LMFDB - Dirichlet character orbit 1536.bf

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1536, base_ring=CyclotomicField(128)) M = H._module chi = DirichletCharacter(H, M([0,1,64])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(5, 1536)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1536.5"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1536$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1536$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$128$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{128})$
Fixed field:	Number field defined by a degree 128 polynomial (not computed)

First 31 of 64 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{1536}(5,\cdot)$	$-1$	$1$	$e\left(\frac{65}{128}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{21}{128}\right)$	$e\left(\frac{111}{128}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{23}{128}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{59}{128}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{1536}(29,\cdot)$	$-1$	$1$	$e\left(\frac{59}{128}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{23}{128}\right)$	$e\left(\frac{85}{128}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{13}{128}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{89}{128}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{1536}(53,\cdot)$	$-1$	$1$	$e\left(\frac{69}{128}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{105}{128}\right)$	$e\left(\frac{43}{128}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{115}{128}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{39}{128}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{1536}(77,\cdot)$	$-1$	$1$	$e\left(\frac{95}{128}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{11}{128}\right)$	$e\left(\frac{113}{128}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{73}{128}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{37}{128}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1536}(101,\cdot)$	$-1$	$1$	$e\left(\frac{9}{128}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{125}{128}\right)$	$e\left(\frac{39}{128}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{15}{128}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{83}{128}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{1536}(125,\cdot)$	$-1$	$1$	$e\left(\frac{67}{128}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{63}{128}\right)$	$e\left(\frac{77}{128}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{69}{128}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{49}{128}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1536}(149,\cdot)$	$-1$	$1$	$e\left(\frac{13}{128}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{99}{128}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{107}{128}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{63}{128}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1536}(173,\cdot)$	$-1$	$1$	$e\left(\frac{103}{128}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{51}{128}\right)$	$e\left(\frac{105}{128}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{1}{128}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{125}{128}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{1536}(197,\cdot)$	$-1$	$1$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{101}{128}\right)$	$e\left(\frac{95}{128}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{7}{128}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{107}{128}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{1536}(221,\cdot)$	$-1$	$1$	$e\left(\frac{75}{128}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{103}{128}\right)$	$e\left(\frac{69}{128}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{125}{128}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{9}{128}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{1536}(245,\cdot)$	$-1$	$1$	$e\left(\frac{85}{128}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{57}{128}\right)$	$e\left(\frac{27}{128}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{99}{128}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{87}{128}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{1536}(269,\cdot)$	$-1$	$1$	$e\left(\frac{111}{128}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{91}{128}\right)$	$e\left(\frac{97}{128}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{57}{128}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{85}{128}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1536}(293,\cdot)$	$-1$	$1$	$e\left(\frac{25}{128}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{77}{128}\right)$	$e\left(\frac{23}{128}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{127}{128}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{3}{128}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{1536}(317,\cdot)$	$-1$	$1$	$e\left(\frac{83}{128}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{15}{128}\right)$	$e\left(\frac{61}{128}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{53}{128}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{97}{128}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1536}(341,\cdot)$	$-1$	$1$	$e\left(\frac{29}{128}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{33}{128}\right)$	$e\left(\frac{83}{128}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{91}{128}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{111}{128}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1536}(365,\cdot)$	$-1$	$1$	$e\left(\frac{119}{128}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{3}{128}\right)$	$e\left(\frac{89}{128}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{113}{128}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{45}{128}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{1536}(389,\cdot)$	$-1$	$1$	$e\left(\frac{97}{128}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{53}{128}\right)$	$e\left(\frac{79}{128}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{119}{128}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{27}{128}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{1536}(413,\cdot)$	$-1$	$1$	$e\left(\frac{91}{128}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{55}{128}\right)$	$e\left(\frac{53}{128}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{109}{128}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{57}{128}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{1536}(437,\cdot)$	$-1$	$1$	$e\left(\frac{101}{128}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{9}{128}\right)$	$e\left(\frac{11}{128}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{83}{128}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{7}{128}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{1536}(461,\cdot)$	$-1$	$1$	$e\left(\frac{127}{128}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{43}{128}\right)$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{41}{128}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{5}{128}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1536}(485,\cdot)$	$-1$	$1$	$e\left(\frac{41}{128}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{29}{128}\right)$	$e\left(\frac{7}{128}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{111}{128}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{51}{128}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{1536}(509,\cdot)$	$-1$	$1$	$e\left(\frac{99}{128}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{95}{128}\right)$	$e\left(\frac{45}{128}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{37}{128}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{17}{128}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1536}(533,\cdot)$	$-1$	$1$	$e\left(\frac{45}{128}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{113}{128}\right)$	$e\left(\frac{67}{128}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{75}{128}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{31}{128}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1536}(557,\cdot)$	$-1$	$1$	$e\left(\frac{7}{128}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{83}{128}\right)$	$e\left(\frac{73}{128}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{97}{128}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{93}{128}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{1536}(581,\cdot)$	$-1$	$1$	$e\left(\frac{113}{128}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{5}{128}\right)$	$e\left(\frac{63}{128}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{103}{128}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{75}{128}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{1536}(605,\cdot)$	$-1$	$1$	$e\left(\frac{107}{128}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{7}{128}\right)$	$e\left(\frac{37}{128}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{93}{128}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{105}{128}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{1536}(629,\cdot)$	$-1$	$1$	$e\left(\frac{117}{128}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{89}{128}\right)$	$e\left(\frac{123}{128}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{67}{128}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{55}{128}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{1536}(653,\cdot)$	$-1$	$1$	$e\left(\frac{15}{128}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{123}{128}\right)$	$e\left(\frac{65}{128}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{25}{128}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{53}{128}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1536}(677,\cdot)$	$-1$	$1$	$e\left(\frac{57}{128}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{109}{128}\right)$	$e\left(\frac{119}{128}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{95}{128}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{99}{128}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{1536}(701,\cdot)$	$-1$	$1$	$e\left(\frac{115}{128}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{47}{128}\right)$	$e\left(\frac{29}{128}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{21}{128}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{65}{128}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1536}(725,\cdot)$	$-1$	$1$	$e\left(\frac{61}{128}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{65}{128}\right)$	$e\left(\frac{51}{128}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{59}{128}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{79}{128}\right)$	$e\left(\frac{13}{16}\right)$

