320712i	$0.896078\pi$
$504$	6.24871	+	23.3205i	0.278340	+	1.03878i
$505$	−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	$-0.889177\pi$
$509$	−3.93782	+	6.82051i	−0.174541	+	0.302314i	0.765461	+	0.643482i	$0.222511\pi$
$510$	−1.26795	−	1.26795i	−0.0561457	−	0.0561457i
$511$	−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
$514$	−8.36603	−	31.2224i	−0.369010	−	1.37716i
$515$	−23.1244			−1.01898
$516$		−	3.71281i		−	0.163447i
$517$	11.6603	+	6.73205i	0.512817	+	0.296075i
$518$	14.7846	+	14.7846i	0.649598	+	0.649598i
$519$	−13.8564			−0.608229
$520$	−38.0526	−	0.732051i	−1.66872	−	0.0321026i
$521$	9.24871			0.405193			0.202597	−	0.979262i	$-0.435062\pi$
$521$	9.24871			0.405193			0.202597	+	0.979262i	$0.435062\pi$
$522$	−7.39230	−	7.39230i	−0.323552	−	0.323552i
$523$	0.803848	+	0.464102i	0.0351498	+	0.0202937i	0.517472	−	0.855700i	$-0.326873\pi$
$523$	0.803848	+	0.464102i	0.0351498	+	0.0202937i	−0.482322	+	0.875994i	$0.660207\pi$
$524$	−21.4641			−0.937664
$525$	22.6410			0.988135
$526$	−6.00000	−	22.3923i	−0.261612	−	0.976351i
$527$	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
$530$	−14.6603	−	14.6603i	−0.636801	−	0.636801i
$531$	−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
$536$	−19.8564	+	5.32051i	−0.857666	+	0.229811i
$537$	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
$540$	−29.8564			−1.28482
$541$	−35.4449			−1.52389			−0.761947	−	0.647640i	$-0.775756\pi$
$541$	−35.4449			−1.52389			−0.761947	+	0.647640i	$0.775756\pi$
$542$	23.6603	−	6.33975i	1.01629	−	0.272315i
$543$	−6.75833	+	11.7058i	−0.290028	+	0.502343i
$544$	2.53590	+	0.679492i	0.108726	+	0.0291330i
$545$	22.3923			0.959181
$546$	−0.248711	+	12.9282i	−0.0106439	+	0.553276i
$547$		−	18.5885i		−	0.794785i	−0.917649	−	0.397393i	$-0.869915\pi$
$547$		−	18.5885i		−	0.794785i	0.917649	−	0.397393i	$-0.130085\pi$
$548$	13.5885	+	23.5359i	0.580470	+	1.00540i
$549$	2.13397	+	1.23205i	0.0910758	+	0.0525826i
$550$	−6.53590	−	24.3923i	−0.278692	−	1.04009i
$551$			3.80385i			0.162049i
$552$	16.3923	+	4.39230i	0.697703	+	0.186949i
$553$	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
$556$	9.46410	+	16.3923i	0.401367	+	0.695189i
$557$	2.40192	−	4.16025i	0.101773	−	0.176276i	−0.810642	−	0.585542i	$-0.800882\pi$
$557$	2.40192	−	4.16025i	0.101773	−	0.176276i	0.912415	+	0.409266i	$0.134215\pi$
$558$	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
$562$	10.6603	+	10.6603i	0.449676	+	0.449676i
$563$	−13.9808	+	8.07180i	−0.589219	+	0.340186i	−0.764789	−	0.644281i	$-0.777157\pi$
$563$	−13.9808	+	8.07180i	−0.589219	+	0.340186i	0.175570	+	0.984467i	$0.443823\pi$
$564$	8.53590	+	4.92820i	0.359426	+	0.207515i
$565$	−5.59808	−	9.69615i	−0.235513	−	0.407920i
$566$	42.0526	−	11.2679i	1.76760	−	0.473627i
$567$		−	15.4641i		−	0.649431i
