Properties

Label 967.m
Modulus $967$
Conductor $967$
Order $161$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(967, base_ring=CyclotomicField(322))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([52]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(8,967))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(967\)
Conductor: \(967\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(161\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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: $\Q(\zeta_{161})$
Fixed field: Number field defined by a degree 161 polynomial (not computed)

First 31 of 132 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{967}(8,\cdot)\) \(1\) \(1\) \(e\left(\frac{64}{161}\right)\) \(e\left(\frac{44}{161}\right)\) \(e\left(\frac{128}{161}\right)\) \(e\left(\frac{26}{161}\right)\) \(e\left(\frac{108}{161}\right)\) \(e\left(\frac{132}{161}\right)\) \(e\left(\frac{31}{161}\right)\) \(e\left(\frac{88}{161}\right)\) \(e\left(\frac{90}{161}\right)\) \(e\left(\frac{65}{161}\right)\)
\(\chi_{967}(9,\cdot)\) \(1\) \(1\) \(e\left(\frac{83}{161}\right)\) \(e\left(\frac{47}{161}\right)\) \(e\left(\frac{5}{161}\right)\) \(e\left(\frac{79}{161}\right)\) \(e\left(\frac{130}{161}\right)\) \(e\left(\frac{141}{161}\right)\) \(e\left(\frac{88}{161}\right)\) \(e\left(\frac{94}{161}\right)\) \(e\left(\frac{1}{161}\right)\) \(e\left(\frac{117}{161}\right)\)
\(\chi_{967}(11,\cdot)\) \(1\) \(1\) \(e\left(\frac{129}{161}\right)\) \(e\left(\frac{139}{161}\right)\) \(e\left(\frac{97}{161}\right)\) \(e\left(\frac{148}{161}\right)\) \(e\left(\frac{107}{161}\right)\) \(e\left(\frac{95}{161}\right)\) \(e\left(\frac{65}{161}\right)\) \(e\left(\frac{117}{161}\right)\) \(e\left(\frac{116}{161}\right)\) \(e\left(\frac{48}{161}\right)\)
\(\chi_{967}(17,\cdot)\) \(1\) \(1\) \(e\left(\frac{130}{161}\right)\) \(e\left(\frac{29}{161}\right)\) \(e\left(\frac{99}{161}\right)\) \(e\left(\frac{83}{161}\right)\) \(e\left(\frac{159}{161}\right)\) \(e\left(\frac{87}{161}\right)\) \(e\left(\frac{68}{161}\right)\) \(e\left(\frac{58}{161}\right)\) \(e\left(\frac{52}{161}\right)\) \(e\left(\frac{127}{161}\right)\)
\(\chi_{967}(30,\cdot)\) \(1\) \(1\) \(e\left(\frac{152}{161}\right)\) \(e\left(\frac{24}{161}\right)\) \(e\left(\frac{143}{161}\right)\) \(e\left(\frac{102}{161}\right)\) \(e\left(\frac{15}{161}\right)\) \(e\left(\frac{72}{161}\right)\) \(e\left(\frac{134}{161}\right)\) \(e\left(\frac{48}{161}\right)\) \(e\left(\frac{93}{161}\right)\) \(e\left(\frac{94}{161}\right)\)
\(\chi_{967}(42,\cdot)\) \(1\) \(1\) \(e\left(\frac{80}{161}\right)\) \(e\left(\frac{55}{161}\right)\) \(e\left(\frac{160}{161}\right)\) \(e\left(\frac{113}{161}\right)\) \(e\left(\frac{135}{161}\right)\) \(e\left(\frac{4}{161}\right)\) \(e\left(\frac{79}{161}\right)\) \(e\left(\frac{110}{161}\right)\) \(e\left(\frac{32}{161}\right)\) \(e\left(\frac{41}{161}\right)\)
