LMFDB - Embedded newform 104.2.s.b.101.1

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			101.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	104.101
Dual form			104.2.s.b.69.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 0.366025i) q^{2} +(2.36603 - 1.36603i) q^{3} +(1.73205 - 1.00000i) q^{4} +0.267949 q^{5} +(-2.73205 + 2.73205i) q^{6} +(-3.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(2.23205 - 3.86603i) q^{9} +O(q^{10})$	\(q+(-1.36603 + 0.366025i) q^{2} +(2.36603 - 1.36603i) q^{3} +(1.73205 - 1.00000i) q^{4} +0.267949 q^{5} +(-2.73205 + 2.73205i) q^{6} +(-3.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(2.23205 - 3.86603i) q^{9} +(-0.366025 + 0.0980762i) q^{10} +(1.00000 + 1.73205i) q^{11} +(2.73205 - 4.73205i) q^{12} +(2.59808 + 2.50000i) q^{13} +(4.73205 + 1.26795i) q^{14} +(0.633975 - 0.366025i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-3.23205 + 5.59808i) q^{17} +(-1.63397 + 6.09808i) q^{18} +(2.36603 - 4.09808i) q^{19} +(0.464102 - 0.267949i) q^{20} -9.46410 q^{21} +(-2.00000 - 2.00000i) q^{22} +(1.09808 + 1.90192i) q^{23} +(-2.00000 + 7.46410i) q^{24} -4.92820 q^{25} +(-4.46410 - 2.46410i) q^{26} -4.00000i q^{27} -6.92820 q^{28} +(-2.59808 + 1.50000i) q^{29} +(-0.732051 + 0.732051i) q^{30} -1.26795i q^{31} +(-1.46410 + 5.46410i) q^{32} +(4.73205 + 2.73205i) q^{33} +(2.36603 - 8.83013i) q^{34} +(-0.803848 - 0.464102i) q^{35} -8.92820i q^{36} +(3.86603 + 6.69615i) q^{37} +(-1.73205 + 6.46410i) q^{38} +(9.56218 + 2.36603i) q^{39} +(-0.535898 + 0.535898i) q^{40} +(-1.03590 + 0.598076i) q^{41} +(12.9282 - 3.46410i) q^{42} +(-8.19615 - 4.73205i) q^{43} +(3.46410 + 2.00000i) q^{44} +(0.598076 - 1.03590i) q^{45} +(-2.19615 - 2.19615i) q^{46} -3.26795i q^{47} -10.9282i q^{48} +(2.50000 + 4.33013i) q^{49} +(6.73205 - 1.80385i) q^{50} +17.6603i q^{51} +(7.00000 + 1.73205i) q^{52} -9.92820i q^{53} +(1.46410 + 5.46410i) q^{54} +(0.267949 + 0.464102i) q^{55} +(9.46410 - 2.53590i) q^{56} -12.9282i q^{57} +(3.00000 - 3.00000i) q^{58} +(3.73205 - 6.46410i) q^{59} +(0.732051 - 1.26795i) q^{60} +(-0.866025 - 0.500000i) q^{61} +(0.464102 + 1.73205i) q^{62} +(-13.3923 + 7.73205i) q^{63} -8.00000i q^{64} +(0.696152 + 0.669873i) q^{65} +(-7.46410 - 2.00000i) q^{66} +(5.36603 + 9.29423i) q^{67} +12.9282i q^{68} +(5.19615 + 3.00000i) q^{69} +(1.26795 + 0.339746i) q^{70} +(-11.0263 - 6.36603i) q^{71} +(3.26795 + 12.1962i) q^{72} -1.73205i q^{73} +(-7.73205 - 7.73205i) q^{74} +(-11.6603 + 6.73205i) q^{75} -9.46410i q^{76} -6.92820i q^{77} +(-13.9282 + 0.267949i) q^{78} +10.3923 q^{79} +(0.535898 - 0.928203i) q^{80} +(1.23205 + 2.13397i) q^{81} +(1.19615 - 1.19615i) q^{82} -5.46410 q^{83} +(-16.3923 + 9.46410i) q^{84} +(-0.866025 + 1.50000i) q^{85} +(12.9282 + 3.46410i) q^{86} +(-4.09808 + 7.09808i) q^{87} +(-5.46410 - 1.46410i) q^{88} +(-0.464102 + 0.267949i) q^{89} +(-0.437822 + 1.63397i) q^{90} +(-3.46410 - 12.0000i) q^{91} +(3.80385 + 2.19615i) q^{92} +(-1.73205 - 3.00000i) q^{93} +(1.19615 + 4.46410i) q^{94} +(0.633975 - 1.09808i) q^{95} +(4.00000 + 14.9282i) q^{96} +(5.19615 + 3.00000i) q^{97} +(-5.00000 - 5.00000i) q^{98} +8.92820 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 $

$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$3$	2.36603	−	1.36603i	1.36603	−	0.788675i	0.375608	−	0.926779i	$-0.377434\pi$
$3$	2.36603	−	1.36603i	1.36603	−	0.788675i	0.990418	+	0.138104i	$0.0441007\pi$
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$	0.267949			0.119831			0.0599153	−	0.998203i	$-0.480917\pi$
$5$	0.267949			0.119831			0.0599153	+	0.998203i	$0.480917\pi$
$6$	−2.73205	+	2.73205i	−1.11536	+	1.11536i
$7$	−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
$9$	2.23205	−	3.86603i	0.744017	−	1.28868i
$10$	−0.366025	+	0.0980762i	−0.115747	+	0.0310144i
$11$	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	$0.735842\pi$
$12$	2.73205	−	4.73205i	0.788675	−	1.36603i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$14$	4.73205	+	1.26795i	1.26469	+	0.338874i
$15$	0.633975	−	0.366025i	0.163692	−	0.0945074i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−3.23205	+	5.59808i	−0.783887	+	1.35773i	0.145774	+	0.989318i	$0.453433\pi$
$17$	−3.23205	+	5.59808i	−0.783887	+	1.35773i	−0.929661	+	0.368415i	$0.879901\pi$
$18$	−1.63397	+	6.09808i	−0.385132	+	1.43733i
$19$	2.36603	−	4.09808i	0.542803	−	0.940163i	−0.455938	−	0.890011i	$-0.650696\pi$
$19$	2.36603	−	4.09808i	0.542803	−	0.940163i	0.998742	−	0.0501517i	$-0.0159705\pi$
$20$	0.464102	−	0.267949i	0.103776	−	0.0599153i
$21$	−9.46410			−2.06524
$22$	−2.00000	−	2.00000i	−0.426401	−	0.426401i
$23$	1.09808	+	1.90192i	0.228965	+	0.396579i	0.957502	−	0.288428i	$-0.0931326\pi$
$23$	1.09808	+	1.90192i	0.228965	+	0.396579i	−0.728537	+	0.685007i	$0.759799\pi$
$24$	−2.00000	+	7.46410i	−0.408248	+	1.52360i
$25$	−4.92820			−0.985641
$26$	−4.46410	−	2.46410i	−0.875482	−	0.483250i
$27$		−	4.00000i		−	0.769800i
$28$	−6.92820			−1.30931
$29$	−2.59808	+	1.50000i	−0.482451	+	0.278543i	−0.721437	−	0.692480i	$-0.756518\pi$
$29$	−2.59808	+	1.50000i	−0.482451	+	0.278543i	0.238987	+	0.971023i	$0.423185\pi$
$30$	−0.732051	+	0.732051i	−0.133654	+	0.133654i
$31$		−	1.26795i		−	0.227730i	−0.993496	−	0.113865i	$-0.963677\pi$
$31$		−	1.26795i		−	0.227730i	0.993496	−	0.113865i	$-0.0363232\pi$
$32$	−1.46410	+	5.46410i	−0.258819	+	0.965926i
$33$	4.73205	+	2.73205i	0.823744	+	0.475589i
$34$	2.36603	−	8.83013i	0.405770	−	1.51435i
$35$	−0.803848	−	0.464102i	−0.135875	−	0.0784475i
$36$		−	8.92820i		−	1.48803i
$37$	3.86603	+	6.69615i	0.635571	+	1.10084i	0.986394	+	0.164399i	$0.0525685\pi$
$37$	3.86603	+	6.69615i	0.635571	+	1.10084i	−0.350823	+	0.936442i	$0.614098\pi$
$38$	−1.73205	+	6.46410i	−0.280976	+	1.04862i
$39$	9.56218	+	2.36603i	1.53117	+	0.378867i
$40$	−0.535898	+	0.535898i	−0.0847330	+	0.0847330i
$41$	−1.03590	+	0.598076i	−0.161780	+	0.0934038i	−0.578704	−	0.815538i	$-0.696441\pi$
$41$	−1.03590	+	0.598076i	−0.161780	+	0.0934038i	0.416924	+	0.908941i	$0.363108\pi$
$42$	12.9282	−	3.46410i	1.99487	−	0.534522i
$43$	−8.19615	−	4.73205i	−1.24990	−	0.721631i	−0.278812	−	0.960346i	$-0.589941\pi$
$43$	−8.19615	−	4.73205i	−1.24990	−	0.721631i	−0.971090	+	0.238715i	$0.923274\pi$
$44$	3.46410	+	2.00000i	0.522233	+	0.301511i
$45$	0.598076	−	1.03590i	0.0891559	−	0.154423i
$46$	−2.19615	−	2.19615i	−0.323805	−	0.323805i
$47$		−	3.26795i		−	0.476679i	−0.971182	−	0.238340i	$-0.923397\pi$
$47$		−	3.26795i		−	0.476679i	0.971182	−	0.238340i	$-0.0766032\pi$
$48$		−	10.9282i		−	1.57735i
$49$	2.50000	+	4.33013i	0.357143	+	0.618590i
$50$	6.73205	−	1.80385i	0.952056	−	0.255103i
$51$			17.6603i			2.47293i
$52$	7.00000	+	1.73205i	0.970725	+	0.240192i
