Properties

Label 529.g
Modulus $529$
Conductor $529$
Order $253$
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(529, base_ring=CyclotomicField(506))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([200]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(2,529))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(529\)
Conductor: \(529\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(253\)
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: $\Q(\zeta_{253})$
Fixed field: Number field defined by a degree 253 polynomial (not computed)

First 31 of 220 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{529}(2,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{253}\right)\) \(e\left(\frac{82}{253}\right)\) \(e\left(\frac{26}{253}\right)\) \(e\left(\frac{100}{253}\right)\) \(e\left(\frac{95}{253}\right)\) \(e\left(\frac{250}{253}\right)\) \(e\left(\frac{39}{253}\right)\) \(e\left(\frac{164}{253}\right)\) \(e\left(\frac{113}{253}\right)\) \(e\left(\frac{119}{253}\right)\)
\(\chi_{529}(3,\cdot)\) \(1\) \(1\) \(e\left(\frac{82}{253}\right)\) \(e\left(\frac{128}{253}\right)\) \(e\left(\frac{164}{253}\right)\) \(e\left(\frac{8}{253}\right)\) \(e\left(\frac{210}{253}\right)\) \(e\left(\frac{20}{253}\right)\) \(e\left(\frac{246}{253}\right)\) \(e\left(\frac{3}{253}\right)\) \(e\left(\frac{90}{253}\right)\) \(e\left(\frac{50}{253}\right)\)
\(\chi_{529}(4,\cdot)\) \(1\) \(1\) \(e\left(\frac{26}{253}\right)\) \(e\left(\frac{164}{253}\right)\) \(e\left(\frac{52}{253}\right)\) \(e\left(\frac{200}{253}\right)\) \(e\left(\frac{190}{253}\right)\) \(e\left(\frac{247}{253}\right)\) \(e\left(\frac{78}{253}\right)\) \(e\left(\frac{75}{253}\right)\) \(e\left(\frac{226}{253}\right)\) \(e\left(\frac{238}{253}\right)\)
\(\chi_{529}(6,\cdot)\) \(1\) \(1\) \(e\left(\frac{95}{253}\right)\) \(e\left(\frac{210}{253}\right)\) \(e\left(\frac{190}{253}\right)\) \(e\left(\frac{108}{253}\right)\) \(e\left(\frac{52}{253}\right)\) \(e\left(\frac{17}{253}\right)\) \(e\left(\frac{32}{253}\right)\) \(e\left(\frac{167}{253}\right)\) \(e\left(\frac{203}{253}\right)\) \(e\left(\frac{169}{253}\right)\)
\(\chi_{529}(8,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{253}\right)\) \(e\left(\frac{246}{253}\right)\) \(e\left(\frac{78}{253}\right)\) \(e\left(\frac{47}{253}\right)\) \(e\left(\frac{32}{253}\right)\) \(e\left(\frac{244}{253}\right)\) \(e\left(\frac{117}{253}\right)\) \(e\left(\frac{239}{253}\right)\) \(e\left(\frac{86}{253}\right)\) \(e\left(\frac{104}{253}\right)\)
\(\chi_{529}(9,\cdot)\) \(1\) \(1\) \(e\left(\frac{164}{253}\right)\) \(e\left(\frac{3}{253}\right)\) \(e\left(\frac{75}{253}\right)\) \(e\left(\frac{16}{253}\right)\) \(e\left(\frac{167}{253}\right)\) \(e\left(\frac{40}{253}\right)\) \(e\left(\frac{239}{253}\right)\) \(e\left(\frac{6}{253}\right)\) \(e\left(\frac{180}{253}\right)\) \(e\left(\frac{100}{253}\right)\)
