Properties

Label 643.f
Modulus $643$
Conductor $643$
Order $214$
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(643, base_ring=CyclotomicField(214))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([151]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(2,643))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(643\)
Conductor: \(643\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(214\)
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: $\Q(\zeta_{107})$
Fixed field: Number field defined by a degree 214 polynomial (not computed)

First 31 of 106 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{643}(2,\cdot)\) \(-1\) \(1\) \(e\left(\frac{137}{214}\right)\) \(e\left(\frac{7}{214}\right)\) \(e\left(\frac{30}{107}\right)\) \(e\left(\frac{11}{214}\right)\) \(e\left(\frac{72}{107}\right)\) \(e\left(\frac{104}{107}\right)\) \(e\left(\frac{197}{214}\right)\) \(e\left(\frac{7}{107}\right)\) \(e\left(\frac{74}{107}\right)\) \(e\left(\frac{151}{214}\right)\)
\(\chi_{643}(3,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{214}\right)\) \(e\left(\frac{155}{214}\right)\) \(e\left(\frac{7}{107}\right)\) \(e\left(\frac{213}{214}\right)\) \(e\left(\frac{81}{107}\right)\) \(e\left(\frac{10}{107}\right)\) \(e\left(\frac{21}{214}\right)\) \(e\left(\frac{48}{107}\right)\) \(e\left(\frac{3}{107}\right)\) \(e\left(\frac{103}{214}\right)\)
\(\chi_{643}(5,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{214}\right)\) \(e\left(\frac{213}{214}\right)\) \(e\left(\frac{11}{107}\right)\) \(e\left(\frac{29}{214}\right)\) \(e\left(\frac{5}{107}\right)\) \(e\left(\frac{31}{107}\right)\) \(e\left(\frac{33}{214}\right)\) \(e\left(\frac{106}{107}\right)\) \(e\left(\frac{20}{107}\right)\) \(e\left(\frac{9}{214}\right)\)
\(\chi_{643}(8,\cdot)\) \(-1\) \(1\) \(e\left(\frac{197}{214}\right)\) \(e\left(\frac{21}{214}\right)\) \(e\left(\frac{90}{107}\right)\) \(e\left(\frac{33}{214}\right)\) \(e\left(\frac{2}{107}\right)\) \(e\left(\frac{98}{107}\right)\) \(e\left(\frac{163}{214}\right)\) \(e\left(\frac{21}{107}\right)\) \(e\left(\frac{8}{107}\right)\) \(e\left(\frac{25}{214}\right)\)
\(\chi_{643}(12,\cdot)\) \(-1\) \(1\) \(e\left(\frac{67}{214}\right)\) \(e\left(\frac{169}{214}\right)\) \(e\left(\frac{67}{107}\right)\) \(e\left(\frac{21}{214}\right)\) \(e\left(\frac{11}{107}\right)\) \(e\left(\frac{4}{107}\right)\) \(e\left(\frac{201}{214}\right)\) \(e\left(\frac{62}{107}\right)\) \(e\left(\frac{44}{107}\right)\) \(e\left(\frac{191}{214}\right)\)
\(\chi_{643}(18,\cdot)\) \(-1\) \(1\) \(e\left(\frac{151}{214}\right)\) \(e\left(\frac{103}{214}\right)\) \(e\left(\frac{44}{107}\right)\) \(e\left(\frac{9}{214}\right)\) \(e\left(\frac{20}{107}\right)\) \(e\left(\frac{17}{107}\right)\) \(e\left(\frac{25}{214}\right)\) \(e\left(\frac{103}{107}\right)\) \(e\left(\frac{80}{107}\right)\) \(e\left(\frac{143}{214}\right)\)
\(\chi_{643}(20,\cdot)\) \(-1\) \(1\) \(e\left(\frac{71}{214}\right)\) \(e\left(\frac{13}{214}\right)\) \(e\left(\frac{71}{107}\right)\) \(e\left(\frac{51}{214}\right)\) \(e\left(\frac{42}{107}\right)\) \(e\left(\frac{25}{107}\right)\) \(e\left(\frac{213}{214}\right)\) \(e\left(\frac{13}{107}\right)\) \(e\left(\frac{61}{107}\right)\) \(e\left(\frac{97}{214}\right)\)