$53$		−	9.92820i		−	1.36374i	−0.731472	−	0.681872i	$-0.761166\pi$
$53$		−	9.92820i		−	1.36374i	0.731472	−	0.681872i	$-0.238834\pi$
$54$	1.46410	+	5.46410i	0.199239	+	0.743570i
$55$	0.267949	+	0.464102i	0.0361303	+	0.0625794i
$56$	9.46410	−	2.53590i	1.26469	−	0.338874i
$57$		−	12.9282i		−	1.71238i
$58$	3.00000	−	3.00000i	0.393919	−	0.393919i
$59$	3.73205	−	6.46410i	0.485872	−	0.841554i	−0.513997	−	0.857792i	$-0.671836\pi$
$59$	3.73205	−	6.46410i	0.485872	−	0.841554i	0.999868	+	0.0162379i	$0.00516892\pi$
$60$	0.732051	−	1.26795i	0.0945074	−	0.163692i
$61$	−0.866025	−	0.500000i	−0.110883	−	0.0640184i	0.443533	−	0.896258i	$-0.353725\pi$
$61$	−0.866025	−	0.500000i	−0.110883	−	0.0640184i	−0.554416	+	0.832240i	$0.687058\pi$
$62$	0.464102	+	1.73205i	0.0589410	+	0.219971i
$63$	−13.3923	+	7.73205i	−1.68727	+	0.974147i
$64$		−	8.00000i		−	1.00000i
$65$	0.696152	+	0.669873i	0.0863471	+	0.0830875i
$66$	−7.46410	−	2.00000i	−0.918767	−	0.246183i
$67$	5.36603	+	9.29423i	0.655564	+	1.13547i	0.981752	+	0.190166i	$0.0609025\pi$
$67$	5.36603	+	9.29423i	0.655564	+	1.13547i	−0.326188	+	0.945305i	$0.605764\pi$
$68$			12.9282i			1.56777i
$69$	5.19615	+	3.00000i	0.625543	+	0.361158i
$70$	1.26795	+	0.339746i	0.151549	+	0.0406074i
$71$	−11.0263	−	6.36603i	−1.30858	−	0.755508i	−0.326720	−	0.945121i	$-0.605943\pi$
$71$	−11.0263	−	6.36603i	−1.30858	−	0.755508i	−0.981859	+	0.189613i	$0.939277\pi$
$72$	3.26795	+	12.1962i	0.385132	+	1.43733i
$73$		−	1.73205i		−	0.202721i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$		−	1.73205i		−	0.202721i	0.994850	−	0.101361i	$-0.0323196\pi$
$74$	−7.73205	−	7.73205i	−0.898833	−	0.898833i
$75$	−11.6603	+	6.73205i	−1.34641	+	0.777350i
$76$		−	9.46410i		−	1.08561i
$77$		−	6.92820i		−	0.789542i
$78$	−13.9282	+	0.267949i	−1.57706	+	0.0303393i
$79$	10.3923			1.16923			0.584613	−	0.811312i	$-0.301246\pi$
$79$	10.3923			1.16923			0.584613	+	0.811312i	$0.301246\pi$
$80$	0.535898	−	0.928203i	0.0599153	−	0.103776i
$81$	1.23205	+	2.13397i	0.136895	+	0.237108i
$82$	1.19615	−	1.19615i	0.132093	−	0.132093i
$83$	−5.46410			−0.599763			−0.299882	−	0.953976i	$-0.596947\pi$
$83$	−5.46410			−0.599763			−0.299882	+	0.953976i	$0.596947\pi$
$84$	−16.3923	+	9.46410i	−1.78855	+	1.03262i
$85$	−0.866025	+	1.50000i	−0.0939336	+	0.162698i
$86$	12.9282	+	3.46410i	1.39408	+	0.373544i
$87$	−4.09808	+	7.09808i	−0.439360	+	0.760994i
$88$	−5.46410	−	1.46410i	−0.582475	−	0.156074i
$89$	−0.464102	+	0.267949i	−0.0491947	+	0.0284026i	−0.524396	−	0.851475i	$-0.675709\pi$
$89$	−0.464102	+	0.267949i	−0.0491947	+	0.0284026i	0.475201	+	0.879877i	$0.342375\pi$
$90$	−0.437822	+	1.63397i	−0.0461505	+	0.172236i
$91$	−3.46410	−	12.0000i	−0.363137	−	1.25794i
$92$	3.80385	+	2.19615i	0.396579	+	0.228965i
$93$	−1.73205	−	3.00000i	−0.179605	−	0.311086i
$94$	1.19615	+	4.46410i	0.123374	+	0.460437i
$95$	0.633975	−	1.09808i	0.0650444	−	0.112660i
$96$	4.00000	+	14.9282i	0.408248	+	1.52360i
$97$	5.19615	+	3.00000i	0.527589	+	0.304604i	0.740034	−	0.672569i	$-0.234809\pi$
$97$	5.19615	+	3.00000i	0.527589	+	0.304604i	−0.212445	+	0.977173i	$0.568143\pi$
$98$	−5.00000	−	5.00000i	−0.505076	−	0.505076i
$99$	8.92820			0.897318
$100$	−8.53590	+	4.92820i	−0.853590	+	0.492820i
$101$	15.9904	−	9.23205i	1.59110	−	0.918623i	0.597984	−	0.801508i	$-0.295969\pi$
$101$	15.9904	−	9.23205i	1.59110	−	0.918623i	0.993118	−	0.117115i	$-0.0373647\pi$
$102$	−6.46410	−	24.1244i	−0.640041	−	2.38867i
$103$	−4.19615			−0.413459			−0.206730	−	0.978398i	$-0.566282\pi$
$103$	−4.19615			−0.413459			−0.206730	+	0.978398i	$0.566282\pi$
$104$	−10.1962	+	0.196152i	−0.999815	+	0.0192343i
$105$	−2.53590			−0.247478
$106$	3.63397	+	13.5622i	0.352963	+	1.31728i
$107$	−0.294229	+	0.169873i	−0.0284442	+	0.0164222i	−0.514155	−	0.857697i	$-0.671894\pi$
$107$	−0.294229	+	0.169873i	−0.0284442	+	0.0164222i	0.485710	+	0.874120i	$0.338561\pi$
$108$	−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	$0.407226\pi$
$110$	−0.535898	−	0.535898i	−0.0510959	−	0.0510959i
$111$	18.2942	+	10.5622i	1.73641	+	1.00252i
$112$	−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	$0.121600\pi$
$114$	4.73205	+	17.6603i	0.443197	+	1.65403i
$115$	0.294229	+	0.509619i	0.0274370	+	0.0475222i
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	15.4641	−	4.46410i	1.42966	−	0.412706i
$118$	−2.73205	+	10.1962i	−0.251506	+	0.938632i
$119$	19.3923	−	11.1962i	1.77769	−	1.02635i
$120$	−0.535898	+	2.00000i	−0.0489206	+	0.182574i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	1.36603	+	0.366025i	0.123674	+	0.0331384i
$123$	−1.63397	+	2.83013i	−0.147331	+	0.255184i
$124$	−1.26795	−	2.19615i	−0.113865	−	0.197220i
$125$	−2.66025			−0.237940
$126$	15.4641	−	15.4641i	1.37765	−	1.37765i
$127$	−8.83013	−	15.2942i	−0.783547	−	1.35714i	−0.929863	−	0.367905i	$-0.880075\pi$
$127$	−8.83013	−	15.2942i	−0.783547	−	1.35714i	0.146316	−	0.989238i	$-0.453258\pi$
$128$	2.92820	+	10.9282i	0.258819	+	0.965926i
$129$	−25.8564			−2.27653
$130$	−1.19615	−	0.660254i	−0.104910	−	0.0579081i
$131$			7.26795i			0.635004i	0.948258	+	0.317502i	$0.102844\pi$
$131$			7.26795i			0.635004i	−0.948258	+	0.317502i	$0.897156\pi$
$132$	10.9282			0.951178
$133$	−14.1962	+	8.19615i	−1.23096	+	0.710697i
$134$	−10.7321	−	10.7321i	−0.927108	−	0.927108i
$135$		−	1.07180i		−	0.0922456i
$136$	−4.73205	−	17.6603i	−0.405770	−	1.51435i
$137$	−15.2321	−	8.79423i	−1.30136	−	0.751342i	−0.320724	−	0.947173i	$-0.603926\pi$
$137$	−15.2321	−	8.79423i	−1.30136	−	0.751342i	−0.980638	+	0.195831i	$0.937260\pi$
$138$	−8.19615	−	2.19615i	−0.697703	−	0.186949i
$139$	−2.19615	−	1.26795i	−0.186275	−	0.107546i	0.403962	−	0.914776i	$-0.367633\pi$
$139$	−2.19615	−	1.26795i	−0.186275	−	0.107546i	−0.590238	+	0.807230i	$0.700966\pi$
$140$	−1.85641			−0.156895
$141$	−4.46410	−	7.73205i	−0.375945	−	0.651156i
$142$	17.3923	+	4.66025i	1.45953	+	0.391080i
$143$	−1.73205	+	7.00000i	−0.144841	+	0.585369i
$144$	−8.92820	−	15.4641i	−0.744017	−	1.28868i
$145$	−0.696152	+	0.401924i	−0.0578123	+	0.0333780i
$146$	0.633975	+	2.36603i	0.0524681	+	0.195814i
$147$	11.8301	+	6.83013i	0.975732	+	0.563339i
$148$	13.3923	+	7.73205i	1.10084	+	0.635571i
$149$	−4.13397	+	7.16025i	−0.338668	+	0.586591i	−0.984183	−	0.177157i	$-0.943310\pi$
$149$	−4.13397	+	7.16025i	−0.338668	+	0.586591i	0.645514	+	0.763748i	$0.276643\pi$
$150$	13.4641	−	13.4641i	1.09934	−	1.09934i
$151$			8.19615i			0.666993i	0.942751	+	0.333497i	$0.108229\pi$
$151$			8.19615i			0.666993i	−0.942751	+	0.333497i	$0.891771\pi$
$152$	3.46410	+	12.9282i	0.280976	+	1.04862i
$153$	14.4282	+	24.9904i	1.16645	+	2.02035i
$154$	2.53590	+	9.46410i	0.204349	+	0.762639i
$155$		−	0.339746i		−	0.0272891i
$156$	18.9282	−	5.46410i	1.51547	−	0.437478i