\(\chi_{529}(12,\cdot)\) \(1\) \(1\) \(e\left(\frac{108}{253}\right)\) \(e\left(\frac{39}{253}\right)\) \(e\left(\frac{216}{253}\right)\) \(e\left(\frac{208}{253}\right)\) \(e\left(\frac{147}{253}\right)\) \(e\left(\frac{14}{253}\right)\) \(e\left(\frac{71}{253}\right)\) \(e\left(\frac{78}{253}\right)\) \(e\left(\frac{63}{253}\right)\) \(e\left(\frac{35}{253}\right)\)
\(\chi_{529}(13,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{253}\right)\) \(e\left(\frac{2}{253}\right)\) \(e\left(\frac{50}{253}\right)\) \(e\left(\frac{95}{253}\right)\) \(e\left(\frac{27}{253}\right)\) \(e\left(\frac{111}{253}\right)\) \(e\left(\frac{75}{253}\right)\) \(e\left(\frac{4}{253}\right)\) \(e\left(\frac{120}{253}\right)\) \(e\left(\frac{151}{253}\right)\)
\(\chi_{529}(16,\cdot)\) \(1\) \(1\) \(e\left(\frac{52}{253}\right)\) \(e\left(\frac{75}{253}\right)\) \(e\left(\frac{104}{253}\right)\) \(e\left(\frac{147}{253}\right)\) \(e\left(\frac{127}{253}\right)\) \(e\left(\frac{241}{253}\right)\) \(e\left(\frac{156}{253}\right)\) \(e\left(\frac{150}{253}\right)\) \(e\left(\frac{199}{253}\right)\) \(e\left(\frac{223}{253}\right)\)
\(\chi_{529}(18,\cdot)\) \(1\) \(1\) \(e\left(\frac{177}{253}\right)\) \(e\left(\frac{85}{253}\right)\) \(e\left(\frac{101}{253}\right)\) \(e\left(\frac{116}{253}\right)\) \(e\left(\frac{9}{253}\right)\) \(e\left(\frac{37}{253}\right)\) \(e\left(\frac{25}{253}\right)\) \(e\left(\frac{170}{253}\right)\) \(e\left(\frac{40}{253}\right)\) \(e\left(\frac{219}{253}\right)\)
\(\chi_{529}(25,\cdot)\) \(1\) \(1\) \(e\left(\frac{200}{253}\right)\) \(e\left(\frac{16}{253}\right)\) \(e\left(\frac{147}{253}\right)\) \(e\left(\frac{1}{253}\right)\) \(e\left(\frac{216}{253}\right)\) \(e\left(\frac{129}{253}\right)\) \(e\left(\frac{94}{253}\right)\) \(e\left(\frac{32}{253}\right)\) \(e\left(\frac{201}{253}\right)\) \(e\left(\frac{196}{253}\right)\)
\(\chi_{529}(26,\cdot)\) \(1\) \(1\) \(e\left(\frac{38}{253}\right)\) \(e\left(\frac{84}{253}\right)\) \(e\left(\frac{76}{253}\right)\) \(e\left(\frac{195}{253}\right)\) \(e\left(\frac{122}{253}\right)\) \(e\left(\frac{108}{253}\right)\) \(e\left(\frac{114}{253}\right)\) \(e\left(\frac{168}{253}\right)\) \(e\left(\frac{233}{253}\right)\) \(e\left(\frac{17}{253}\right)\)
\(\chi_{529}(27,\cdot)\) \(1\) \(1\) \(e\left(\frac{246}{253}\right)\) \(e\left(\frac{131}{253}\right)\) \(e\left(\frac{239}{253}\right)\) \(e\left(\frac{24}{253}\right)\) \(e\left(\frac{124}{253}\right)\) \(e\left(\frac{60}{253}\right)\) \(e\left(\frac{232}{253}\right)\) \(e\left(\frac{9}{253}\right)\) \(e\left(\frac{17}{253}\right)\) \(e\left(\frac{150}{253}\right)\)
\(\chi_{529}(29,\cdot)\) \(1\) \(1\) \(e\left(\frac{73}{253}\right)\) \(e\left(\frac{188}{253}\right)\) \(e\left(\frac{146}{253}\right)\) \(e\left(\frac{75}{253}\right)\) \(e\left(\frac{8}{253}\right)\) \(e\left(\frac{61}{253}\right)\) \(e\left(\frac{219}{253}\right)\) \(e\left(\frac{123}{253}\right)\) \(e\left(\frac{148}{253}\right)\) \(e\left(\frac{26}{253}\right)\)
\(\chi_{529}(31,\cdot)\) \(1\) \(1\) \(e\left(\frac{149}{253}\right)\) \(e\left(\frac{103}{253}\right)\) \(e\left(\frac{45}{253}\right)\) \(e\left(\frac{212}{253}\right)\) \(e\left(\frac{252}{253}\right)\) \(e\left(\frac{24}{253}\right)\) \(e\left(\frac{194}{253}\right)\) \(e\left(\frac{206}{253}\right)\) \(e\left(\frac{108}{253}\right)\) \(e\left(\frac{60}{253}\right)\)
