Properties

Label 4235.di
Modulus $4235$
Conductor $4235$
Order $330$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4235, base_ring=CyclotomicField(330))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([165,220,237]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(39,4235))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4235\)
Conductor: \(4235\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(330\)
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: $\Q(\zeta_{165})$
Fixed field: Number field defined by a degree 330 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(8\) \(9\) \(12\) \(13\) \(16\) \(17\)
\(\chi_{4235}(39,\cdot)\) \(-1\) \(1\) \(e\left(\frac{91}{165}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{165}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{34}{165}\right)\) \(e\left(\frac{59}{165}\right)\)
\(\chi_{4235}(74,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{165}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{74}{165}\right)\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{148}{165}\right)\) \(e\left(\frac{53}{165}\right)\)
\(\chi_{4235}(79,\cdot)\) \(-1\) \(1\) \(e\left(\frac{89}{165}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{165}\right)\) \(e\left(\frac{19}{110}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{26}{165}\right)\) \(e\left(\frac{16}{165}\right)\)
\(\chi_{4235}(149,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{165}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{82}{165}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{164}{165}\right)\) \(e\left(\frac{139}{165}\right)\)
\(\chi_{4235}(184,\cdot)\) \(-1\) \(1\) \(e\left(\frac{137}{165}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{109}{165}\right)\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{53}{165}\right)\) \(e\left(\frac{58}{165}\right)\)
\(\chi_{4235}(249,\cdot)\) \(-1\) \(1\) \(e\left(\frac{148}{165}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{131}{165}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{97}{165}\right)\) \(e\left(\frac{47}{165}\right)\)
\(\chi_{4235}(359,\cdot)\) \(-1\) \(1\) \(e\left(\frac{113}{165}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{61}{165}\right)\) \(e\left(\frac{13}{110}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{122}{165}\right)\) \(e\left(\frac{37}{165}\right)\)
\(\chi_{4235}(424,\cdot)\) \(-1\) \(1\) \(e\left(\frac{136}{165}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{107}{165}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{49}{165}\right)\) \(e\left(\frac{119}{165}\right)\)
\(\chi_{4235}(459,\cdot)\) \(-1\) \(1\) \(e\left(\frac{112}{165}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{59}{165}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{118}{165}\right)\) \(e\left(\frac{98}{165}\right)\)
\(\chi_{4235}(464,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{165}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{118}{165}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{71}{165}\right)\) \(e\left(\frac{31}{165}\right)\)
\(\chi_{4235}(534,\cdot)\) \(-1\) \(1\) \(e\left(\frac{86}{165}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{165}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{14}{165}\right)\) \(e\left(\frac{34}{165}\right)\)
\(\chi_{4235}(569,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{165}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{94}{165}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{23}{165}\right)\) \(e\left(\frac{103}{165}\right)\)
\(\chi_{4235}(634,\cdot)\) \(-1\) \(1\) \(e\left(\frac{163}{165}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{161}{165}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{157}{165}\right)\) \(e\left(\frac{122}{165}\right)\)
\(\chi_{4235}(739,\cdot)\) \(-1\) \(1\) \(e\left(\frac{124}{165}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{83}{165}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{26}{165}\right)\)
\(\chi_{4235}(744,\cdot)\) \(-1\) \(1\) \(e\left(\frac{128}{165}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{91}{165}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{17}{165}\right)\) \(e\left(\frac{112}{165}\right)\)
\(\chi_{4235}(809,\cdot)\) \(-1\) \(1\) \(e\left(\frac{16}{165}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{32}{165}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{64}{165}\right)\) \(e\left(\frac{14}{165}\right)\)
\(\chi_{4235}(849,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{165}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{58}{165}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{116}{165}\right)\) \(e\left(\frac{46}{165}\right)\)
\(\chi_{4235}(919,\cdot)\) \(-1\) \(1\) \(e\left(\frac{131}{165}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{97}{165}\right)\) \(e\left(\frac{91}{110}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{29}{165}\right)\) \(e\left(\frac{94}{165}\right)\)
\(\chi_{4235}(954,\cdot)\) \(-1\) \(1\) \(e\left(\frac{122}{165}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{79}{165}\right)\) \(e\left(\frac{107}{110}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{158}{165}\right)\) \(e\left(\frac{148}{165}\right)\)
\(\chi_{4235}(1019,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{165}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{26}{165}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{52}{165}\right)\) \(e\left(\frac{32}{165}\right)\)
\(\chi_{4235}(1124,\cdot)\) \(-1\) \(1\) \(e\left(\frac{94}{165}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{23}{165}\right)\) \(e\left(\frac{59}{110}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{46}{165}\right)\) \(e\left(\frac{41}{165}\right)\)
\(\chi_{4235}(1194,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{165}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{122}{165}\right)\) \(e\left(\frac{81}{110}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{79}{165}\right)\) \(e\left(\frac{74}{165}\right)\)
\(\chi_{4235}(1229,\cdot)\) \(-1\) \(1\) \(e\left(\frac{97}{165}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{29}{165}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{58}{165}\right)\) \(e\left(\frac{23}{165}\right)\)
\(\chi_{4235}(1234,\cdot)\) \(-1\) \(1\) \(e\left(\frac{164}{165}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{163}{165}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{161}{165}\right)\) \(e\left(\frac{61}{165}\right)\)
\(\chi_{4235}(1339,\cdot)\) \(-1\) \(1\) \(e\left(\frac{32}{165}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{64}{165}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{128}{165}\right)\) \(e\left(\frac{28}{165}\right)\)
\(\chi_{4235}(1404,\cdot)\) \(-1\) \(1\) \(e\left(\frac{28}{165}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{56}{165}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{112}{165}\right)\) \(e\left(\frac{107}{165}\right)\)
\(\chi_{4235}(1509,\cdot)\) \(-1\) \(1\) \(e\left(\frac{64}{165}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{128}{165}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{91}{165}\right)\) \(e\left(\frac{56}{165}\right)\)
\(\chi_{4235}(1514,\cdot)\) \(-1\) \(1\) \(e\left(\frac{158}{165}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{151}{165}\right)\) \(e\left(\frac{43}{110}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{137}{165}\right)\) \(e\left(\frac{97}{165}\right)\)
\(\chi_{4235}(1579,\cdot)\) \(-1\) \(1\) \(e\left(\frac{106}{165}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{47}{165}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{94}{165}\right)\) \(e\left(\frac{134}{165}\right)\)
\(\chi_{4235}(1614,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{165}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{14}{165}\right)\) \(e\left(\frac{67}{110}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{28}{165}\right)\) \(e\left(\frac{68}{165}\right)\)
\(\chi_{4235}(1619,\cdot)\) \(-1\) \(1\) \(e\left(\frac{134}{165}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{103}{165}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{41}{165}\right)\) \(e\left(\frac{76}{165}\right)\)