$157$			9.92820i			0.792357i	0.918174	+	0.396178i	$0.129664\pi$
$157$			9.92820i			0.792357i	−0.918174	+	0.396178i	$0.870336\pi$
$158$	−14.1962	+	3.80385i	−1.12939	+	0.302618i
$159$	−13.5622	−	23.4904i	−1.07555	−	1.86291i
$160$	−0.392305	+	1.46410i	−0.0310144	+	0.115747i
$161$		−	7.60770i		−	0.599570i
$162$	−2.46410	−	2.46410i	−0.193598	−	0.193598i
$163$	2.19615	−	3.80385i	0.172016	−	0.297940i	−0.767109	−	0.641517i	$-0.778305\pi$
$163$	2.19615	−	3.80385i	0.172016	−	0.297940i	0.939125	+	0.343577i	$0.111639\pi$
$164$	−1.19615	+	2.07180i	−0.0934038	+	0.161780i
$165$	1.26795	+	0.732051i	0.0987097	+	0.0569901i
$166$	7.46410	−	2.00000i	0.579327	−	0.155230i
$167$	−7.73205	+	4.46410i	−0.598324	+	0.345443i	−0.768382	−	0.639992i	$-0.778938\pi$
$167$	−7.73205	+	4.46410i	−0.598324	+	0.345443i	0.170058	+	0.985434i	$0.445605\pi$
$168$	18.9282	−	18.9282i	1.46034	−	1.46034i
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	0.633975	−	2.36603i	0.0486236	−	0.181466i
$171$	−10.5622	−	18.2942i	−0.807710	−	1.39899i
$172$	−18.9282			−1.44326
$173$	4.39230	+	2.53590i	0.333941	+	0.192801i	0.657589	−	0.753377i	$-0.271576\pi$
$173$	4.39230	+	2.53590i	0.333941	+	0.192801i	−0.323649	+	0.946177i	$0.604910\pi$
$174$	3.00000	−	11.1962i	0.227429	−	0.848778i
$175$	14.7846	+	8.53590i	1.11761	+	0.645253i
$176$	8.00000			0.603023
$177$		−	20.3923i		−	1.53278i
$178$	0.535898	−	0.535898i	0.0401673	−	0.0401673i
$179$	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	$0.160070\pi$
$180$		−	2.39230i		−	0.178312i
$181$			11.5359i			0.857457i	0.903433	+	0.428728i	$0.141038\pi$
$181$			11.5359i			0.857457i	−0.903433	+	0.428728i	$0.858962\pi$
$182$	9.12436	+	15.1244i	0.676342	+	1.12109i
$183$	−2.73205			−0.201959
$184$	−6.00000	−	1.60770i	−0.442326	−	0.118521i
$185$	1.03590	+	1.79423i	0.0761608	+	0.131914i
$186$	3.46410	+	3.46410i	0.254000	+	0.254000i
$187$	−12.9282			−0.945404
$188$	−3.26795	−	5.66025i	−0.238340	−	0.412816i
$189$	−6.92820	+	12.0000i	−0.503953	+	0.872872i
$190$	−0.464102	+	1.73205i	−0.0336695	+	0.125656i
$191$	−7.09808	+	12.2942i	−0.513599	+	0.889579i	0.486277	+	0.873805i	$0.338355\pi$
$191$	−7.09808	+	12.2942i	−0.513599	+	0.889579i	−0.999876	+	0.0157743i	$0.994979\pi$
$192$	−10.9282	−	18.9282i	−0.788675	−	1.36603i
$193$	21.6962	−	12.5263i	1.56172	−	0.901661i	0.564640	−	0.825337i	$-0.309015\pi$
$193$	21.6962	−	12.5263i	1.56172	−	0.901661i	0.997083	−	0.0763241i	$-0.0243184\pi$
$194$	−8.19615	−	2.19615i	−0.588449	−	0.157675i
$195$	2.56218	+	0.633975i	0.183481	+	0.0453999i
$196$	8.66025	+	5.00000i	0.618590	+	0.357143i
$197$	−9.73205	−	16.8564i	−0.693380	−	1.20097i	−0.970724	−	0.240199i	$-0.922787\pi$
$197$	−9.73205	−	16.8564i	−0.693380	−	1.20097i	0.277344	−	0.960771i	$-0.410546\pi$
$198$	−12.1962	+	3.26795i	−0.866743	+	0.232243i
$199$	−4.56218	+	7.90192i	−0.323404	+	0.560153i	−0.981188	−	0.193054i	$-0.938161\pi$
$199$	−4.56218	+	7.90192i	−0.323404	+	0.560153i	0.657784	+	0.753207i	$0.271494\pi$
$200$	9.85641	−	9.85641i	0.696953	−	0.696953i
$201$	25.3923	+	14.6603i	1.79104	+	1.03405i
$202$	−18.4641	+	18.4641i	−1.29913	+	1.29913i
$203$	10.3923			0.729397
$204$	17.6603	+	30.5885i	1.23647	+	2.14162i
$205$	−0.277568	+	0.160254i	−0.0193862	+	0.0111926i
$206$	5.73205	−	1.53590i	0.399371	−	0.107011i
$207$	9.80385			0.681415
$208$	13.8564	−	4.00000i	0.960769	−	0.277350i
$209$	9.46410			0.654646
$210$	3.46410	−	0.928203i	0.239046	−	0.0640521i
$211$	−2.24167	+	1.29423i	−0.154323	+	0.0890984i	−0.575173	−	0.818032i	$-0.695065\pi$
$211$	−2.24167	+	1.29423i	−0.154323	+	0.0890984i	0.420850	+	0.907130i	$0.361732\pi$
$212$	−9.92820	−	17.1962i	−0.681872	−	1.18104i
$213$	−34.7846			−2.38340
$214$	0.339746	−	0.339746i	0.0232246	−	0.0232246i
$215$	−2.19615	−	1.26795i	−0.149776	−	0.0864734i
$216$	8.00000	+	8.00000i	0.544331	+	0.544331i
$217$	−2.19615	+	3.80385i	−0.149085	+	0.258222i
$218$	−8.19615	+	2.19615i	−0.555113	+	0.148742i
$219$	−2.36603	−	4.09808i	−0.159881	−	0.276922i
$220$	0.928203	+	0.535898i	0.0625794	+	0.0361303i
$221$	−22.3923	+	6.46410i	−1.50627	+	0.434823i
$222$	−28.8564	−	7.73205i	−1.93672	−	0.518941i
$223$	−16.9019	+	9.75833i	−1.13184	+	0.653466i	−0.944396	−	0.328810i	$-0.893352\pi$
$223$	−16.9019	+	9.75833i	−1.13184	+	0.653466i	−0.187440	+	0.982276i	$0.560019\pi$
$224$	13.8564	−	13.8564i	0.925820	−	0.925820i
$225$	−11.0000	+	19.0526i	−0.733333	+	1.27017i
$226$	−1.09808	+	4.09808i	−0.0730429	+	0.272600i
$227$	−6.02628	+	10.4378i	−0.399978	+	0.692783i	−0.993723	−	0.111871i	$-0.964316\pi$
$227$	−6.02628	+	10.4378i	−0.399978	+	0.692783i	0.593745	+	0.804654i	$0.297649\pi$
$228$	−12.9282	−	22.3923i	−0.856191	−	1.48297i
$229$	−0.928203			−0.0613374			−0.0306687	−	0.999530i	$-0.509764\pi$
$229$	−0.928203			−0.0613374			−0.0306687	+	0.999530i	$0.509764\pi$
$230$	−0.588457	−	0.588457i	−0.0388017	−	0.0388017i
$231$	−9.46410	−	16.3923i	−0.622692	−	1.07853i
$232$	2.19615	−	8.19615i	0.144184	−	0.538104i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$	−19.4904	+	11.7583i	−1.27413	+	0.768666i
$235$		−	0.875644i		−	0.0571207i
$236$		−	14.9282i		−	0.971743i
$237$	24.5885	−	14.1962i	1.59719	−	0.922139i
$238$	−22.3923	+	22.3923i	−1.45148	+	1.45148i
$239$		−	2.39230i		−	0.154745i	−0.997002	−	0.0773727i	$-0.975347\pi$
$239$		−	2.39230i		−	0.154745i	0.997002	−	0.0773727i	$-0.0246531\pi$
$240$		−	2.92820i		−	0.189015i
$241$	−0.696152	−	0.401924i	−0.0448431	−	0.0258902i	0.477411	−	0.878680i	$-0.341575\pi$
$241$	−0.696152	−	0.401924i	−0.0448431	−	0.0258902i	−0.522254	+	0.852790i	$0.674909\pi$
$242$	−2.56218	+	9.56218i	−0.164703	+	0.614680i
$243$	16.2224	+	9.36603i	1.04067	+	0.600831i
$244$	−2.00000			−0.128037
$245$	0.669873	+	1.16025i	0.0427966	+	0.0741259i
$246$	1.19615	−	4.46410i	0.0762639	−	0.284621i
$247$	16.3923	−	4.73205i	1.04302	−	0.301093i
$248$	2.53590	+	2.53590i	0.161030	+	0.161030i
$249$	−12.9282	+	7.46410i	−0.819292	+	0.473018i
$250$	3.63397	−	0.973721i	0.229833	−	0.0615835i
$251$	−1.90192	−	1.09808i	−0.120048	−	0.0693100i	0.438773	−	0.898598i	$-0.355413\pi$
$251$	−1.90192	−	1.09808i	−0.120048	−	0.0693100i	−0.558822	+	0.829288i	$0.688746\pi$
$252$	−15.4641	+	26.7846i	−0.974147	+	1.68727i
$253$	−2.19615	+	3.80385i	−0.138071	+	0.239146i
$254$	17.6603	+	17.6603i	1.10810	+	1.10810i
$255$			4.73205i			0.296333i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	2.42820	+	4.20577i	0.151467	+	0.262349i	0.931767	−	0.363057i	$-0.118267\pi$
$257$	2.42820	+	4.20577i	0.151467	+	0.262349i	−0.780300	+	0.625406i	$0.784934\pi$
$258$	35.3205	−	9.46410i	2.19896	−	0.589209i
$259$		−	26.7846i		−	1.66431i
$260$	1.87564	+	0.464102i	0.116323	+	0.0287824i
$261$			13.3923i			0.828963i
$262$	−2.66025	−	9.92820i	−0.164351	−	0.613366i
$263$	2.19615	+	3.80385i	0.135421	+	0.234555i	0.925758	−	0.378116i	$-0.123428\pi$