\(\chi_{643}(27,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{214}\right)\) \(e\left(\frac{37}{214}\right)\) \(e\left(\frac{21}{107}\right)\) \(e\left(\frac{211}{214}\right)\) \(e\left(\frac{29}{107}\right)\) \(e\left(\frac{30}{107}\right)\) \(e\left(\frac{63}{214}\right)\) \(e\left(\frac{37}{107}\right)\) \(e\left(\frac{9}{107}\right)\) \(e\left(\frac{95}{214}\right)\)
\(\chi_{643}(30,\cdot)\) \(-1\) \(1\) \(e\left(\frac{155}{214}\right)\) \(e\left(\frac{161}{214}\right)\) \(e\left(\frac{48}{107}\right)\) \(e\left(\frac{39}{214}\right)\) \(e\left(\frac{51}{107}\right)\) \(e\left(\frac{38}{107}\right)\) \(e\left(\frac{37}{214}\right)\) \(e\left(\frac{54}{107}\right)\) \(e\left(\frac{97}{107}\right)\) \(e\left(\frac{49}{214}\right)\)
\(\chi_{643}(32,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{214}\right)\) \(e\left(\frac{35}{214}\right)\) \(e\left(\frac{43}{107}\right)\) \(e\left(\frac{55}{214}\right)\) \(e\left(\frac{39}{107}\right)\) \(e\left(\frac{92}{107}\right)\) \(e\left(\frac{129}{214}\right)\) \(e\left(\frac{35}{107}\right)\) \(e\left(\frac{49}{107}\right)\) \(e\left(\frac{113}{214}\right)\)
\(\chi_{643}(43,\cdot)\) \(-1\) \(1\) \(e\left(\frac{119}{214}\right)\) \(e\left(\frac{67}{214}\right)\) \(e\left(\frac{12}{107}\right)\) \(e\left(\frac{197}{214}\right)\) \(e\left(\frac{93}{107}\right)\) \(e\left(\frac{63}{107}\right)\) \(e\left(\frac{143}{214}\right)\) \(e\left(\frac{67}{107}\right)\) \(e\left(\frac{51}{107}\right)\) \(e\left(\frac{39}{214}\right)\)
\(\chi_{643}(45,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{214}\right)\) \(e\left(\frac{95}{214}\right)\) \(e\left(\frac{25}{107}\right)\) \(e\left(\frac{27}{214}\right)\) \(e\left(\frac{60}{107}\right)\) \(e\left(\frac{51}{107}\right)\) \(e\left(\frac{75}{214}\right)\) \(e\left(\frac{95}{107}\right)\) \(e\left(\frac{26}{107}\right)\) \(e\left(\frac{1}{214}\right)\)
\(\chi_{643}(48,\cdot)\) \(-1\) \(1\) \(e\left(\frac{127}{214}\right)\) \(e\left(\frac{183}{214}\right)\) \(e\left(\frac{20}{107}\right)\) \(e\left(\frac{43}{214}\right)\) \(e\left(\frac{48}{107}\right)\) \(e\left(\frac{105}{107}\right)\) \(e\left(\frac{167}{214}\right)\) \(e\left(\frac{76}{107}\right)\) \(e\left(\frac{85}{107}\right)\) \(e\left(\frac{65}{214}\right)\)
\(\chi_{643}(50,\cdot)\) \(-1\) \(1\) \(e\left(\frac{159}{214}\right)\) \(e\left(\frac{5}{214}\right)\) \(e\left(\frac{52}{107}\right)\) \(e\left(\frac{69}{214}\right)\) \(e\left(\frac{82}{107}\right)\) \(e\left(\frac{59}{107}\right)\) \(e\left(\frac{49}{214}\right)\) \(e\left(\frac{5}{107}\right)\) \(e\left(\frac{7}{107}\right)\) \(e\left(\frac{169}{214}\right)\)
\(\chi_{643}(67,\cdot)\) \(-1\) \(1\) \(e\left(\frac{87}{214}\right)\) \(e\left(\frac{31}{214}\right)\) \(e\left(\frac{87}{107}\right)\) \(e\left(\frac{171}{214}\right)\) \(e\left(\frac{59}{107}\right)\) \(e\left(\frac{2}{107}\right)\) \(e\left(\frac{47}{214}\right)\) \(e\left(\frac{31}{107}\right)\) \(e\left(\frac{22}{107}\right)\) \(e\left(\frac{149}{214}\right)\)