\(\chi_{529}(32,\cdot)\) \(1\) \(1\) \(e\left(\frac{65}{253}\right)\) \(e\left(\frac{157}{253}\right)\) \(e\left(\frac{130}{253}\right)\) \(e\left(\frac{247}{253}\right)\) \(e\left(\frac{222}{253}\right)\) \(e\left(\frac{238}{253}\right)\) \(e\left(\frac{195}{253}\right)\) \(e\left(\frac{61}{253}\right)\) \(e\left(\frac{59}{253}\right)\) \(e\left(\frac{89}{253}\right)\)
\(\chi_{529}(35,\cdot)\) \(1\) \(1\) \(e\left(\frac{97}{253}\right)\) \(e\left(\frac{28}{253}\right)\) \(e\left(\frac{194}{253}\right)\) \(e\left(\frac{65}{253}\right)\) \(e\left(\frac{125}{253}\right)\) \(e\left(\frac{36}{253}\right)\) \(e\left(\frac{38}{253}\right)\) \(e\left(\frac{56}{253}\right)\) \(e\left(\frac{162}{253}\right)\) \(e\left(\frac{90}{253}\right)\)
\(\chi_{529}(36,\cdot)\) \(1\) \(1\) \(e\left(\frac{190}{253}\right)\) \(e\left(\frac{167}{253}\right)\) \(e\left(\frac{127}{253}\right)\) \(e\left(\frac{216}{253}\right)\) \(e\left(\frac{104}{253}\right)\) \(e\left(\frac{34}{253}\right)\) \(e\left(\frac{64}{253}\right)\) \(e\left(\frac{81}{253}\right)\) \(e\left(\frac{153}{253}\right)\) \(e\left(\frac{85}{253}\right)\)
\(\chi_{529}(39,\cdot)\) \(1\) \(1\) \(e\left(\frac{107}{253}\right)\) \(e\left(\frac{130}{253}\right)\) \(e\left(\frac{214}{253}\right)\) \(e\left(\frac{103}{253}\right)\) \(e\left(\frac{237}{253}\right)\) \(e\left(\frac{131}{253}\right)\) \(e\left(\frac{68}{253}\right)\) \(e\left(\frac{7}{253}\right)\) \(e\left(\frac{210}{253}\right)\) \(e\left(\frac{201}{253}\right)\)
\(\chi_{529}(41,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{253}\right)\) \(e\left(\frac{162}{253}\right)\) \(e\left(\frac{2}{253}\right)\) \(e\left(\frac{105}{253}\right)\) \(e\left(\frac{163}{253}\right)\) \(e\left(\frac{136}{253}\right)\) \(e\left(\frac{3}{253}\right)\) \(e\left(\frac{71}{253}\right)\) \(e\left(\frac{106}{253}\right)\) \(e\left(\frac{87}{253}\right)\)
\(\chi_{529}(48,\cdot)\) \(1\) \(1\) \(e\left(\frac{134}{253}\right)\) \(e\left(\frac{203}{253}\right)\) \(e\left(\frac{15}{253}\right)\) \(e\left(\frac{155}{253}\right)\) \(e\left(\frac{84}{253}\right)\) \(e\left(\frac{8}{253}\right)\) \(e\left(\frac{149}{253}\right)\) \(e\left(\frac{153}{253}\right)\) \(e\left(\frac{36}{253}\right)\) \(e\left(\frac{20}{253}\right)\)
\(\chi_{529}(49,\cdot)\) \(1\) \(1\) \(e\left(\frac{247}{253}\right)\) \(e\left(\frac{40}{253}\right)\) \(e\left(\frac{241}{253}\right)\) \(e\left(\frac{129}{253}\right)\) \(e\left(\frac{34}{253}\right)\) \(e\left(\frac{196}{253}\right)\) \(e\left(\frac{235}{253}\right)\) \(e\left(\frac{80}{253}\right)\) \(e\left(\frac{123}{253}\right)\) \(e\left(\frac{237}{253}\right)\)
\(\chi_{529}(50,\cdot)\) \(1\) \(1\) \(e\left(\frac{213}{253}\right)\) \(e\left(\frac{98}{253}\right)\) \(e\left(\frac{173}{253}\right)\) \(e\left(\frac{101}{253}\right)\) \(e\left(\frac{58}{253}\right)\) \(e\left(\frac{126}{253}\right)\) \(e\left(\frac{133}{253}\right)\) \(e\left(\frac{196}{253}\right)\) \(e\left(\frac{61}{253}\right)\) \(e\left(\frac{62}{253}\right)\)