$263$	2.19615	+	3.80385i	0.135421	+	0.234555i	−0.790337	+	0.612672i	$0.790095\pi$
$264$	−14.9282	+	4.00000i	−0.918767	+	0.246183i
$265$		−	2.66025i		−	0.163418i
$266$	16.3923	−	16.3923i	1.00508	−	1.00508i
$267$	−0.732051	+	1.26795i	−0.0448008	+	0.0775972i
$268$	18.5885	+	10.7321i	1.13547	+	0.655564i
$269$	−2.19615	−	1.26795i	−0.133902	−	0.0773082i	0.431553	−	0.902088i	$-0.357966\pi$
$269$	−2.19615	−	1.26795i	−0.133902	−	0.0773082i	−0.565455	+	0.824779i	$0.691299\pi$
$270$	0.392305	+	1.46410i	0.0238749	+	0.0891024i
$271$	−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	$0.509669\pi$
$272$	12.9282	+	22.3923i	0.783887	+	1.35773i
$273$	−24.5885	−	23.6603i	−1.48816	−	1.43198i
$274$	24.0263	+	6.43782i	1.45148	+	0.388923i
$275$	−4.92820	−	8.53590i	−0.297182	−	0.514734i
$276$	12.0000			0.722315
$277$	17.5981	+	10.1603i	1.05737	+	0.610471i	0.924702	−	0.380691i	$-0.124314\pi$
$277$	17.5981	+	10.1603i	1.05737	+	0.610471i	0.132663	+	0.991161i	$0.457647\pi$
$278$	3.46410	+	0.928203i	0.207763	+	0.0556699i
$279$	−4.90192	−	2.83013i	−0.293471	−	0.169435i
$280$	2.53590	−	0.679492i	0.151549	−	0.0406074i
$281$			6.66025i			0.397317i	0.980069	+	0.198659i	$0.0636585\pi$
$281$			6.66025i			0.397317i	−0.980069	+	0.198659i	$0.936341\pi$
$282$	8.92820	+	8.92820i	0.531667	+	0.531667i
$283$	9.33975	−	5.39230i	0.555190	−	0.320539i	−0.196022	−	0.980599i	$-0.562803\pi$
$283$	9.33975	−	5.39230i	0.555190	−	0.320539i	0.751213	+	0.660060i	$0.229469\pi$
$284$	−25.4641			−1.51102
$285$		−	3.46410i		−	0.205196i
$286$	−0.196152	−	10.1962i	−0.0115987	−	0.602911i
$287$	4.14359			0.244589
$288$	17.8564	+	17.8564i	1.05220	+	1.05220i
$289$	−12.3923	−	21.4641i	−0.728959	−	1.26259i
$290$	0.803848	−	0.803848i	0.0472036	−	0.0472036i
$291$	16.3923			0.960934
$292$	−1.73205	−	3.00000i	−0.101361	−	0.175562i
$293$	6.59808	−	11.4282i	0.385464	−	0.667643i	−0.606370	−	0.795183i	$-0.707375\pi$
$293$	6.59808	−	11.4282i	0.385464	−	0.667643i	0.991833	+	0.127540i	$0.0407082\pi$
$294$	−18.6603	−	5.00000i	−1.08829	−	0.291606i
$295$	1.00000	−	1.73205i	0.0582223	−	0.100844i
$296$	−21.1244	−	5.66025i	−1.22783	−	0.328996i
$297$	6.92820	−	4.00000i	0.402015	−	0.232104i
$298$	3.02628	−	11.2942i	0.175308	−	0.654257i
$299$	−1.90192	+	7.68653i	−0.109991	+	0.444524i
$300$	−13.4641	+	23.3205i	−0.777350	+	1.34641i
$301$	16.3923	+	28.3923i	0.944837	+	1.63651i
$302$	−3.00000	−	11.1962i	−0.172631	−	0.644266i
$303$	25.2224	−	43.6865i	1.44899	−	2.50973i
$304$	−9.46410	−	16.3923i	−0.542803	−	0.940163i
$305$	−0.232051	−	0.133975i	−0.0132872	−	0.00767136i
$306$	−28.8564	−	28.8564i	−1.64961	−	1.64961i
$307$	−8.19615			−0.467779			−0.233890	−	0.972263i	$-0.575145\pi$
$307$	−8.19615			−0.467779			−0.233890	+	0.972263i	$0.575145\pi$
$308$	−6.92820	−	12.0000i	−0.394771	−	0.683763i
$309$	−9.92820	+	5.73205i	−0.564796	+	0.326085i
$310$	0.124356	+	0.464102i	0.00706293	+	0.0263592i
$311$	12.5885			0.713826			0.356913	−	0.934138i	$-0.383829\pi$
$311$	12.5885			0.713826			0.356913	+	0.934138i	$0.383829\pi$
$312$	−23.8564	+	14.3923i	−1.35060	+	0.814804i
$313$	−9.46410			−0.534943			−0.267471	−	0.963566i	$-0.586188\pi$
$313$	−9.46410			−0.534943			−0.267471	+	0.963566i	$0.586188\pi$
$314$	−3.63397	−	13.5622i	−0.205077	−	0.765358i
$315$	−3.58846	+	2.07180i	−0.202187	+	0.116733i
$316$	18.0000	−	10.3923i	1.01258	−	0.584613i
$317$	14.8038			0.831467			0.415733	−	0.909486i	$-0.363525\pi$
$317$	14.8038			0.831467			0.415733	+	0.909486i	$0.363525\pi$
$318$	27.1244	+	27.1244i	1.52106	+	1.52106i
$319$	−5.19615	−	3.00000i	−0.290929	−	0.167968i
$320$		−	2.14359i		−	0.119831i
$321$	−0.464102	+	0.803848i	−0.0259036	+	0.0448664i
$322$	2.78461	+	10.3923i	0.155180	+	0.579141i
$323$	15.2942	+	26.4904i	0.850994	+	1.47396i
$324$	4.26795	+	2.46410i	0.237108	+	0.136895i
$325$	−12.8038	−	12.3205i	−0.710230	−	0.683419i
$326$	−1.60770	+	6.00000i	−0.0890420	+	0.332309i
$327$	14.1962	−	8.19615i	0.785049	−	0.453248i
$328$	0.875644	−	3.26795i	0.0483494	−	0.180442i
$329$	−5.66025	+	9.80385i	−0.312060	+	0.540504i
$330$	−2.00000	−	0.535898i	−0.110096	−	0.0295002i
$331$	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	$0.0596888\pi$
$332$	−9.46410	+	5.46410i	−0.519410	+	0.299882i
$333$	34.5167			1.89150
$334$	8.92820	−	8.92820i	0.488530	−	0.488530i
$335$	1.43782	+	2.49038i	0.0785566	+	0.136064i
$336$	−18.9282	+	32.7846i	−1.03262	+	1.78855i
$337$	15.2487			0.830650			0.415325	−	0.909673i	$-0.363668\pi$
$337$	15.2487			0.830650			0.415325	+	0.909673i	$0.363668\pi$
$338$	−5.43782	−	17.5622i	−0.295779	−	0.955257i
$339$		−	8.19615i		−	0.445154i
$340$			3.46410i			0.187867i
$341$	2.19615	−	1.26795i	0.118928	−	0.0686633i
$342$	21.1244	+	21.1244i	1.14227	+	1.14227i
$343$			6.92820i			0.374088i
$344$	25.8564	−	6.92820i	1.39408	−	0.373544i
$345$	1.39230	+	0.803848i	0.0749592	+	0.0432777i
$346$	−6.92820	−	1.85641i	−0.372463	−	0.0998010i
$347$	4.09808	+	2.36603i	0.219996	+	0.127015i	0.605949	−	0.795504i	$-0.292794\pi$
$347$	4.09808	+	2.36603i	0.219996	+	0.127015i	−0.385952	+	0.922519i	$0.626127\pi$
$348$			16.3923i			0.878720i
$349$	−14.6603	−	25.3923i	−0.784745	−	1.35922i	−0.929151	−	0.369700i	$-0.879460\pi$
$349$	−14.6603	−	25.3923i	−0.784745	−	1.35922i	0.144406	−	0.989519i	$-0.453873\pi$
$350$	−23.3205	−	6.24871i	−1.24653	−	0.334008i
$351$	10.0000	−	10.3923i	0.533761	−	0.554700i
$352$	−10.9282	+	2.92820i	−0.582475	+	0.156074i
$353$	18.8205	−	10.8660i	1.00171	−	0.578340i	0.0929594	−	0.995670i	$-0.470367\pi$
$353$	18.8205	−	10.8660i	1.00171	−	0.578340i	0.908755	+	0.417330i	$0.137034\pi$
$354$	7.46410	+	27.8564i	0.396713	+	1.48055i
$355$	−2.95448	−	1.70577i	−0.156808	−	0.0905329i
$356$	−0.535898	+	0.928203i	−0.0284026	+	0.0491947i
$357$	30.5885	−	52.9808i	1.61891	−	2.80404i
$358$	−13.8564	+	13.8564i	−0.732334	+	0.732334i
$359$			26.9282i			1.42122i	0.703588	+	0.710608i	$0.251580\pi$
$359$			26.9282i			1.42122i	−0.703588	+	0.710608i	$0.748420\pi$
$360$	0.875644	+	3.26795i	0.0461505	+	0.172236i
$361$	−1.69615	−	2.93782i	−0.0892712	−	0.154622i
$362$	−4.22243	−	15.7583i	−0.221926	−	0.828239i
$363$		−	19.1244i		−	1.00377i
$364$	−18.0000	−	17.3205i	−0.943456	−	0.907841i
$365$		−	0.464102i		−	0.0242922i
$366$	3.73205	−	1.00000i	0.195077	−	0.0522708i
$367$	8.90192	+	15.4186i	0.464677	+	0.804844i	0.999187	−	0.0403184i	$-0.0128372\pi$
$367$	8.90192	+	15.4186i	0.464677	+	0.804844i	−0.534510	+	0.845162i	$0.679504\pi$
$368$	8.78461			0.457929
$369$			5.33975i			0.277976i
$370$	−2.07180	−	2.07180i	−0.107708	−	0.107708i
$371$	−17.1962	+	29.7846i	−0.892780	+	1.54634i
$372$	−6.00000	−	3.46410i	−0.311086	−	0.179605i
$373$	13.6699	+	7.89230i	0.707799	+	0.408648i	0.810246	−	0.586090i	$-0.199334\pi$