$568$	25.3205	+	6.78461i	1.06242	+	0.284676i
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	−0.496928	−	0.867792i	$-0.665539\pi$
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	0.999994	−	0.00354413i	$-0.00112814\pi$
$570$	3.46410	+	3.46410i	0.145095	+	0.145095i
$571$			2.39230i			0.100115i	0.998746	+	0.0500574i	$0.0159404\pi$
$571$			2.39230i			0.100115i	−0.998746	+	0.0500574i	$0.984060\pi$
$572$	14.0000	−	3.46410i	0.585369	−	0.144841i
$573$			2.78461i			0.116329i
$574$	−31.8564	+	31.8564i	−1.32966	+	1.32966i
$575$	−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	$0.252799\pi$
$577$			34.2679i			1.42659i	−0.700862	+	0.713297i	$0.747201\pi$
$578$	6.14359	+	22.9282i	0.255540	+	0.953688i
$579$	−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
$582$	−4.39230	+	4.39230i	−0.182067	+	0.182067i
$583$	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	0.152990	−	0.988228i	$-0.451110\pi$
$587$	22.5885	−	39.1244i	0.932325	−	1.61483i	0.779335	−	0.626607i	$-0.215557\pi$
$588$	3.66025	+	6.33975i	0.150946	+	0.261447i
$589$	−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
$592$	8.53590	−	14.7846i	0.350823	−	0.607644i
$593$		−	1.58846i		−	0.0652301i	−0.999468	−	0.0326151i	$-0.989616\pi$
$593$		−	1.58846i		−	0.0652301i	0.999468	−	0.0326151i	$-0.0103835\pi$
$594$	10.9282	−	2.92820i	0.448390	−	0.120146i
$595$	5.19615	+	3.00000i	0.213021	+	0.122988i
$596$	20.3205	−	11.7321i	0.832360	−	0.480564i
$597$		−	11.0718i		−	0.453138i
$598$	−35.7846	−	21.5885i	−1.46334	−	0.882818i
$599$	−13.2679			−0.542114			−0.271057	−	0.962563i	$-0.587373\pi$
$599$	−13.2679			−0.542114			−0.271057	+	0.962563i	$0.587373\pi$
$600$	−4.78461	−	17.8564i	−0.195331	−	0.728985i
$601$	−13.0359	+	22.5788i	−0.531745	+	0.921010i	0.467568	+	0.883957i	$0.345130\pi$
$601$	−13.0359	+	22.5788i	−0.531745	+	0.921010i	−0.999313	+	0.0370529i	$0.988203\pi$
$602$	3.21539	+	12.0000i	0.131050	+	0.489083i
$603$	17.9090			0.729309
$604$	−4.39230			−0.178720
$605$	−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	0.838564	−	0.544803i	$-0.183396\pi$
$607$	−1.29423	−	2.24167i	−0.0525311	−	0.0909866i	−0.891095	+	0.453816i	$0.850062\pi$
$608$	−6.92820	−	1.85641i	−0.280976	−	0.0752872i
$609$	−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	0.0887617	+	0.996053i	$0.471709\pi$
$613$	−20.2583	+	35.0885i	−0.818226	+	1.41721i	−0.906988	+	0.421157i	$0.861624\pi$
$614$	2.19615	−	2.19615i	0.0886295	−	0.0886295i
$615$	−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	−0.157952	−	0.987447i	$-0.550489\pi$
$617$	15.3564	−	8.86603i	0.618226	−	0.356933i	0.776178	+	0.630514i	$0.217156\pi$
$618$	6.19615	−	1.66025i	0.249246	−	0.0667852i
$619$	24.2487			0.974638			0.487319	−	0.873224i	$-0.337975\pi$
$619$	24.2487			0.974638			0.487319	+	0.873224i	$0.337975\pi$