\(\chi_{529}(52,\cdot)\) \(1\) \(1\) \(e\left(\frac{51}{253}\right)\) \(e\left(\frac{166}{253}\right)\) \(e\left(\frac{102}{253}\right)\) \(e\left(\frac{42}{253}\right)\) \(e\left(\frac{217}{253}\right)\) \(e\left(\frac{105}{253}\right)\) \(e\left(\frac{153}{253}\right)\) \(e\left(\frac{79}{253}\right)\) \(e\left(\frac{93}{253}\right)\) \(e\left(\frac{136}{253}\right)\)
\(\chi_{529}(54,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{253}\right)\) \(e\left(\frac{213}{253}\right)\) \(e\left(\frac{12}{253}\right)\) \(e\left(\frac{124}{253}\right)\) \(e\left(\frac{219}{253}\right)\) \(e\left(\frac{57}{253}\right)\) \(e\left(\frac{18}{253}\right)\) \(e\left(\frac{173}{253}\right)\) \(e\left(\frac{130}{253}\right)\) \(e\left(\frac{16}{253}\right)\)
\(\chi_{529}(55,\cdot)\) \(1\) \(1\) \(e\left(\frac{219}{253}\right)\) \(e\left(\frac{58}{253}\right)\) \(e\left(\frac{185}{253}\right)\) \(e\left(\frac{225}{253}\right)\) \(e\left(\frac{24}{253}\right)\) \(e\left(\frac{183}{253}\right)\) \(e\left(\frac{151}{253}\right)\) \(e\left(\frac{116}{253}\right)\) \(e\left(\frac{191}{253}\right)\) \(e\left(\frac{78}{253}\right)\)
\(\chi_{529}(58,\cdot)\) \(1\) \(1\) \(e\left(\frac{86}{253}\right)\) \(e\left(\frac{17}{253}\right)\) \(e\left(\frac{172}{253}\right)\) \(e\left(\frac{175}{253}\right)\) \(e\left(\frac{103}{253}\right)\) \(e\left(\frac{58}{253}\right)\) \(e\left(\frac{5}{253}\right)\) \(e\left(\frac{34}{253}\right)\) \(e\left(\frac{8}{253}\right)\) \(e\left(\frac{145}{253}\right)\)
\(\chi_{529}(59,\cdot)\) \(1\) \(1\) \(e\left(\frac{102}{253}\right)\) \(e\left(\frac{79}{253}\right)\) \(e\left(\frac{204}{253}\right)\) \(e\left(\frac{84}{253}\right)\) \(e\left(\frac{181}{253}\right)\) \(e\left(\frac{210}{253}\right)\) \(e\left(\frac{53}{253}\right)\) \(e\left(\frac{158}{253}\right)\) \(e\left(\frac{186}{253}\right)\) \(e\left(\frac{19}{253}\right)\)
\(\chi_{529}(62,\cdot)\) \(1\) \(1\) \(e\left(\frac{162}{253}\right)\) \(e\left(\frac{185}{253}\right)\) \(e\left(\frac{71}{253}\right)\) \(e\left(\frac{59}{253}\right)\) \(e\left(\frac{94}{253}\right)\) \(e\left(\frac{21}{253}\right)\) \(e\left(\frac{233}{253}\right)\) \(e\left(\frac{117}{253}\right)\) \(e\left(\frac{221}{253}\right)\) \(e\left(\frac{179}{253}\right)\)
\(\chi_{529}(64,\cdot)\) \(1\) \(1\) \(e\left(\frac{78}{253}\right)\) \(e\left(\frac{239}{253}\right)\) \(e\left(\frac{156}{253}\right)\) \(e\left(\frac{94}{253}\right)\) \(e\left(\frac{64}{253}\right)\) \(e\left(\frac{235}{253}\right)\) \(e\left(\frac{234}{253}\right)\) \(e\left(\frac{225}{253}\right)\) \(e\left(\frac{172}{253}\right)\) \(e\left(\frac{208}{253}\right)\)
\(\chi_{529}(71,\cdot)\) \(1\) \(1\) \(e\left(\frac{68}{253}\right)\) \(e\left(\frac{137}{253}\right)\) \(e\left(\frac{136}{253}\right)\) \(e\left(\frac{56}{253}\right)\) \(e\left(\frac{205}{253}\right)\) \(e\left(\frac{140}{253}\right)\) \(e\left(\frac{204}{253}\right)\) \(e\left(\frac{21}{253}\right)\) \(e\left(\frac{124}{253}\right)\) \(e\left(\frac{97}{253}\right)\)