$373$	13.6699	+	7.89230i	0.707799	+	0.408648i	−0.102446	+	0.994739i	$0.532667\pi$
$374$	17.6603	−	4.73205i	0.913190	−	0.244689i
$375$	−6.29423	+	3.63397i	−0.325033	+	0.187658i
$376$	6.53590	+	6.53590i	0.337063	+	0.337063i
$377$	−10.5000	−	2.59808i	−0.540778	−	0.133808i
$378$	5.07180	−	18.9282i	0.260865	−	0.973562i
$379$	8.02628	+	13.9019i	0.412282	+	0.714094i	0.995139	−	0.0984811i	$-0.0313984\pi$
$379$	8.02628	+	13.9019i	0.412282	+	0.714094i	−0.582857	+	0.812575i	$0.698065\pi$
$380$		−	2.53590i		−	0.130089i
$381$	−41.7846	−	24.1244i	−2.14069	−	1.23593i
$382$	5.19615	−	19.3923i	0.265858	−	0.992197i
$383$	−17.3205	−	10.0000i	−0.885037	−	0.510976i	−0.0127209	−	0.999919i	$-0.504049\pi$
$383$	−17.3205	−	10.0000i	−0.885037	−	0.510976i	−0.872316	+	0.488943i	$0.837383\pi$
$384$	21.8564	+	21.8564i	1.11536	+	1.11536i
$385$		−	1.85641i		−	0.0946112i
$386$	−25.0526	+	25.0526i	−1.27514	+	1.27514i
$387$	−36.5885	+	21.1244i	−1.85990	+	1.07381i
$388$	12.0000			0.609208
$389$			36.7128i			1.86141i	0.365766	+	0.930707i	$0.380807\pi$
$389$			36.7128i			1.86141i	−0.365766	+	0.930707i	$0.619193\pi$
$390$	−3.73205	+	0.0717968i	−0.188980	+	0.00363557i
$391$	−14.1962			−0.717930
$392$	−13.6603	−	3.66025i	−0.689947	−	0.184871i
$393$	9.92820	+	17.1962i	0.500812	+	0.867431i
$394$	19.4641	+	19.4641i	0.980587	+	0.980587i
$395$	2.78461			0.140109
$396$	15.4641	−	8.92820i	0.777100	−	0.448659i
$397$	12.1244	−	21.0000i	0.608504	−	1.05396i	−0.382983	−	0.923755i	$-0.625103\pi$
$397$	12.1244	−	21.0000i	0.608504	−	1.05396i	0.991487	−	0.130204i	$-0.0415634\pi$
$398$	3.33975	−	12.4641i	0.167406	−	0.624769i
$399$	−22.3923	+	38.7846i	−1.12102	+	1.94166i
$400$	−9.85641	+	17.0718i	−0.492820	+	0.853590i
$401$	−5.42820	+	3.13397i	−0.271072	+	0.156503i	−0.629374	−	0.777102i	$-0.716689\pi$
$401$	−5.42820	+	3.13397i	−0.271072	+	0.156503i	0.358303	+	0.933605i	$0.383355\pi$
$402$	−40.0526	−	10.7321i	−1.99764	−	0.535266i
$403$	3.16987	−	3.29423i	0.157903	−	0.164097i
$404$	18.4641	−	31.9808i	0.918623	−	1.59110i
$405$	0.330127	+	0.571797i	0.0164041	+	0.0284128i
$406$	−14.1962	+	3.80385i	−0.704543	+	0.188782i
$407$	−7.73205	+	13.3923i	−0.383264	+	0.663832i
$408$	−35.3205	−	35.3205i	−1.74863	−	1.74863i
$409$	−9.69615	−	5.59808i	−0.479444	−	0.276807i	0.240741	−	0.970589i	$-0.422610\pi$
$409$	−9.69615	−	5.59808i	−0.479444	−	0.276807i	−0.720185	+	0.693782i	$0.755943\pi$
$410$	0.320508	−	0.320508i	0.0158288	−	0.0158288i
$411$	−48.0526			−2.37026
$412$	−7.26795	+	4.19615i	−0.358066	+	0.206730i
$413$	−22.3923	+	12.9282i	−1.10185	+	0.636155i
$414$	−13.3923	+	3.58846i	−0.658196	+	0.176363i
$415$	−1.46410			−0.0718699
$416$	−17.4641	+	10.5359i	−0.856248	+	0.516565i
$417$	−6.92820			−0.339276
$418$	−12.9282	+	3.46410i	−0.632339	+	0.169435i
$419$	−22.0981	+	12.7583i	−1.07956	+	0.623285i	−0.930778	−	0.365585i	$-0.880869\pi$
$419$	−22.0981	+	12.7583i	−1.07956	+	0.623285i	−0.148784	+	0.988870i	$0.547536\pi$
$420$	−4.39230	+	2.53590i	−0.214323	+	0.123739i
$421$	−5.87564			−0.286361			−0.143181	−	0.989697i	$-0.545733\pi$
$421$	−5.87564			−0.286361			−0.143181	+	0.989697i	$0.545733\pi$
$422$	2.58846	−	2.58846i	0.126004	−	0.126004i
$423$	−12.6340	−	7.29423i	−0.614285	−	0.354658i
$424$	19.8564	+	19.8564i	0.964312	+	0.964312i
$425$	15.9282	−	27.5885i	0.772631	−	1.33824i
$426$	47.5167	−	12.7321i	2.30219	−	0.616870i
$427$	1.73205	+	3.00000i	0.0838198	+	0.145180i
$428$	−0.339746	+	0.588457i	−0.0164222	+	0.0284442i
$429$	5.46410	+	18.9282i	0.263809	+	0.913862i
$430$	3.46410	+	0.928203i	0.167054	+	0.0447619i
$431$	8.53590	−	4.92820i	0.411160	−	0.237383i	−0.280128	−	0.959963i	$-0.590377\pi$
$431$	8.53590	−	4.92820i	0.411160	−	0.237383i	0.691288	+	0.722579i	$0.257044\pi$
$432$	−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	$0.998307\pi$
$434$	1.60770	−	6.00000i	0.0771718	−	0.288009i
$435$	−1.09808	+	1.90192i	−0.0526487	+	0.0911903i
$436$	10.3923	−	6.00000i	0.497701	−	0.287348i
$437$	10.3923			0.497131
$438$	4.73205	+	4.73205i	0.226106	+	0.226106i
$439$	−18.1962	−	31.5167i	−0.868455	−	1.50421i	−0.863575	−	0.504220i	$-0.831780\pi$
$439$	−18.1962	−	31.5167i	−0.868455	−	1.50421i	−0.00487976	−	0.999988i	$-0.501553\pi$
$440$	−1.46410	−	0.392305i	−0.0697983	−	0.0187024i
$441$	22.3205			1.06288
$442$	28.2224	−	17.0263i	1.34240	−	0.809858i
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	42.2487			2.00504
$445$	−0.124356	+	0.0717968i	−0.00589502	+	0.00340349i
$446$	19.5167	−	19.5167i	0.924141	−	0.924141i
$447$			22.5885i			1.06840i
$448$	−13.8564	+	24.0000i	−0.654654	+	1.13389i
$449$	11.5359	+	6.66025i	0.544413	+	0.314317i	0.746865	−	0.664975i	$-0.231558\pi$
$449$	11.5359	+	6.66025i	0.544413	+	0.314317i	−0.202453	+	0.979292i	$0.564891\pi$
$450$	8.05256	−	30.0526i	0.379601	−	1.41669i
$451$	−2.07180	−	1.19615i	−0.0975571	−	0.0563246i
$452$		−	6.00000i		−	0.282216i
$453$	11.1962	+	19.3923i	0.526041	+	0.911130i
$454$	4.41154	−	16.4641i	0.207044	−	0.772699i
$455$	−0.928203	−	3.21539i	−0.0435148	−	0.150740i
$456$	25.8564	+	25.8564i	1.21084	+	1.21084i
$457$	−3.69615	+	2.13397i	−0.172899	+	0.0998231i	−0.583952	−	0.811788i	$-0.698494\pi$
$457$	−3.69615	+	2.13397i	−0.172899	+	0.0998231i	0.411053	+	0.911611i	$0.365161\pi$
$458$	1.26795	−	0.339746i	0.0592474	−	0.0158753i
$459$	22.3923	+	12.9282i	1.04518	+	0.603437i
$460$	1.01924	+	0.588457i	0.0475222	+	0.0274370i
$461$	−5.66987	+	9.82051i	−0.264072	+	0.457387i	−0.967320	−	0.253558i	$-0.918399\pi$
$461$	−5.66987	+	9.82051i	−0.264072	+	0.457387i	0.703248	+	0.710945i	$0.251732\pi$
$462$	18.9282	+	18.9282i	0.880620	+	0.880620i
$463$		−	4.39230i		−	0.204128i	−0.994778	−	0.102064i	$-0.967455\pi$
$463$		−	4.39230i		−	0.204128i	0.994778	−	0.102064i	$-0.0325446\pi$
$464$			12.0000i			0.557086i
$465$	−0.464102	−	0.803848i	−0.0215222	−	0.0372775i
$466$		0			0
$467$		−	27.4641i		−	1.27089i	−0.772147	−	0.635444i	$-0.780817\pi$
$467$		−	27.4641i		−	1.27089i	0.772147	−	0.635444i	$-0.219183\pi$
$468$	22.3205	−	23.1962i	1.03177	−	1.07224i
$469$		−	37.1769i		−	1.71667i
$470$	0.320508	+	1.19615i	0.0147839	+	0.0551744i
$471$	13.5622	+	23.4904i	0.624912	+	1.08238i
$472$	5.46410	+	20.3923i	0.251506	+	0.938632i
$473$		−	18.9282i		−	0.870320i
$474$	−28.3923	+	28.3923i	−1.30410	+	1.30410i
$475$	−11.6603	+	20.1962i	−0.535009	+	0.926663i
$476$	22.3923	−	38.7846i	1.02635	−	1.77769i
$477$	−38.3827	−	22.1603i	−1.75742	−	1.01465i
$478$	0.875644	+	3.26795i	0.0400510	+	0.149473i
$479$	28.3468	−	16.3660i	1.29520	−	0.747783i	0.315627	−	0.948883i	$-0.397785\pi$
$479$	28.3468	−	16.3660i	1.29520	−	0.747783i	0.979571	+	0.201100i	$0.0644518\pi$
$480$	1.07180	+	4.00000i	0.0489206	+	0.182574i
$481$	−6.69615	+	27.0622i	−0.305318	+	1.23393i
$482$	1.09808	+	0.294229i	0.0500160	+	0.0134017i