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 $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{1536}(5,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{128}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{21}{128}\right)\)	\(e\left(\frac{111}{128}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{23}{128}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{59}{128}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{1536}(29,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{128}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{23}{128}\right)\)	\(e\left(\frac{85}{128}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{13}{128}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{89}{128}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{1536}(53,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{69}{128}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{105}{128}\right)\)	\(e\left(\frac{43}{128}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{115}{128}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{39}{128}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{1536}(77,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{128}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{11}{128}\right)\)	\(e\left(\frac{113}{128}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{73}{128}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{37}{128}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1536}(101,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{128}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{125}{128}\right)\)	\(e\left(\frac{39}{128}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{15}{128}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{83}{128}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{1536}(125,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{128}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{63}{128}\right)\)	\(e\left(\frac{77}{128}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{69}{128}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{49}{128}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1536}(149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{128}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{81}{128}\right)\)	\(e\left(\frac{99}{128}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{107}{128}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{63}{128}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1536}(173,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{128}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{51}{128}\right)\)	\(e\left(\frac{105}{128}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{1}{128}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{125}{128}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1536}(197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{81}{128}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{101}{128}\right)\)	\(e\left(\frac{95}{128}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{7}{128}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{107}{128}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{1536}(221,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{75}{128}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{103}{128}\right)\)	\(e\left(\frac{69}{128}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{125}{128}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{9}{128}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{1536}(245,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{128}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{57}{128}\right)\)	\(e\left(\frac{27}{128}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{99}{128}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{87}{128}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{1536}(269,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{111}{128}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{91}{128}\right)\)	\(e\left(\frac{97}{128}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{57}{128}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{85}{128}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1536}(293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{128}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{77}{128}\right)\)	\(e\left(\frac{23}{128}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{127}{128}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{3}{128}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{1536}(317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{128}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{15}{128}\right)\)	\(e\left(\frac{61}{128}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{53}{128}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{97}{128}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1536}(341,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{128}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{33}{128}\right)\)	\(e\left(\frac{83}{128}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{91}{128}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{111}{128}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1536}(365,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{128}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{3}{128}\right)\)	\(e\left(\frac{89}{128}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{113}{128}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{45}{128}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1536}(389,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{128}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{53}{128}\right)\)	\(e\left(\frac{79}{128}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{119}{128}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{27}{128}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{1536}(413,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{128}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{55}{128}\right)\)	\(e\left(\frac{53}{128}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{109}{128}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{57}{128}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{1536}(437,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{128}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{9}{128}\right)\)	\(e\left(\frac{11}{128}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{83}{128}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{7}{128}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{1536}(461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{128}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{43}{128}\right)\)	\(e\left(\frac{81}{128}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{41}{128}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{5}{128}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1536}(485,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{128}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{29}{128}\right)\)	\(e\left(\frac{7}{128}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{111}{128}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{51}{128}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{1536}(509,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{99}{128}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{95}{128}\right)\)	\(e\left(\frac{45}{128}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{37}{128}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{17}{128}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1536}(533,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{128}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{113}{128}\right)\)	\(e\left(\frac{67}{128}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{75}{128}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{31}{128}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1536}(557,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{128}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{83}{128}\right)\)	\(e\left(\frac{73}{128}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{97}{128}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{93}{128}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1536}(581,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{128}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{5}{128}\right)\)	\(e\left(\frac{63}{128}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{103}{128}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{75}{128}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{1536}(605,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{128}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{7}{128}\right)\)	\(e\left(\frac{37}{128}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{93}{128}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{105}{128}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{1536}(629,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{117}{128}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{89}{128}\right)\)	\(e\left(\frac{123}{128}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{67}{128}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{55}{128}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{1536}(653,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{128}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{123}{128}\right)\)	\(e\left(\frac{65}{128}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{25}{128}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{53}{128}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1536}(677,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{128}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{109}{128}\right)\)	\(e\left(\frac{119}{128}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{95}{128}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{99}{128}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{1536}(701,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{115}{128}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{47}{128}\right)\)	\(e\left(\frac{29}{128}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{21}{128}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{65}{128}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1536}(725,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{128}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{65}{128}\right)\)	\(e\left(\frac{51}{128}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{59}{128}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{79}{128}\right)\)	\(e\left(\frac{13}{16}\right)\)

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First 31 of 64 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1536.bf
Modulus	$1536$
Conductor	$1536$
Order	$128$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(1536\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1536\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(128\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);