\(\chi_{967}(62,\cdot)\) \(1\) \(1\) \(e\left(\frac{93}{161}\right)\) \(e\left(\frac{74}{161}\right)\) \(e\left(\frac{25}{161}\right)\) \(e\left(\frac{73}{161}\right)\) \(e\left(\frac{6}{161}\right)\) \(e\left(\frac{61}{161}\right)\) \(e\left(\frac{118}{161}\right)\) \(e\left(\frac{148}{161}\right)\) \(e\left(\frac{5}{161}\right)\) \(e\left(\frac{102}{161}\right)\)
\(\chi_{967}(64,\cdot)\) \(1\) \(1\) \(e\left(\frac{128}{161}\right)\) \(e\left(\frac{88}{161}\right)\) \(e\left(\frac{95}{161}\right)\) \(e\left(\frac{52}{161}\right)\) \(e\left(\frac{55}{161}\right)\) \(e\left(\frac{103}{161}\right)\) \(e\left(\frac{62}{161}\right)\) \(e\left(\frac{15}{161}\right)\) \(e\left(\frac{19}{161}\right)\) \(e\left(\frac{130}{161}\right)\)
\(\chi_{967}(71,\cdot)\) \(1\) \(1\) \(e\left(\frac{86}{161}\right)\) \(e\left(\frac{39}{161}\right)\) \(e\left(\frac{11}{161}\right)\) \(e\left(\frac{45}{161}\right)\) \(e\left(\frac{125}{161}\right)\) \(e\left(\frac{117}{161}\right)\) \(e\left(\frac{97}{161}\right)\) \(e\left(\frac{78}{161}\right)\) \(e\left(\frac{131}{161}\right)\) \(e\left(\frac{32}{161}\right)\)
\(\chi_{967}(78,\cdot)\) \(1\) \(1\) \(e\left(\frac{68}{161}\right)\) \(e\left(\frac{87}{161}\right)\) \(e\left(\frac{136}{161}\right)\) \(e\left(\frac{88}{161}\right)\) \(e\left(\frac{155}{161}\right)\) \(e\left(\frac{100}{161}\right)\) \(e\left(\frac{43}{161}\right)\) \(e\left(\frac{13}{161}\right)\) \(e\left(\frac{156}{161}\right)\) \(e\left(\frac{59}{161}\right)\)
\(\chi_{967}(81,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{161}\right)\) \(e\left(\frac{94}{161}\right)\) \(e\left(\frac{10}{161}\right)\) \(e\left(\frac{158}{161}\right)\) \(e\left(\frac{99}{161}\right)\) \(e\left(\frac{121}{161}\right)\) \(e\left(\frac{15}{161}\right)\) \(e\left(\frac{27}{161}\right)\) \(e\left(\frac{2}{161}\right)\) \(e\left(\frac{73}{161}\right)\)
\(\chi_{967}(87,\cdot)\) \(1\) \(1\) \(e\left(\frac{62}{161}\right)\) \(e\left(\frac{103}{161}\right)\) \(e\left(\frac{124}{161}\right)\) \(e\left(\frac{156}{161}\right)\) \(e\left(\frac{4}{161}\right)\) \(e\left(\frac{148}{161}\right)\) \(e\left(\frac{25}{161}\right)\) \(e\left(\frac{45}{161}\right)\) \(e\left(\frac{57}{161}\right)\) \(e\left(\frac{68}{161}\right)\)
\(\chi_{967}(88,\cdot)\) \(1\) \(1\) \(e\left(\frac{32}{161}\right)\) \(e\left(\frac{22}{161}\right)\) \(e\left(\frac{64}{161}\right)\) \(e\left(\frac{13}{161}\right)\) \(e\left(\frac{54}{161}\right)\) \(e\left(\frac{66}{161}\right)\) \(e\left(\frac{96}{161}\right)\) \(e\left(\frac{44}{161}\right)\) \(e\left(\frac{45}{161}\right)\) \(e\left(\frac{113}{161}\right)\)
\(\chi_{967}(95,\cdot)\) \(1\) \(1\) \(e\left(\frac{100}{161}\right)\) \(e\left(\frac{109}{161}\right)\) \(e\left(\frac{39}{161}\right)\) \(e\left(\frac{101}{161}\right)\) \(e\left(\frac{48}{161}\right)\) \(e\left(\frac{5}{161}\right)\) \(e\left(\frac{139}{161}\right)\) \(e\left(\frac{57}{161}\right)\) \(e\left(\frac{40}{161}\right)\) \(e\left(\frac{11}{161}\right)\)
\(\chi_{967}(99,\cdot)\) \(1\) \(1\) \(e\left(\frac{51}{161}\right)\) \(e\left(\frac{25}{161}\right)\) \(e\left(\frac{102}{161}\right)\) \(e\left(\frac{66}{161}\right)\) \(e\left(\frac{76}{161}\right)\) \(e\left(\frac{75}{161}\right)\) \(e\left(\frac{153}{161}\right)\) \(e\left(\frac{50}{161}\right)\) \(e\left(\frac{117}{161}\right)\) \(e\left(\frac{4}{161}\right)\)