$483$	−10.3923	−	18.0000i	−0.472866	−	0.819028i
$484$		−	14.0000i		−	0.636364i
$485$	1.39230	+	0.803848i	0.0632213	+	0.0365008i
$486$	−25.5885	−	6.85641i	−1.16072	−	0.311013i
$487$	9.80385	+	5.66025i	0.444255	+	0.256491i	0.705401	−	0.708809i	$-0.250767\pi$
$487$	9.80385	+	5.66025i	0.444255	+	0.256491i	−0.261146	+	0.965299i	$0.584100\pi$
$488$	2.73205	−	0.732051i	0.123674	−	0.0331384i
$489$		−	12.0000i		−	0.542659i
$490$	−1.33975	−	1.33975i	−0.0605236	−	0.0605236i
$491$	24.5885	−	14.1962i	1.10966	−	0.640663i	0.170920	−	0.985285i	$-0.445326\pi$
$491$	24.5885	−	14.1962i	1.10966	−	0.640663i	0.938742	+	0.344622i	$0.111993\pi$
$492$			6.53590i			0.294661i
$493$		−	19.3923i		−	0.873385i
$494$	−20.6603	+	12.4641i	−0.929549	+	0.560786i
$495$	2.39230			0.107526
$496$	−4.39230	−	2.53590i	−0.197220	−	0.113865i
$497$	22.0526	+	38.1962i	0.989192	+	1.71333i
$498$	14.9282	−	14.9282i	0.668949	−	0.668949i
$499$	33.1244			1.48285			0.741425	−	0.671036i	$-0.234150\pi$
$499$	33.1244			1.48285			0.741425	+	0.671036i	$0.234150\pi$
$500$	−4.60770	+	2.66025i	−0.206062	+	0.118970i
$501$	−12.1962	+	21.1244i	−0.544884	+	0.943767i
$502$	3.00000	+	0.803848i	0.133897	+	0.0358775i
$503$	16.3923	−	28.3923i	0.730897	−	1.26595i	−0.225604	−	0.974219i	$-0.572435\pi$
$503$	16.3923	−	28.3923i	0.730897	−	1.26595i	0.956500	−	0.291731i	$-0.0942312\pi$
$504$	11.3205	−	42.2487i	0.504256	−	1.88191i
$505$	4.28461	−	2.47372i	0.190663	−	0.110079i
$506$	1.60770	−	6.00000i	0.0714708	−	0.266733i
$507$	18.9282	+	30.0526i	0.840631	+	1.33468i
$508$	−30.5885	−	17.6603i	−1.35714	−	0.783547i
$509$	16.0622	+	27.8205i	0.711944	+	1.23312i	0.964127	+	0.265443i	$0.0855181\pi$
$509$	16.0622	+	27.8205i	0.711944	+	1.23312i	−0.252183	+	0.967680i	$0.581149\pi$
$510$	−1.73205	−	6.46410i	−0.0766965	−	0.286235i
$511$	−3.00000	+	5.19615i	−0.132712	+	0.229864i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−16.3923	−	9.46410i	−0.723738	−	0.417850i
$514$	−4.85641	−	4.85641i	−0.214207	−	0.214207i
$515$	−1.12436			−0.0495450
$516$	−44.7846	+	25.8564i	−1.97153	+	1.13826i
$517$	5.66025	−	3.26795i	0.248938	−	0.143724i
$518$	9.80385	+	36.5885i	0.430756	+	1.60760i
$519$	13.8564			0.608229
$520$	−2.73205	+	0.0525589i	−0.119808	+	0.00230486i
$521$	−39.2487			−1.71952			−0.859759	−	0.510701i	$-0.829386\pi$
$521$	−39.2487			−1.71952			−0.859759	+	0.510701i	$0.829386\pi$
$522$	−4.90192	−	18.2942i	−0.214551	−	0.800717i
$523$	−11.1962	+	6.46410i	−0.489574	+	0.282655i	−0.724398	−	0.689382i	$-0.757882\pi$
$523$	−11.1962	+	6.46410i	−0.489574	+	0.282655i	0.234824	+	0.972038i	$0.424549\pi$
$524$	7.26795	+	12.5885i	0.317502	+	0.549929i
$525$	46.6410			2.03558
$526$	−4.39230	−	4.39230i	−0.191514	−	0.191514i
$527$	7.09808	+	4.09808i	0.309197	+	0.178515i
$528$	18.9282	−	10.9282i	0.823744	−	0.475589i
$529$	9.08846	−	15.7417i	0.395150	−	0.684420i
$530$	0.973721	+	3.63397i	0.0422957	+	0.157850i
$531$	−16.6603	−	28.8564i	−0.722993	−	1.25226i
$532$	−16.3923	+	28.3923i	−0.710697	+	1.23096i
$533$	−4.18653	−	1.03590i	−0.181339	−	0.0448697i
$534$	0.535898	−	2.00000i	0.0231906	−	0.0865485i
$535$	−0.0788383	+	0.0455173i	−0.00340848	+	0.00196789i
$536$	−29.3205	−	7.85641i	−1.26645	−	0.339345i
$537$	18.9282	−	32.7846i	0.816812	−	1.41476i
$538$	3.46410	+	0.928203i	0.149348	+	0.0400177i
$539$	−5.00000	+	8.66025i	−0.215365	+	0.373024i
$540$	−1.07180	−	1.85641i	−0.0461228	−	0.0798870i
$541$	−23.4449			−1.00797			−0.503987	−	0.863711i	$-0.668134\pi$
$541$	−23.4449			−1.00797			−0.503987	+	0.863711i	$0.668134\pi$
$542$	17.3205	−	17.3205i	0.743980	−	0.743980i
$543$	15.7583	+	27.2942i	0.676255	+	1.17131i
$544$	−25.8564	−	25.8564i	−1.10858	−	1.10858i
$545$	1.60770			0.0688661
$546$	42.2487	+	23.3205i	1.80808	+	0.998026i
$547$		−	12.5885i		−	0.538244i	−0.963106	−	0.269122i	$-0.913267\pi$
$547$		−	12.5885i		−	0.538244i	0.963106	−	0.269122i	$-0.0867334\pi$
$548$	−35.1769			−1.50268
$549$	−3.86603	+	2.23205i	−0.164998	+	0.0952616i
$550$	9.85641	+	9.85641i	0.420279	+	0.420279i
$551$			14.1962i			0.604776i
$552$	−16.3923	+	4.39230i	−0.697703	+	0.186949i
$553$	−31.1769	−	18.0000i	−1.32578	−	0.765438i
$554$	−27.7583	−	7.43782i	−1.17934	−	0.316003i
$555$	4.90192	+	2.83013i	0.208075	+	0.120132i
$556$	−5.07180			−0.215092
$557$	−7.59808	−	13.1603i	−0.321941	−	0.557618i	0.658948	−	0.752189i	$-0.271002\pi$
$557$	−7.59808	−	13.1603i	−0.321941	−	0.557618i	−0.980888	+	0.194571i	$0.937669\pi$
$558$	7.73205	+	2.07180i	0.327324	+	0.0877062i
$559$	−9.46410	−	32.7846i	−0.400289	−	1.38664i
$560$	−3.21539	+	1.85641i	−0.135875	+	0.0784475i
$561$	−30.5885	+	17.6603i	−1.29145	+	0.745617i
$562$	−2.43782	−	9.09808i	−0.102833	−	0.383779i
$563$	−37.9808	−	21.9282i	−1.60070	−	0.924164i	−0.991348	−	0.131263i	$-0.958097\pi$
$563$	−37.9808	−	21.9282i	−1.60070	−	0.924164i	−0.609351	−	0.792901i	$-0.708570\pi$
$564$	−15.4641	−	8.92820i	−0.651156	−	0.375945i
$565$	0.401924	−	0.696152i	0.0169091	−	0.0292874i
$566$	−10.7846	+	10.7846i	−0.453311	+	0.453311i
$567$		−	8.53590i		−	0.358474i
$568$	34.7846	−	9.32051i	1.45953	−	0.391080i
$569$	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	$0.665539\pi$
$570$	1.26795	+	4.73205i	0.0531085	+	0.198204i
$571$			18.3923i			0.769694i	0.922980	+	0.384847i	$0.125746\pi$
$571$			18.3923i			0.769694i	−0.922980	+	0.384847i	$0.874254\pi$
$572$	4.00000	+	13.8564i	0.167248	+	0.579365i
$573$			38.7846i			1.62025i
$574$	−5.66025	+	1.51666i	−0.236254	+	0.0633042i
$575$	−5.41154	−	9.37307i	−0.225677	−	0.390884i
$576$	−30.9282	−	17.8564i	−1.28868	−	0.744017i
$577$			37.7321i			1.57081i	0.618985	+	0.785403i	$0.287544\pi$
$577$			37.7321i			1.57081i	−0.618985	+	0.785403i	$0.712456\pi$
$578$	24.7846	+	24.7846i	1.03090	+	1.03090i
$579$	34.2224	−	59.2750i	1.42224	−	2.46338i
$580$	−0.803848	+	1.39230i	−0.0333780	+	0.0578123i
$581$	16.3923	+	9.46410i	0.680067	+	0.392637i
$582$	−22.3923	+	6.00000i	−0.928191	+	0.248708i
$583$	17.1962	−	9.92820i	0.712192	−	0.411184i
$584$	3.46410	+	3.46410i	0.143346	+	0.143346i
$585$	4.14359	−	1.19615i	0.171317	−	0.0494548i
$586$	−4.83013	+	18.0263i	−0.199531	+	0.744659i
$587$	8.58846	+	14.8756i	0.354484	+	0.613984i	0.987029	−	0.160539i	$-0.0513234\pi$
$587$	8.58846	+	14.8756i	0.354484	+	0.613984i	−0.632546	+	0.774523i	$0.717990\pi$
$588$	27.3205			1.12668
$589$	−5.19615	−	3.00000i	−0.214104	−	0.123613i
$590$	−0.732051	+	2.73205i	−0.0301381	+	0.112477i
$591$	−46.0526	−	26.5885i	−1.89435	−	1.09370i
$592$	30.9282			1.27114
$593$			29.5885i			1.21505i	0.794300	+	0.607526i	$0.207838\pi$
$593$			29.5885i			1.21505i	−0.794300	+	0.607526i	$0.792162\pi$
$594$	−8.00000	+	8.00000i	−0.328244	+	0.328244i
$595$	5.19615	−	3.00000i	0.213021	−	0.122988i
$596$			16.5359i			0.677337i
$597$			24.9282i			1.02024i