$620$	35.3205			1.41851
$621$	−28.3923	−	16.3923i	−1.13934	−	0.657801i
$622$	18.5885	−	18.5885i	0.745329	−	0.745329i
$623$	−25.8564			−1.03592
$624$	10.2487	−	2.53590i	0.410277	−	0.101517i
$625$	10.0718			0.402872
$626$	2.53590	−	2.53590i	0.101355	−	0.101355i
$627$	−1.60770	−	0.928203i	−0.0642052	−	0.0370689i
$628$	7.85641			0.313505
$629$	−1.98076			−0.0789782
$630$	43.5167	−	11.6603i	1.73375	−	0.464556i
$631$	−14.7846	+	8.53590i	−0.588566	+	0.339809i	−0.764530	−	0.644588i	$-0.777029\pi$
$631$	−14.7846	+	8.53590i	−0.588566	+	0.339809i	0.175964	+	0.984397i	$0.443696\pi$
$632$	−20.7846	−	20.7846i	−0.826767	−	0.826767i
$633$	−10.4641	−	18.1244i	−0.415911	−	0.720378i
$634$	25.1962	−	25.1962i	1.00067	−	1.00067i
$635$	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
$640$	29.8564	+	29.8564i	1.18018	+	1.18018i
$641$	7.03590	+	12.1865i	0.277901	+	0.481339i	0.970863	−	0.239635i	$-0.0770279\pi$
$641$	7.03590	+	12.1865i	0.277901	+	0.481339i	−0.692962	+	0.720974i	$0.743695\pi$
$642$	−17.6603	−	4.73205i	−0.696995	−	0.186759i
$643$	19.3923	+	33.5885i	0.764758	+	1.32460i	0.940375	+	0.340141i	$0.110475\pi$
$643$	19.3923	+	33.5885i	0.764758	+	1.32460i	−0.175617	+	0.984459i	$0.556192\pi$
$644$	−56.7846			−2.23763
$645$	−6.92820			−0.272798
$646$	0.215390	+	0.803848i	0.00847442	+	0.0316270i
$647$	−14.8301	+	25.6865i	−0.583032	+	1.00984i	0.412085	+	0.911145i	$0.364801\pi$
$647$	−14.8301	+	25.6865i	−0.583032	+	1.00984i	−0.995118	+	0.0986965i	$0.968533\pi$
$648$	−12.1962	+	3.26795i	−0.479110	+	0.128377i
$649$	1.07180			0.0420717
$650$	−0.875644	+	45.5167i	−0.0343456	+	1.78531i
$651$		−	12.0000i		−	0.470317i
$652$	28.3923	−	16.3923i	1.11193	−	0.641972i
$653$	31.1769	+	18.0000i	1.22005	+	0.704394i	0.964928	−	0.262515i	$-0.0845520\pi$
$653$	31.1769	+	18.0000i	1.22005	+	0.704394i	0.255119	+	0.966910i	$0.417885\pi$
$654$	−6.00000	+	1.60770i	−0.234619	+	0.0628659i
$655$			40.0526i			1.56498i
$656$	31.8564	+	18.3923i	1.24378	+	0.718099i
$657$	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	$-0.872454\pi$
$659$	−26.7846	+	15.4641i	−1.04338	+	0.602396i	−0.122591	+	0.992457i	$0.539120\pi$
$660$	5.46410	+	9.46410i	0.212690	+	0.368390i
$661$	−6.06218	+	10.5000i	−0.235791	+	0.408403i	−0.959502	−	0.281701i	$-0.909102\pi$
$661$	−6.06218	+	10.5000i	−0.235791	+	0.408403i	0.723711	+	0.690103i	$0.242435\pi$
$662$	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
$666$	−10.5167	+	10.5167i	−0.407512	+	0.407512i
$667$	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
$670$	9.92820	+	37.0526i	0.383560	+	1.43147i
$671$		−	2.00000i		−	0.0772091i
$672$	10.1436	−	10.1436i	0.391298	−	0.391298i
$673$	5.50000	−	9.52628i	0.212009	−	0.367211i	−0.740334	−	0.672239i	$-0.765333\pi$
$673$	5.50000	−	9.52628i	0.212009	−	0.367211i	0.952343	+	0.305028i	$0.0986659\pi$