\(\chi_{643}(71,\cdot)\) \(-1\) \(1\) \(e\left(\frac{153}{214}\right)\) \(e\left(\frac{25}{214}\right)\) \(e\left(\frac{46}{107}\right)\) \(e\left(\frac{131}{214}\right)\) \(e\left(\frac{89}{107}\right)\) \(e\left(\frac{81}{107}\right)\) \(e\left(\frac{31}{214}\right)\) \(e\left(\frac{25}{107}\right)\) \(e\left(\frac{35}{107}\right)\) \(e\left(\frac{203}{214}\right)\)
\(\chi_{643}(72,\cdot)\) \(-1\) \(1\) \(e\left(\frac{211}{214}\right)\) \(e\left(\frac{117}{214}\right)\) \(e\left(\frac{104}{107}\right)\) \(e\left(\frac{31}{214}\right)\) \(e\left(\frac{57}{107}\right)\) \(e\left(\frac{11}{107}\right)\) \(e\left(\frac{205}{214}\right)\) \(e\left(\frac{10}{107}\right)\) \(e\left(\frac{14}{107}\right)\) \(e\left(\frac{17}{214}\right)\)
\(\chi_{643}(75,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{214}\right)\) \(e\left(\frac{153}{214}\right)\) \(e\left(\frac{29}{107}\right)\) \(e\left(\frac{57}{214}\right)\) \(e\left(\frac{91}{107}\right)\) \(e\left(\frac{72}{107}\right)\) \(e\left(\frac{87}{214}\right)\) \(e\left(\frac{46}{107}\right)\) \(e\left(\frac{43}{107}\right)\) \(e\left(\frac{121}{214}\right)\)
\(\chi_{643}(77,\cdot)\) \(-1\) \(1\) \(e\left(\frac{145}{214}\right)\) \(e\left(\frac{123}{214}\right)\) \(e\left(\frac{38}{107}\right)\) \(e\left(\frac{71}{214}\right)\) \(e\left(\frac{27}{107}\right)\) \(e\left(\frac{39}{107}\right)\) \(e\left(\frac{7}{214}\right)\) \(e\left(\frac{16}{107}\right)\) \(e\left(\frac{1}{107}\right)\) \(e\left(\frac{177}{214}\right)\)
\(\chi_{643}(80,\cdot)\) \(-1\) \(1\) \(e\left(\frac{131}{214}\right)\) \(e\left(\frac{27}{214}\right)\) \(e\left(\frac{24}{107}\right)\) \(e\left(\frac{73}{214}\right)\) \(e\left(\frac{79}{107}\right)\) \(e\left(\frac{19}{107}\right)\) \(e\left(\frac{179}{214}\right)\) \(e\left(\frac{27}{107}\right)\) \(e\left(\frac{102}{107}\right)\) \(e\left(\frac{185}{214}\right)\)
\(\chi_{643}(103,\cdot)\) \(-1\) \(1\) \(e\left(\frac{199}{214}\right)\) \(e\left(\frac{157}{214}\right)\) \(e\left(\frac{92}{107}\right)\) \(e\left(\frac{155}{214}\right)\) \(e\left(\frac{71}{107}\right)\) \(e\left(\frac{55}{107}\right)\) \(e\left(\frac{169}{214}\right)\) \(e\left(\frac{50}{107}\right)\) \(e\left(\frac{70}{107}\right)\) \(e\left(\frac{85}{214}\right)\)
\(\chi_{643}(107,\cdot)\) \(-1\) \(1\) \(e\left(\frac{177}{214}\right)\) \(e\left(\frac{159}{214}\right)\) \(e\left(\frac{70}{107}\right)\) \(e\left(\frac{97}{214}\right)\) \(e\left(\frac{61}{107}\right)\) \(e\left(\frac{100}{107}\right)\) \(e\left(\frac{103}{214}\right)\) \(e\left(\frac{52}{107}\right)\) \(e\left(\frac{30}{107}\right)\) \(e\left(\frac{67}{214}\right)\)
\(\chi_{643}(108,\cdot)\) \(-1\) \(1\) \(e\left(\frac{81}{214}\right)\) \(e\left(\frac{51}{214}\right)\) \(e\left(\frac{81}{107}\right)\) \(e\left(\frac{19}{214}\right)\) \(e\left(\frac{66}{107}\right)\) \(e\left(\frac{24}{107}\right)\) \(e\left(\frac{29}{214}\right)\) \(e\left(\frac{51}{107}\right)\) \(e\left(\frac{50}{107}\right)\) \(e\left(\frac{183}{214}\right)\)