$598$	−0.215390	−	11.1962i	−0.00880796	−	0.457845i
$599$	−16.7321			−0.683653			−0.341827	−	0.939763i	$-0.611046\pi$
$599$	−16.7321			−0.683653			−0.341827	+	0.939763i	$0.611046\pi$
$600$	9.85641	−	36.7846i	0.402386	−	1.50173i
$601$	−19.9641	−	34.5788i	−0.814353	−	1.41050i	−0.909792	−	0.415065i	$-0.863759\pi$
$601$	−19.9641	−	34.5788i	−0.814353	−	1.41050i	0.0954391	−	0.995435i	$-0.469574\pi$
$602$	−32.7846	−	32.7846i	−1.33620	−	1.33620i
$603$	47.9090			1.95100
$604$	8.19615	+	14.1962i	0.333497	+	0.577633i
$605$	0.937822	−	1.62436i	0.0381279	−	0.0660394i
$606$	−18.4641	+	68.9090i	−0.750053	+	2.79924i
$607$	14.2942	−	24.7583i	0.580185	−	1.00491i	−0.415272	−	0.909697i	$-0.636314\pi$
$607$	14.2942	−	24.7583i	0.580185	−	1.00491i	0.995457	−	0.0952124i	$-0.0303530\pi$
$608$	18.9282	+	18.9282i	0.767640	+	0.767640i
$609$	24.5885	−	14.1962i	0.996375	−	0.575257i
$610$	0.366025	+	0.0980762i	0.0148199	+	0.00397099i
$611$	8.16987	−	8.49038i	0.330518	−	0.343484i
$612$	49.9808	+	28.8564i	2.02035	+	1.16645i
$613$	−2.25833	−	3.91154i	−0.0912131	−	0.157986i	0.816809	−	0.576909i	$-0.195741\pi$
$613$	−2.25833	−	3.91154i	−0.0912131	−	0.157986i	−0.908022	+	0.418923i	$0.862408\pi$
$614$	11.1962	−	3.00000i	0.451840	−	0.121070i
$615$	−0.437822	+	0.758330i	−0.0176547	+	0.0305788i
$616$	13.8564	+	13.8564i	0.558291	+	0.558291i
$617$	−12.3564	−	7.13397i	−0.497450	−	0.287203i	0.230210	−	0.973141i	$-0.426059\pi$
$617$	−12.3564	−	7.13397i	−0.497450	−	0.287203i	−0.727660	+	0.685938i	$0.759392\pi$
$618$	11.4641	−	11.4641i	0.461154	−	0.461154i
$619$	24.2487			0.974638			0.487319	−	0.873224i	$-0.337975\pi$
$619$	24.2487			0.974638			0.487319	+	0.873224i	$0.337975\pi$
$620$	−0.339746	−	0.588457i	−0.0136445	−	0.0236330i
$621$	7.60770	−	4.39230i	0.305286	−	0.176257i
$622$	−17.1962	+	4.60770i	−0.689503	+	0.184752i
$623$	1.85641			0.0743754
$624$	27.3205	−	28.3923i	1.09370	−	1.13660i
$625$	23.9282			0.957128
$626$	12.9282	−	3.46410i	0.516715	−	0.138453i
$627$	22.3923	−	12.9282i	0.894263	−	0.516303i
$628$	9.92820	+	17.1962i	0.396178	+	0.686201i
$629$	−49.9808			−1.99286
$630$	4.14359	−	4.14359i	0.165085	−	0.165085i
$631$	26.7846	+	15.4641i	1.06628	+	0.615616i	0.927162	−	0.374660i	$-0.122241\pi$
$631$	26.7846	+	15.4641i	1.06628	+	0.615616i	0.139116	+	0.990276i	$0.455574\pi$
$632$	−20.7846	+	20.7846i	−0.826767	+	0.826767i
$633$	−3.53590	+	6.12436i	−0.140539	+	0.243421i
$634$	−20.2224	+	5.41858i	−0.803135	+	0.215199i
$635$	−2.36603	−	4.09808i	−0.0938929	−	0.162627i
$636$	−46.9808	−	27.1244i	−1.86291	−	1.07555i
$637$	−4.33013	+	17.5000i	−0.171566	+	0.693375i
$638$	8.19615	+	2.19615i	0.324489	+	0.0869465i
$639$	−49.2224	+	28.4186i	−1.94721	+	1.12422i
$640$	0.784610	+	2.92820i	0.0310144	+	0.115747i
$641$	13.9641	−	24.1865i	0.551549	−	0.955311i	−0.446614	−	0.894727i	$-0.647370\pi$
$641$	13.9641	−	24.1865i	0.551549	−	0.955311i	0.998163	−	0.0605840i	$-0.0192963\pi$
$642$	0.339746	−	1.26795i	0.0134087	−	0.0500420i
$643$	1.39230	−	2.41154i	0.0549071	−	0.0951020i	−0.837265	−	0.546797i	$-0.815847\pi$
$643$	1.39230	−	2.41154i	0.0549071	−	0.0951020i	0.892173	+	0.451695i	$0.149180\pi$
$644$	−7.60770	−	13.1769i	−0.299785	−	0.519243i
$645$	−6.92820			−0.272798
$646$	−30.5885	−	30.5885i	−1.20349	−	1.20349i
$647$	−6.16987	−	10.6865i	−0.242563	−	0.420131i	0.718881	−	0.695133i	$-0.244655\pi$
$647$	−6.16987	−	10.6865i	−0.242563	−	0.420131i	−0.961444	+	0.275002i	$0.911321\pi$
$648$	−6.73205	−	1.80385i	−0.264460	−	0.0708618i
$649$	14.9282			0.585983
$650$	22.0000	+	12.1436i	0.862911	+	0.476311i
$651$			12.0000i			0.470317i
$652$		−	8.78461i		−	0.344032i
$653$	31.1769	−	18.0000i	1.22005	−	0.704394i	0.255119	−	0.966910i	$-0.417885\pi$
$653$	31.1769	−	18.0000i	1.22005	−	0.704394i	0.964928	+	0.262515i	$0.0845520\pi$
$654$	−16.3923	+	16.3923i	−0.640990	+	0.640990i
$655$			1.94744i			0.0760928i
$656$			4.78461i			0.186808i
$657$	−6.69615	−	3.86603i	−0.261242	−	0.150828i
$658$	4.14359	−	15.4641i	0.161534	−	0.602853i
$659$	−14.7846	−	8.53590i	−0.575927	−	0.332511i	0.183586	−	0.983004i	$-0.441229\pi$
$659$	−14.7846	−	8.53590i	−0.575927	−	0.332511i	−0.759513	+	0.650492i	$0.774563\pi$
$660$	2.92820			0.113980
$661$	−6.06218	−	10.5000i	−0.235791	−	0.408403i	0.723711	−	0.690103i	$-0.242435\pi$
$661$	−6.06218	−	10.5000i	−0.235791	−	0.408403i	−0.959502	+	0.281701i	$0.909102\pi$
$662$	−4.39230	+	16.3923i	−0.170712	+	0.637105i
$663$	−44.1506	+	45.8827i	−1.71467	+	1.78194i
$664$	10.9282	−	10.9282i	0.424097	−	0.424097i
$665$	−3.80385	+	2.19615i	−0.147507	+	0.0851631i
$666$	−47.1506	+	12.6340i	−1.82705	+	0.489557i
$667$	−5.70577	−	3.29423i	−0.220928	−	0.127553i
$668$	−8.92820	+	15.4641i	−0.345443	+	0.598324i
$669$	−26.6603	+	46.1769i	−1.03074	+	1.78530i
$670$	−2.87564	−	2.87564i	−0.111096	−	0.111096i
$671$		−	2.00000i		−	0.0772091i
$672$	13.8564	−	51.7128i	0.534522	−	1.99487i
$673$	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	$0.765333\pi$
$674$	−20.8301	+	5.58142i	−0.802347	+	0.214988i
$675$			19.7128i			0.758747i
$676$	13.8564	+	22.0000i	0.532939	+	0.846154i
$677$			19.8564i			0.763144i	0.924339	+	0.381572i	$0.124617\pi$
$677$			19.8564i			0.763144i	−0.924339	+	0.381572i	$0.875383\pi$
$678$	3.00000	+	11.1962i	0.115214	+	0.429986i
$679$	−10.3923	−	18.0000i	−0.398820	−	0.690777i
$680$	−1.26795	−	4.73205i	−0.0486236	−	0.181466i
$681$			32.9282i			1.26181i
$682$	−2.53590	+	2.53590i	−0.0971046	+	0.0971046i
$683$	7.36603	−	12.7583i	0.281853	−	0.488184i	−0.689988	−	0.723821i	$-0.742384\pi$
$683$	7.36603	−	12.7583i	0.281853	−	0.488184i	0.971841	+	0.235637i	$0.0757176\pi$
$684$	−36.5885	−	21.1244i	−1.39899	−	0.807710i
$685$	−4.08142	−	2.35641i	−0.155943	−	0.0900337i
$686$	−2.53590	−	9.46410i	−0.0968211	−	0.361341i
$687$	−2.19615	+	1.26795i	−0.0837884	+	0.0483753i
$688$	−32.7846	+	18.9282i	−1.24990	+	0.721631i
$689$	24.8205	−	25.7942i	0.945586	−	0.982682i
$690$	−2.19615	−	0.588457i	−0.0836061	−	0.0224022i
$691$	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	$0.722102\pi$
$692$	10.1436			0.385602
$693$	−26.7846	−	15.4641i	−1.01746	−	0.587433i
$694$	−6.46410	−	1.73205i	−0.245374	−	0.0657477i
$695$	−0.588457	−	0.339746i	−0.0223215	−	0.0128873i
$696$	−6.00000	−	22.3923i	−0.227429	−	0.848778i
$697$		−	7.73205i		−	0.292872i
$698$	29.3205	+	29.3205i	1.10980	+	1.10980i
$699$		0			0
$700$	34.1436			1.29051
$701$		−	32.7846i		−	1.23826i	−0.785289	−	0.619129i	$-0.787486\pi$
$701$		−	32.7846i		−	1.23826i	0.785289	−	0.619129i	$-0.212514\pi$
$702$	−9.85641	+	17.8564i	−0.372006	+	0.673947i
$703$	36.5885			1.37996
$704$	13.8564	−	8.00000i	0.522233	−	0.301511i
$705$	−1.19615	−	2.07180i	−0.0450497	−	0.0780284i
$706$	−21.7321	+	21.7321i	−0.817897	+	0.817897i
$707$	−63.9615			−2.40552