\(\chi_{967}(100,\cdot)\) \(1\) \(1\) \(e\left(\frac{60}{161}\right)\) \(e\left(\frac{1}{161}\right)\) \(e\left(\frac{120}{161}\right)\) \(e\left(\frac{125}{161}\right)\) \(e\left(\frac{61}{161}\right)\) \(e\left(\frac{3}{161}\right)\) \(e\left(\frac{19}{161}\right)\) \(e\left(\frac{2}{161}\right)\) \(e\left(\frac{24}{161}\right)\) \(e\left(\frac{71}{161}\right)\)
\(\chi_{967}(118,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{161}\right)\) \(e\left(\frac{62}{161}\right)\) \(e\left(\frac{34}{161}\right)\) \(e\left(\frac{22}{161}\right)\) \(e\left(\frac{79}{161}\right)\) \(e\left(\frac{25}{161}\right)\) \(e\left(\frac{51}{161}\right)\) \(e\left(\frac{124}{161}\right)\) \(e\left(\frac{39}{161}\right)\) \(e\left(\frac{55}{161}\right)\)
\(\chi_{967}(121,\cdot)\) \(1\) \(1\) \(e\left(\frac{97}{161}\right)\) \(e\left(\frac{117}{161}\right)\) \(e\left(\frac{33}{161}\right)\) \(e\left(\frac{135}{161}\right)\) \(e\left(\frac{53}{161}\right)\) \(e\left(\frac{29}{161}\right)\) \(e\left(\frac{130}{161}\right)\) \(e\left(\frac{73}{161}\right)\) \(e\left(\frac{71}{161}\right)\) \(e\left(\frac{96}{161}\right)\)
\(\chi_{967}(122,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{161}\right)\) \(e\left(\frac{3}{161}\right)\) \(e\left(\frac{38}{161}\right)\) \(e\left(\frac{53}{161}\right)\) \(e\left(\frac{22}{161}\right)\) \(e\left(\frac{9}{161}\right)\) \(e\left(\frac{57}{161}\right)\) \(e\left(\frac{6}{161}\right)\) \(e\left(\frac{72}{161}\right)\) \(e\left(\frac{52}{161}\right)\)
\(\chi_{967}(123,\cdot)\) \(1\) \(1\) \(e\left(\frac{66}{161}\right)\) \(e\left(\frac{146}{161}\right)\) \(e\left(\frac{132}{161}\right)\) \(e\left(\frac{57}{161}\right)\) \(e\left(\frac{51}{161}\right)\) \(e\left(\frac{116}{161}\right)\) \(e\left(\frac{37}{161}\right)\) \(e\left(\frac{131}{161}\right)\) \(e\left(\frac{123}{161}\right)\) \(e\left(\frac{62}{161}\right)\)
\(\chi_{967}(131,\cdot)\) \(1\) \(1\) \(e\left(\frac{102}{161}\right)\) \(e\left(\frac{50}{161}\right)\) \(e\left(\frac{43}{161}\right)\) \(e\left(\frac{132}{161}\right)\) \(e\left(\frac{152}{161}\right)\) \(e\left(\frac{150}{161}\right)\) \(e\left(\frac{145}{161}\right)\) \(e\left(\frac{100}{161}\right)\) \(e\left(\frac{73}{161}\right)\) \(e\left(\frac{8}{161}\right)\)
\(\chi_{967}(136,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{161}\right)\) \(e\left(\frac{73}{161}\right)\) \(e\left(\frac{66}{161}\right)\) \(e\left(\frac{109}{161}\right)\) \(e\left(\frac{106}{161}\right)\) \(e\left(\frac{58}{161}\right)\) \(e\left(\frac{99}{161}\right)\) \(e\left(\frac{146}{161}\right)\) \(e\left(\frac{142}{161}\right)\) \(e\left(\frac{31}{161}\right)\)
\(\chi_{967}(140,\cdot)\) \(1\) \(1\) \(e\left(\frac{149}{161}\right)\) \(e\left(\frac{32}{161}\right)\) \(e\left(\frac{137}{161}\right)\) \(e\left(\frac{136}{161}\right)\) \(e\left(\frac{20}{161}\right)\) \(e\left(\frac{96}{161}\right)\) \(e\left(\frac{125}{161}\right)\) \(e\left(\frac{64}{161}\right)\) \(e\left(\frac{124}{161}\right)\) \(e\left(\frac{18}{161}\right)\)
