Properties

Label 1792.ca
Modulus $1792$
Conductor $1792$
Order $192$
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(192))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,3,160]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(5,1792))
 
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: \(192\)
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: $\Q(\zeta_{192})$
Fixed field: Number field defined by a degree 192 polynomial (not computed)

First 31 of 64 characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{1792}(5,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{192}\right)\) \(e\left(\frac{35}{192}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{127}{192}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{101}{192}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{35}{96}\right)\)
\(\chi_{1792}(45,\cdot)\) \(-1\) \(1\) \(e\left(\frac{191}{192}\right)\) \(e\left(\frac{181}{192}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{185}{192}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{67}{192}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{85}{96}\right)\)
\(\chi_{1792}(61,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{192}\right)\) \(e\left(\frac{89}{192}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{109}{192}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{191}{192}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{89}{96}\right)\)
\(\chi_{1792}(101,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{192}\right)\) \(e\left(\frac{187}{192}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{119}{192}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{13}{192}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{91}{96}\right)\)
\(\chi_{1792}(117,\cdot)\) \(-1\) \(1\) \(e\left(\frac{157}{192}\right)\) \(e\left(\frac{191}{192}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{139}{192}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{41}{192}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{95}{96}\right)\)
\(\chi_{1792}(157,\cdot)\) \(-1\) \(1\) \(e\left(\frac{179}{192}\right)\) \(e\left(\frac{49}{192}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{101}{192}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{103}{192}\right)\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{49}{96}\right)\)
\(\chi_{1792}(173,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{192}\right)\) \(e\left(\frac{149}{192}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{25}{192}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{35}{192}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{53}{96}\right)\)
\(\chi_{1792}(213,\cdot)\) \(-1\) \(1\) \(e\left(\frac{101}{192}\right)\) \(e\left(\frac{151}{192}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{131}{192}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{145}{192}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{55}{96}\right)\)
\(\chi_{1792}(229,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{192}\right)\) \(e\left(\frac{155}{192}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{151}{192}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{173}{192}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{59}{96}\right)\)
\(\chi_{1792}(269,\cdot)\) \(-1\) \(1\) \(e\left(\frac{167}{192}\right)\) \(e\left(\frac{109}{192}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{17}{192}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{139}{192}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{13}{96}\right)\)
\(\chi_{1792}(285,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{192}\right)\) \(e\left(\frac{17}{192}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{133}{192}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{71}{192}\right)\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{17}{96}\right)\)
\(\chi_{1792}(325,\cdot)\) \(-1\) \(1\) \(e\left(\frac{185}{192}\right)\) \(e\left(\frac{115}{192}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{143}{192}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{85}{192}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{19}{96}\right)\)
\(\chi_{1792}(341,\cdot)\) \(-1\) \(1\) \(e\left(\frac{133}{192}\right)\) \(e\left(\frac{119}{192}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{163}{192}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{113}{192}\right)\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{23}{96}\right)\)
\(\chi_{1792}(381,\cdot)\) \(-1\) \(1\) \(e\left(\frac{155}{192}\right)\) \(e\left(\frac{169}{192}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{125}{192}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{175}{192}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{73}{96}\right)\)
\(\chi_{1792}(397,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{192}\right)\) \(e\left(\frac{77}{192}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{49}{192}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{107}{192}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{77}{96}\right)\)
\(\chi_{1792}(437,\cdot)\) \(-1\) \(1\) \(e\left(\frac{77}{192}\right)\) \(e\left(\frac{79}{192}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{155}{192}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{25}{192}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{79}{96}\right)\)
\(\chi_{1792}(453,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{192}\right)\) \(e\left(\frac{83}{192}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{175}{192}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{53}{192}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{83}{96}\right)\)
\(\chi_{1792}(493,\cdot)\) \(-1\) \(1\) \(e\left(\frac{143}{192}\right)\) \(e\left(\frac{37}{192}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{41}{192}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{19}{192}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{37}{96}\right)\)
\(\chi_{1792}(509,\cdot)\) \(-1\) \(1\) \(e\left(\frac{187}{192}\right)\) \(e\left(\frac{137}{192}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{157}{192}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{143}{192}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{41}{96}\right)\)
\(\chi_{1792}(549,\cdot)\) \(-1\) \(1\) \(e\left(\frac{161}{192}\right)\) \(e\left(\frac{43}{192}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{167}{192}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{157}{192}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{43}{96}\right)\)
\(\chi_{1792}(565,\cdot)\) \(-1\) \(1\) \(e\left(\frac{109}{192}\right)\) \(e\left(\frac{47}{192}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{187}{192}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{185}{192}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{47}{96}\right)\)
\(\chi_{1792}(605,\cdot)\) \(-1\) \(1\) \(e\left(\frac{131}{192}\right)\) \(e\left(\frac{97}{192}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{149}{192}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{55}{192}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{1}{96}\right)\)
\(\chi_{1792}(621,\cdot)\) \(-1\) \(1\) \(e\left(\frac{175}{192}\right)\) \(e\left(\frac{5}{192}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{73}{192}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{179}{192}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{5}{96}\right)\)
\(\chi_{1792}(661,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{192}\right)\) \(e\left(\frac{7}{192}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{179}{192}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{97}{192}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{7}{96}\right)\)
\(\chi_{1792}(677,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{192}\right)\) \(e\left(\frac{11}{192}\right)\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{7}{192}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{125}{192}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{11}{96}\right)\)
\(\chi_{1792}(717,\cdot)\) \(-1\) \(1\) \(e\left(\frac{119}{192}\right)\) \(e\left(\frac{157}{192}\right)\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{65}{192}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{91}{192}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{61}{96}\right)\)
\(\chi_{1792}(733,\cdot)\) \(-1\) \(1\) \(e\left(\frac{163}{192}\right)\) \(e\left(\frac{65}{192}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{181}{192}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{23}{192}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{65}{96}\right)\)
\(\chi_{1792}(773,\cdot)\) \(-1\) \(1\) \(e\left(\frac{137}{192}\right)\) \(e\left(\frac{163}{192}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{191}{192}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{37}{192}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{67}{96}\right)\)
\(\chi_{1792}(789,\cdot)\) \(-1\) \(1\) \(e\left(\frac{85}{192}\right)\) \(e\left(\frac{167}{192}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{19}{192}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{65}{192}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{71}{96}\right)\)
\(\chi_{1792}(829,\cdot)\) \(-1\) \(1\) \(e\left(\frac{107}{192}\right)\) \(e\left(\frac{25}{192}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{173}{192}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{127}{192}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{25}{96}\right)\)
\(\chi_{1792}(845,\cdot)\) \(-1\) \(1\) \(e\left(\frac{151}{192}\right)\) \(e\left(\frac{125}{192}\right)\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{97}{192}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{59}{192}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{29}{96}\right)\)