$708$	−20.3923	−	35.3205i	−0.766390	−	1.32743i
$709$	15.4019	−	26.6769i	0.578431	−	1.00187i	−0.417228	−	0.908802i	$-0.636998\pi$
$709$	15.4019	−	26.6769i	0.578431	−	1.00187i	0.995659	−	0.0930708i	$-0.0296683\pi$
$710$	4.66025	+	1.24871i	0.174896	+	0.0468633i
$711$	23.1962	−	40.1769i	0.869924	−	1.50675i
$712$	0.392305	−	1.46410i	0.0147022	−	0.0548695i
$713$	2.41154	−	1.39230i	0.0903130	−	0.0521422i
$714$	−22.3923	+	83.5692i	−0.838011	+	3.12750i
$715$	−0.464102	+	1.87564i	−0.0173564	+	0.0701451i
$716$	13.8564	−	24.0000i	0.517838	−	0.896922i
$717$	−3.26795	−	5.66025i	−0.122044	−	0.211386i
$718$	−9.85641	−	36.7846i	−0.367838	−	1.37279i
$719$	−10.8564	+	18.8038i	−0.404876	+	0.701265i	−0.994307	−	0.106553i	$-0.966019\pi$
$719$	−10.8564	+	18.8038i	−0.404876	+	0.701265i	0.589431	+	0.807818i	$0.299352\pi$
$720$	−2.39230	−	4.14359i	−0.0891559	−	0.154423i
$721$	12.5885	+	7.26795i	0.468819	+	0.270673i
$722$	3.39230	+	3.39230i	0.126249	+	0.126249i
$723$	−2.19615			−0.0816758
$724$	11.5359	+	19.9808i	0.428728	+	0.742579i
$725$	12.8038	−	7.39230i	0.475523	−	0.274543i
$726$	7.00000	+	26.1244i	0.259794	+	0.969566i
$727$	−34.3923			−1.27554			−0.637770	−	0.770227i	$-0.720143\pi$
$727$	−34.3923			−1.27554			−0.637770	+	0.770227i	$0.720143\pi$
$728$	30.9282	+	17.0718i	1.14628	+	0.632723i
$729$	43.7846			1.62165
$730$	0.169873	+	0.633975i	0.00628728	+	0.0234645i
$731$	52.9808	−	30.5885i	1.95956	−	1.13135i
$732$	−4.73205	+	2.73205i	−0.174902	+	0.100980i
$733$	43.0526			1.59018			0.795091	−	0.606490i	$-0.207423\pi$
$733$	43.0526			1.59018			0.795091	+	0.606490i	$0.207423\pi$
$734$	−17.8038	−	17.8038i	−0.657152	−	0.657152i
$735$	3.16987	+	1.83013i	0.116923	+	0.0675053i
$736$	−12.0000	+	3.21539i	−0.442326	+	0.118521i
$737$	−10.7321	+	18.5885i	−0.395320	+	0.684715i
$738$	−1.95448	−	7.29423i	−0.0719455	−	0.268504i
$739$	2.53590	+	4.39230i	0.0932845	+	0.161574i	0.908891	−	0.417033i	$-0.136930\pi$
$739$	2.53590	+	4.39230i	0.0932845	+	0.161574i	−0.815607	+	0.578607i	$0.803597\pi$
$740$	3.58846	+	2.07180i	0.131914	+	0.0761608i
$741$	32.3205	−	33.5885i	1.18732	−	1.23390i
$742$	12.5885	−	46.9808i	0.462137	−	1.72472i
$743$	1.26795	−	0.732051i	0.0465165	−	0.0268563i	−0.476561	−	0.879141i	$-0.658117\pi$
$743$	1.26795	−	0.732051i	0.0465165	−	0.0268563i	0.523078	+	0.852285i	$0.324784\pi$
$744$	9.46410	+	2.53590i	0.346971	+	0.0929705i
$745$	−1.10770	+	1.91858i	−0.0405828	+	0.0702915i
$746$	−21.5622	−	5.77757i	−0.789447	−	0.211532i
$747$	−12.1962	+	21.1244i	−0.446234	+	0.772900i
$748$	−22.3923	+	12.9282i	−0.818744	+	0.472702i
$749$	1.17691			0.0430035
$750$	7.26795	−	7.26795i	0.265388	−	0.265388i
$751$	7.80385	+	13.5167i	0.284766	+	0.493230i	0.972553	−	0.232683i	$-0.0747506\pi$
$751$	7.80385	+	13.5167i	0.284766	+	0.493230i	−0.687786	+	0.725913i	$0.741417\pi$
$752$	−11.3205	−	6.53590i	−0.412816	−	0.238340i
$753$	−6.00000			−0.218652
$754$	15.2942	−	0.294229i	0.556983	−	0.0107152i
$755$			2.19615i			0.0799262i
$756$			27.7128i			1.00791i
$757$	−35.6603	+	20.5885i	−1.29609	+	0.748300i	−0.979727	−	0.200337i	$-0.935796\pi$
$757$	−35.6603	+	20.5885i	−1.29609	+	0.748300i	−0.316367	+	0.948637i	$0.602463\pi$
$758$	−16.0526	−	16.0526i	−0.583055	−	0.583055i
$759$			12.0000i			0.435572i
$760$	0.928203	+	3.46410i	0.0336695	+	0.125656i
$761$	16.8564	+	9.73205i	0.611044	+	0.352787i	0.773374	−	0.633950i	$-0.218568\pi$
$761$	16.8564	+	9.73205i	0.611044	+	0.352787i	−0.162330	+	0.986737i	$0.551901\pi$
$762$	65.9090	+	17.6603i	2.38763	+	0.639764i
$763$	−18.0000	−	10.3923i	−0.651644	−	0.376227i
$764$			28.3923i			1.02720i
$765$	3.86603	+	6.69615i	0.139776	+	0.242100i
$766$	27.3205	+	7.32051i	0.987130	+	0.264501i

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)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(2.36603 - 1.36603i) q^{3} +(1.73205 - 1.00000i) q^{4} +0.267949 q^{5} +(-2.73205 + 2.73205i) q^{6} +(-3.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(2.23205 - 3.86603i) q^{9} +O(q^{10})\)	\(q+(-1.36603 + 0.366025i) q^{2} +(2.36603 - 1.36603i) q^{3} +(1.73205 - 1.00000i) q^{4} +0.267949 q^{5} +(-2.73205 + 2.73205i) q^{6} +(-3.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(2.23205 - 3.86603i) q^{9} +(-0.366025 + 0.0980762i) q^{10} +(1.00000 + 1.73205i) q^{11} +(2.73205 - 4.73205i) q^{12} +(2.59808 + 2.50000i) q^{13} +(4.73205 + 1.26795i) q^{14} +(0.633975 - 0.366025i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-3.23205 + 5.59808i) q^{17} +(-1.63397 + 6.09808i) q^{18} +(2.36603 - 4.09808i) q^{19} +(0.464102 - 0.267949i) q^{20} -9.46410 q^{21} +(-2.00000 - 2.00000i) q^{22} +(1.09808 + 1.90192i) q^{23} +(-2.00000 + 7.46410i) q^{24} -4.92820 q^{25} +(-4.46410 - 2.46410i) q^{26} -4.00000i q^{27} -6.92820 q^{28} +(-2.59808 + 1.50000i) q^{29} +(-0.732051 + 0.732051i) q^{30} -1.26795i q^{31} +(-1.46410 + 5.46410i) q^{32} +(4.73205 + 2.73205i) q^{33} +(2.36603 - 8.83013i) q^{34} +(-0.803848 - 0.464102i) q^{35} -8.92820i q^{36} +(3.86603 + 6.69615i) q^{37} +(-1.73205 + 6.46410i) q^{38} +(9.56218 + 2.36603i) q^{39} +(-0.535898 + 0.535898i) q^{40} +(-1.03590 + 0.598076i) q^{41} +(12.9282 - 3.46410i) q^{42} +(-8.19615 - 4.73205i) q^{43} +(3.46410 + 2.00000i) q^{44} +(0.598076 - 1.03590i) q^{45} +(-2.19615 - 2.19615i) q^{46} -3.26795i q^{47} -10.9282i q^{48} +(2.50000 + 4.33013i) q^{49} +(6.73205 - 1.80385i) q^{50} +17.6603i q^{51} +(7.00000 + 1.73205i) q^{52} -9.92820i q^{53} +(1.46410 + 5.46410i) q^{54} +(0.267949 + 0.464102i) q^{55} +(9.46410 - 2.53590i) q^{56} -12.9282i q^{57} +(3.00000 - 3.00000i) q^{58} +(3.73205 - 6.46410i) q^{59} +(0.732051 - 1.26795i) q^{60} +(-0.866025 - 0.500000i) q^{61} +(0.464102 + 1.73205i) q^{62} +(-13.3923 + 7.73205i) q^{63} -8.00000i q^{64} +(0.696152 + 0.669873i) q^{65} +(-7.46410 - 2.00000i) q^{66} +(5.36603 + 9.29423i) q^{67} +12.9282i q^{68} +(5.19615 + 3.00000i) q^{69} +(1.26795 + 0.339746i) q^{70} +(-11.0263 - 6.36603i) q^{71} +(3.26795 + 12.1962i) q^{72} -1.73205i q^{73} +(-7.73205 - 7.73205i) q^{74} +(-11.6603 + 6.73205i) q^{75} -9.46410i q^{76} -6.92820i q^{77} +(-13.9282 + 0.267949i) q^{78} +10.3923 q^{79} +(0.535898 - 0.928203i) q^{80} +(1.23205 + 2.13397i) q^{81} +(1.19615 - 1.19615i) q^{82} -5.46410 q^{83} +(-16.3923 + 9.46410i) q^{84} +(-0.866025 + 1.50000i) q^{85} +(12.9282 + 3.46410i) q^{86} +(-4.09808 + 7.09808i) q^{87} +(-5.46410 - 1.46410i) q^{88} +(-0.464102 + 0.267949i) q^{89} +(-0.437822 + 1.63397i) q^{90} +(-3.46410 - 12.0000i) q^{91} +(3.80385 + 2.19615i) q^{92} +(-1.73205 - 3.00000i) q^{93} +(1.19615 + 4.46410i) q^{94} +(0.633975 - 1.09808i) q^{95} +(4.00000 + 14.9282i) q^{96} +(5.19615 + 3.00000i) q^{97} +(-5.00000 - 5.00000i) q^{98} +8.92820 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