Properties

Label 1792.bs
Modulus $1792$
Conductor $256$
Order $64$
Real no
Primitive no
Minimal yes
Parity even

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([0,59,0]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(29,1792))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1792\)
Conductor: \(256\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(64\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 256.m
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
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 \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{1792}(29,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{27}{32}\right)\)
\(\chi_{1792}(85,\cdot)\) \(1\) \(1\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{29}{32}\right)\)
\(\chi_{1792}(141,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{15}{32}\right)\)
\(\chi_{1792}(197,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{17}{32}\right)\)
\(\chi_{1792}(253,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{32}\right)\)
\(\chi_{1792}(309,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{5}{32}\right)\)
\(\chi_{1792}(365,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{23}{32}\right)\)
\(\chi_{1792}(421,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{25}{32}\right)\)
\(\chi_{1792}(477,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{11}{32}\right)\)
\(\chi_{1792}(533,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{13}{32}\right)\)
\(\chi_{1792}(589,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{31}{32}\right)\)
\(\chi_{1792}(645,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{32}\right)\)
\(\chi_{1792}(701,\cdot)\) \(1\) \(1\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{19}{32}\right)\)
\(\chi_{1792}(757,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{21}{32}\right)\)
\(\chi_{1792}(813,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{32}\right)\)
\(\chi_{1792}(869,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{9}{32}\right)\)
\(\chi_{1792}(925,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{27}{32}\right)\)
\(\chi_{1792}(981,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{29}{32}\right)\)
\(\chi_{1792}(1037,\cdot)\) \(1\) \(1\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{15}{32}\right)\)
\(\chi_{1792}(1093,\cdot)\) \(1\) \(1\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{17}{32}\right)\)
\(\chi_{1792}(1149,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{32}\right)\)
\(\chi_{1792}(1205,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{5}{32}\right)\)
\(\chi_{1792}(1261,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{23}{32}\right)\)
\(\chi_{1792}(1317,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{25}{32}\right)\)
\(\chi_{1792}(1373,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{11}{32}\right)\)
\(\chi_{1792}(1429,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{13}{32}\right)\)
\(\chi_{1792}(1485,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{31}{32}\right)\)
\(\chi_{1792}(1541,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{32}\right)\)
\(\chi_{1792}(1597,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{19}{32}\right)\)
\(\chi_{1792}(1653,\cdot)\) \(1\) \(1\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{21}{32}\right)\)
\(\chi_{1792}(1709,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{32}\right)\)