\(\chi_{967}(146,\cdot)\) \(1\) \(1\) \(e\left(\frac{40}{161}\right)\) \(e\left(\frac{108}{161}\right)\) \(e\left(\frac{80}{161}\right)\) \(e\left(\frac{137}{161}\right)\) \(e\left(\frac{148}{161}\right)\) \(e\left(\frac{2}{161}\right)\) \(e\left(\frac{120}{161}\right)\) \(e\left(\frac{55}{161}\right)\) \(e\left(\frac{16}{161}\right)\) \(e\left(\frac{101}{161}\right)\)
\(\chi_{967}(153,\cdot)\) \(1\) \(1\) \(e\left(\frac{52}{161}\right)\) \(e\left(\frac{76}{161}\right)\) \(e\left(\frac{104}{161}\right)\) \(e\left(\frac{1}{161}\right)\) \(e\left(\frac{128}{161}\right)\) \(e\left(\frac{67}{161}\right)\) \(e\left(\frac{156}{161}\right)\) \(e\left(\frac{152}{161}\right)\) \(e\left(\frac{53}{161}\right)\) \(e\left(\frac{83}{161}\right)\)
\(\chi_{967}(201,\cdot)\) \(1\) \(1\) \(e\left(\frac{104}{161}\right)\) \(e\left(\frac{152}{161}\right)\) \(e\left(\frac{47}{161}\right)\) \(e\left(\frac{2}{161}\right)\) \(e\left(\frac{95}{161}\right)\) \(e\left(\frac{134}{161}\right)\) \(e\left(\frac{151}{161}\right)\) \(e\left(\frac{143}{161}\right)\) \(e\left(\frac{106}{161}\right)\) \(e\left(\frac{5}{161}\right)\)
\(\chi_{967}(206,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{161}\right)\) \(e\left(\frac{78}{161}\right)\) \(e\left(\frac{22}{161}\right)\) \(e\left(\frac{90}{161}\right)\) \(e\left(\frac{89}{161}\right)\) \(e\left(\frac{73}{161}\right)\) \(e\left(\frac{33}{161}\right)\) \(e\left(\frac{156}{161}\right)\) \(e\left(\frac{101}{161}\right)\) \(e\left(\frac{64}{161}\right)\)
\(\chi_{967}(212,\cdot)\) \(1\) \(1\) \(e\left(\frac{24}{161}\right)\) \(e\left(\frac{97}{161}\right)\) \(e\left(\frac{48}{161}\right)\) \(e\left(\frac{50}{161}\right)\) \(e\left(\frac{121}{161}\right)\) \(e\left(\frac{130}{161}\right)\) \(e\left(\frac{72}{161}\right)\) \(e\left(\frac{33}{161}\right)\) \(e\left(\frac{74}{161}\right)\) \(e\left(\frac{125}{161}\right)\)
\(\chi_{967}(215,\cdot)\) \(1\) \(1\) \(e\left(\frac{78}{161}\right)\) \(e\left(\frac{114}{161}\right)\) \(e\left(\frac{156}{161}\right)\) \(e\left(\frac{82}{161}\right)\) \(e\left(\frac{31}{161}\right)\) \(e\left(\frac{20}{161}\right)\) \(e\left(\frac{73}{161}\right)\) \(e\left(\frac{67}{161}\right)\) \(e\left(\frac{160}{161}\right)\) \(e\left(\frac{44}{161}\right)\)
\(\chi_{967}(222,\cdot)\) \(1\) \(1\) \(e\left(\frac{45}{161}\right)\) \(e\left(\frac{41}{161}\right)\) \(e\left(\frac{90}{161}\right)\) \(e\left(\frac{134}{161}\right)\) \(e\left(\frac{86}{161}\right)\) \(e\left(\frac{123}{161}\right)\) \(e\left(\frac{135}{161}\right)\) \(e\left(\frac{82}{161}\right)\) \(e\left(\frac{18}{161}\right)\) \(e\left(\frac{13}{161}\right)\)
\(\chi_{967}(228,\cdot)\) \(1\) \(1\) \(e\left(\frac{95}{161}\right)\) \(e\left(\frac{15}{161}\right)\) \(e\left(\frac{29}{161}\right)\) \(e\left(\frac{104}{161}\right)\) \(e\left(\frac{110}{161}\right)\) \(e\left(\frac{45}{161}\right)\) \(e\left(\frac{124}{161}\right)\) \(e\left(\frac{30}{161}\right)\) \(e\left(\frac{38}{161}\right)\) \(e\left(\frac{99}{161}\right)\)