$674$	33.2487	−	33.2487i	1.28069	−	1.28069i
$675$			35.7128i			1.37459i
$676$	−25.9808	−	1.00000i	−0.999260	−	0.0384615i
$677$			7.85641i			0.301946i	0.988538	+	0.150973i	$0.0482407\pi$
$677$			7.85641i			0.301946i	−0.988538	+	0.150973i	$0.951759\pi$
$678$	2.19615	+	2.19615i	0.0843427	+	0.0843427i
$679$	10.3923	−	18.0000i	0.398820	−	0.690777i
$680$	1.26795	−	4.73205i	0.0486236	−	0.181466i
$681$			19.0718i			0.730833i
$682$	−12.9282	+	3.46410i	−0.495046	+	0.132647i
$683$	−5.63397	−	9.75833i	−0.215578	−	0.373392i	0.737873	−	0.674939i	$-0.235830\pi$
$683$	−5.63397	−	9.75833i	−0.215578	−	0.373392i	−0.953451	+	0.301547i	$0.902497\pi$
$684$	5.41154	+	3.12436i	0.206916	+	0.119463i
$685$	43.9186	−	25.3564i	1.67804	−	0.968818i
$686$	6.92820	+	6.92820i	0.264520	+	0.264520i
$687$	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	$-0.944565\pi$
$691$	−9.00000	+	15.5885i	−0.342376	+	0.593013i	0.642497	+	0.766288i	$0.277898\pi$
$692$	−18.9282	−	32.7846i	−0.719542	−	1.24628i
$693$	−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
$696$	−1.60770	+	6.00000i	−0.0609395	+	0.227429i
$697$		−	4.26795i		−	0.161660i
$698$	−1.94744	−	7.26795i	−0.0737117	−	0.275096i
$699$		0			0
$700$	30.9282	+	53.5692i	1.16898	+	2.02473i
$701$		−	8.78461i		−	0.331790i	−0.986143	−	0.165895i	$-0.946949\pi$
$701$		−	8.78461i		−	0.331790i	0.986143	−	0.165895i	$-0.0530513\pi$
$702$	−20.3923	−	0.392305i	−0.769658	−	0.0148066i
$703$	5.41154			0.204100
$704$	−13.8564	−	8.00000i	−0.522233	−	0.301511i
$705$	9.19615	−	15.9282i	0.346347	−	0.599891i
$706$	24.9545	−	6.68653i	0.939174	−	0.251651i
$707$	−39.9615			−1.50291
$708$	0.784610			0.0294874
$709$	−20.5981	−	35.6769i	−0.773577	−	1.33987i	−0.935591	−	0.353086i	$-0.885132\pi$
$709$	−20.5981	−	35.6769i	−0.773577	−	1.33987i	0.162014	−	0.986788i	$-0.448201\pi$
$710$	12.6603	−	47.2487i	0.475131	−	1.77321i
$711$	12.8038	+	22.1769i	0.480182	+	0.831699i
$712$	5.46410	+	20.3923i	0.204776	+	0.764234i
$713$	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
$718$	−13.0718	−	13.0718i	−0.487835	−	0.487835i
$719$	16.8564	+	29.1962i	0.628638	+	1.08883i	0.987825	+	0.155567i	$0.0497206\pi$
$719$	16.8564	+	29.1962i	0.628638	+	1.08883i	−0.359187	+	0.933265i	$0.616946\pi$
$720$	−18.3923	−	31.8564i	−0.685441	−	1.18722i
$721$	−18.5885	+	10.7321i	−0.692270	+	0.399682i
$722$	6.36603	+	23.7583i	0.236919	+	0.884193i
$723$	−8.19615			−0.304818
$724$	−36.9282			−1.37243
$725$	−23.1962	−	13.3923i	−0.861483	−	0.497378i
$726$	5.12436	+	5.12436i	0.190183	+	0.190183i
$727$	−13.6077			−0.504681			−0.252341	−	0.967638i	$-0.581200\pi$
$727$	−13.6077			−0.504681			−0.252341	+	0.967638i	$0.581200\pi$
$728$	−30.9282	+	17.0718i	−1.14628	+	0.632723i
$729$	2.21539			0.0820515
$730$	6.46410	+	6.46410i	0.239247	+	0.239247i