\(\chi_{643}(119,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{214}\right)\) \(e\left(\frac{77}{214}\right)\) \(e\left(\frac{9}{107}\right)\) \(e\left(\frac{121}{214}\right)\) \(e\left(\frac{43}{107}\right)\) \(e\left(\frac{74}{107}\right)\) \(e\left(\frac{27}{214}\right)\) \(e\left(\frac{77}{107}\right)\) \(e\left(\frac{65}{107}\right)\) \(e\left(\frac{163}{214}\right)\)
\(\chi_{643}(120,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{214}\right)\) \(e\left(\frac{175}{214}\right)\) \(e\left(\frac{1}{107}\right)\) \(e\left(\frac{61}{214}\right)\) \(e\left(\frac{88}{107}\right)\) \(e\left(\frac{32}{107}\right)\) \(e\left(\frac{3}{214}\right)\) \(e\left(\frac{68}{107}\right)\) \(e\left(\frac{31}{107}\right)\) \(e\left(\frac{137}{214}\right)\)
\(\chi_{643}(125,\cdot)\) \(-1\) \(1\) \(e\left(\frac{33}{214}\right)\) \(e\left(\frac{211}{214}\right)\) \(e\left(\frac{33}{107}\right)\) \(e\left(\frac{87}{214}\right)\) \(e\left(\frac{15}{107}\right)\) \(e\left(\frac{93}{107}\right)\) \(e\left(\frac{99}{214}\right)\) \(e\left(\frac{104}{107}\right)\) \(e\left(\frac{60}{107}\right)\) \(e\left(\frac{27}{214}\right)\)
\(\chi_{643}(127,\cdot)\) \(-1\) \(1\) \(e\left(\frac{79}{214}\right)\) \(e\left(\frac{129}{214}\right)\) \(e\left(\frac{79}{107}\right)\) \(e\left(\frac{111}{214}\right)\) \(e\left(\frac{104}{107}\right)\) \(e\left(\frac{67}{107}\right)\) \(e\left(\frac{23}{214}\right)\) \(e\left(\frac{22}{107}\right)\) \(e\left(\frac{95}{107}\right)\) \(e\left(\frac{123}{214}\right)\)
\(\chi_{643}(128,\cdot)\) \(-1\) \(1\) \(e\left(\frac{103}{214}\right)\) \(e\left(\frac{49}{214}\right)\) \(e\left(\frac{103}{107}\right)\) \(e\left(\frac{77}{214}\right)\) \(e\left(\frac{76}{107}\right)\) \(e\left(\frac{86}{107}\right)\) \(e\left(\frac{95}{214}\right)\) \(e\left(\frac{49}{107}\right)\) \(e\left(\frac{90}{107}\right)\) \(e\left(\frac{201}{214}\right)\)
\(\chi_{643}(157,\cdot)\) \(-1\) \(1\) \(e\left(\frac{65}{214}\right)\) \(e\left(\frac{33}{214}\right)\) \(e\left(\frac{65}{107}\right)\) \(e\left(\frac{113}{214}\right)\) \(e\left(\frac{49}{107}\right)\) \(e\left(\frac{47}{107}\right)\) \(e\left(\frac{195}{214}\right)\) \(e\left(\frac{33}{107}\right)\) \(e\left(\frac{89}{107}\right)\) \(e\left(\frac{131}{214}\right)\)
\(\chi_{643}(162,\cdot)\) \(-1\) \(1\) \(e\left(\frac{165}{214}\right)\) \(e\left(\frac{199}{214}\right)\) \(e\left(\frac{58}{107}\right)\) \(e\left(\frac{7}{214}\right)\) \(e\left(\frac{75}{107}\right)\) \(e\left(\frac{37}{107}\right)\) \(e\left(\frac{67}{214}\right)\) \(e\left(\frac{92}{107}\right)\) \(e\left(\frac{86}{107}\right)\) \(e\left(\frac{135}{214}\right)\)
\(\chi_{643}(172,\cdot)\) \(-1\) \(1\) \(e\left(\frac{179}{214}\right)\) \(e\left(\frac{81}{214}\right)\) \(e\left(\frac{72}{107}\right)\) \(e\left(\frac{5}{214}\right)\) \(e\left(\frac{23}{107}\right)\) \(e\left(\frac{57}{107}\right)\) \(e\left(\frac{109}{214}\right)\) \(e\left(\frac{81}{107}\right)\) \(e\left(\frac{92}{107}\right)\) \(e\left(\frac{127}{214}\right)\)