Properties

Label 1792.bt
Modulus $1792$
Conductor $1792$
Order $64$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1792, base_ring=CyclotomicField(64))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,47,32]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(13,1792))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1792\)
Conductor: \(1792\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(64\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: $\Q(\zeta_{64})$
Fixed field: Number field defined by a degree 64 polynomial

First 31 of 32 characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{1792}(13,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{15}{32}\right)\)
\(\chi_{1792}(69,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{17}{32}\right)\)
\(\chi_{1792}(125,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{32}\right)\)
\(\chi_{1792}(181,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{5}{32}\right)\)
\(\chi_{1792}(237,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{23}{32}\right)\)
\(\chi_{1792}(293,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{25}{32}\right)\)
\(\chi_{1792}(349,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{11}{32}\right)\)
\(\chi_{1792}(405,\cdot)\) \(-1\) \(1\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{13}{32}\right)\)
\(\chi_{1792}(461,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{31}{32}\right)\)
\(\chi_{1792}(517,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{32}\right)\)
\(\chi_{1792}(573,\cdot)\) \(-1\) \(1\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{19}{32}\right)\)
\(\chi_{1792}(629,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{21}{32}\right)\)
\(\chi_{1792}(685,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{32}\right)\)
\(\chi_{1792}(741,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{9}{32}\right)\)
\(\chi_{1792}(797,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{27}{32}\right)\)
\(\chi_{1792}(853,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{29}{32}\right)\)
\(\chi_{1792}(909,\cdot)\) \(-1\) \(1\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{15}{32}\right)\)
\(\chi_{1792}(965,\cdot)\) \(-1\) \(1\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{17}{32}\right)\)
\(\chi_{1792}(1021,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{32}\right)\)
\(\chi_{1792}(1077,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{5}{32}\right)\)
\(\chi_{1792}(1133,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{23}{32}\right)\)
\(\chi_{1792}(1189,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{25}{32}\right)\)
\(\chi_{1792}(1245,\cdot)\) \(-1\) \(1\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{11}{32}\right)\)
\(\chi_{1792}(1301,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{13}{32}\right)\)
\(\chi_{1792}(1357,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{31}{32}\right)\)
\(\chi_{1792}(1413,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{32}\right)\)
\(\chi_{1792}(1469,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{19}{32}\right)\)
\(\chi_{1792}(1525,\cdot)\) \(-1\) \(1\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{21}{32}\right)\)
\(\chi_{1792}(1581,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{32}\right)\)
\(\chi_{1792}(1637,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{9}{32}\right)\)
\(\chi_{1792}(1693,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{27}{32}\right)\)