$731$	−1.01924	−	0.588457i	−0.0376979	−	0.0217649i
$732$		−	1.46410i		−	0.0541148i
$733$	−4.94744			−0.182738			−0.0913690	−	0.995817i	$-0.529124\pi$
$733$	−4.94744			−0.182738			−0.0913690	+	0.995817i	$0.529124\pi$
$734$	10.3205	+	38.5167i	0.380937	+	1.42168i
$735$	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
$738$	−22.6603	−	22.6603i	−0.834135	−	0.834135i
$739$	−9.46410	+	16.3923i	−0.348143	+	0.603001i	−0.985920	−	0.167220i	$-0.946521\pi$
$739$	−9.46410	+	16.3923i	−0.348143	+	0.603001i	0.637777	+	0.770221i	$0.279854\pi$
$740$	−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	0.584283	−	0.811550i	$-0.301376\pi$
$743$	4.73205	+	2.73205i	0.173602	+	0.100229i	−0.410681	+	0.911779i	$0.634709\pi$
$744$	−9.46410	+	2.53590i	−0.346971	+	0.0929705i
$745$	−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
$748$			1.85641i			0.0678769i
$749$	61.1769			2.23536
$750$	−14.6603	+	3.92820i	−0.535317	+	0.143438i
$751$	18.1962	−	31.5167i	0.663987	−	1.15006i	−0.315572	−	0.948902i	$-0.602196\pi$
$751$	18.1962	−	31.5167i	0.663987	−	1.15006i	0.979559	−	0.201158i	$-0.0644703\pi$
$752$			26.9282i			0.981971i
$753$	−6.00000			−0.218652
$754$	7.90192	−	13.0981i	0.287771	−	0.477004i
$755$			8.19615i			0.298289i
$756$	−24.0000	+	13.8564i	−0.872872	+	0.503953i
$757$	18.3397	+	10.5885i	0.666569	+	0.384844i	0.794776	−	0.606904i	$-0.207589\pi$
$757$	18.3397	+	10.5885i	0.666569	+	0.384844i	−0.128206	+	0.991748i	$0.540922\pi$
$758$	8.07180	+	30.1244i	0.293181	+	1.09417i
$759$			12.0000i			0.435572i
$760$	−3.46410	+	12.9282i	−0.125656	+	0.468955i
$761$	−10.8564	+	6.26795i	−0.393544	+	0.227213i	−0.683695	−	0.729768i	$-0.739628\pi$
$761$	−10.8564	+	6.26795i	−0.393544	+	0.227213i	0.290150	+	0.956981i	$0.406295\pi$
$762$	−0.0910347	+	0.339746i	−0.00329784	+	0.0123077i
$763$	18.0000	−	10.3923i	0.651644	−	0.376227i
$764$	−6.58846	+	3.80385i	−0.238362	+	0.137618i
$765$	−2.13397	+	3.69615i	−0.0771540	+	0.133635i
$766$	−7.32051	+	27.3205i	−0.264501	+	0.987130i
$767$	−1.85641	−	0.535898i	−0.0670310	−	0.0193502i

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+(-1.00000 + 1.00000i) q^{2} +(-0.633975 - 0.366025i) q^{3} -2.00000i q^{4} -3.73205 q^{5} +(1.00000 - 0.267949i) q^{6} +(-3.00000 + 1.73205i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.23205 - 2.13397i) q^{9} +(3.73205 - 3.73205i) 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} -4.00000 q^{16} +(0.232051 + 0.401924i) q^{17} +(3.36603 + 0.901924i) q^{18} +(-0.633975 - 1.09808i) q^{19} +7.46410i q^{20} +2.53590 q^{21} +(-0.732051 - 2.73205i) q^{22} +(-4.09808 + 7.09808i) q^{23} +(-0.535898 - 2.00000i) q^{24} +8.92820 q^{25} +(-0.0980762 + 5.09808i) q^{26} +4.00000i q^{27} +(3.46410 + 6.00000i) q^{28} +(-2.59808 - 1.50000i) q^{29} +(-3.73205 + 1.00000i) q^{30} -4.73205i q^{31} +(4.00000 - 4.00000i) q^{32} +(1.26795 - 0.732051i) q^{33} +(-0.633975 - 0.169873i) q^{34} +(11.1962 - 6.46410i) q^{35} +(-4.26795 + 2.46410i) 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} +(-2.53590 + 2.53590i) q^{42} +(-2.19615 + 1.26795i) q^{43} +(3.46410 + 2.00000i) q^{44} +(4.59808 + 7.96410i) q^{45} +(-3.00000 - 11.1962i) q^{46} -6.73205i q^{47} +(2.53590 + 1.46410i) q^{48} +(2.50000 - 4.33013i) q^{49} +(-8.92820 + 8.92820i) q^{50} -0.339746i q^{51} +(-5.00000 - 5.19615i) q^{52} -3.92820i q^{53} +(-4.00000 - 4.00000i) q^{54} +(3.73205 - 6.46410i) q^{55} +(-9.46410 - 2.53590i) q^{56} +0.928203i q^{57} +(4.09808 - 1.09808i) q^{58} +(-0.267949 - 0.464102i) q^{59} +(2.73205 - 4.73205i) q^{60} +(-0.866025 + 0.500000i) q^{61} +(4.73205 + 4.73205i) 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} +(0.803848 - 0.464102i) q^{68} +(5.19615 - 3.00000i) q^{69} +(-4.73205 + 17.6603i) q^{70} +(8.02628 - 4.63397i) q^{71} +(1.80385 - 6.73205i) q^{72} +1.73205i q^{73} +(-1.56218 - 5.83013i) q^{74} +(-5.66025 - 3.26795i) q^{75} +(-2.19615 + 1.26795i) q^{76} -6.92820i q^{77} +(1.92820 - 3.19615i) q^{78} -10.3923 q^{79} +14.9282 q^{80} +(-2.23205 + 3.86603i) q^{81} +(12.5622 - 3.36603i) q^{82} -1.46410 q^{83} -5.07180i q^{84} +(-0.866025 - 1.50000i) q^{85} +(0.928203 - 3.46410i) q^{86} +(1.09808 + 1.90192i) q^{87} +(-5.46410 + 1.46410i) 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} +(6.73205 + 6.73205i) q^{94} +(2.36603 + 4.09808i) q^{95} +(-4.00000 + 1.07180i) q^{96} +(-5.19615 + 3.00000i) q^{97} +(1.83013 + 6.83013i) q^{98} +4.92820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{5} + 4 q^{6} - 12 q^{7} + 8 q^{8} + 2 q^{9} + 8 q^{10} - 4 q^{11} + 4 q^{12} + 12 q^{14} + 6 q^{15} - 16 q^{16} - 6 q^{17} + 10 q^{18} - 6 q^{19} + 24 q^{21} + 4 q^{22} - 6 q^{23}+ \cdots - 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^5 + 4 * q^6 - 12 * q^7 + 8 * q^8 + 2 * q^9 + 8 * q^10 - 4 * q^11 + 4 * q^12 + 12 * q^14 + 6 * q^15 - 16 * q^16 - 6 * q^17 + 10 * q^18 - 6 * q^19 + 24 * q^21 + 4 * q^22 - 6 * q^23 - 16 * q^24 + 8 * q^25 + 10 * q^26 - 8 * q^30 + 16 * q^32 + 12 * q^33 - 6 * q^34 + 24 * q^35 - 24 * q^36 - 12 * q^37 + 14 * q^39 - 16 * q^40 - 18 * q^41 - 24 * q^42 + 12 * q^43 + 8 * q^45 - 12 * q^46 + 24 * q^48 + 10 * q^49 - 8 * q^50 - 20 * q^52 - 16 * q^54 + 8 * q^55 - 24 * q^56 + 6 * q^58 - 8 * q^59 + 4 * q^60 + 12 * q^62 - 12 * q^63 - 18 * q^65 - 16 * q^66 - 18 * q^67 + 24 * q^68 - 12 * q^70 - 6 * q^71 + 28 * q^72 + 18 * q^74 + 12 * q^75 + 12 * q^76 - 20 * q^78 + 32 * q^80 - 2 * q^81 + 26 * q^82 + 8 * q^83 - 24 * q^86 - 6 * q^87 - 8 * q^88 + 12 * q^89 - 26 * q^90 + 36 * q^92 + 20 * q^94 + 6 * q^95 - 16 * q^96 - 10 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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