Properties

Label 4235.dj
Modulus $4235$
Conductor $4235$
Order $330$
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(4235, base_ring=CyclotomicField(330))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([165,275,249]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(19,4235))
 
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: even
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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(8\) \(9\) \(12\) \(13\) \(16\) \(17\)
\(\chi_{4235}(19,\cdot)\) \(1\) \(1\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{139}{165}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{113}{165}\right)\) \(e\left(\frac{101}{330}\right)\)
\(\chi_{4235}(24,\cdot)\) \(1\) \(1\) \(e\left(\frac{109}{165}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{53}{165}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{106}{165}\right)\) \(e\left(\frac{67}{330}\right)\)
\(\chi_{4235}(129,\cdot)\) \(1\) \(1\) \(e\left(\frac{142}{165}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{119}{165}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{73}{165}\right)\) \(e\left(\frac{1}{330}\right)\)
\(\chi_{4235}(194,\cdot)\) \(1\) \(1\) \(e\left(\frac{83}{165}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{107}{110}\right)\) \(e\left(\frac{2}{165}\right)\) \(e\left(\frac{269}{330}\right)\)
\(\chi_{4235}(299,\cdot)\) \(1\) \(1\) \(e\left(\frac{119}{165}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{73}{165}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{146}{165}\right)\) \(e\left(\frac{167}{330}\right)\)
\(\chi_{4235}(304,\cdot)\) \(1\) \(1\) \(e\left(\frac{103}{165}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{41}{165}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{82}{165}\right)\) \(e\left(\frac{139}{330}\right)\)
\(\chi_{4235}(369,\cdot)\) \(1\) \(1\) \(e\left(\frac{161}{165}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{157}{165}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{149}{165}\right)\) \(e\left(\frac{323}{330}\right)\)
\(\chi_{4235}(404,\cdot)\) \(1\) \(1\) \(e\left(\frac{62}{165}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{124}{165}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{13}{110}\right)\) \(e\left(\frac{83}{165}\right)\) \(e\left(\frac{191}{330}\right)\)
\(\chi_{4235}(409,\cdot)\) \(1\) \(1\) \(e\left(\frac{79}{165}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{158}{165}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{151}{165}\right)\) \(e\left(\frac{97}{330}\right)\)
\(\chi_{4235}(479,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{165}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{4}{165}\right)\) \(e\left(\frac{43}{330}\right)\)
\(\chi_{4235}(514,\cdot)\) \(1\) \(1\) \(e\left(\frac{52}{165}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{104}{165}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{43}{165}\right)\) \(e\left(\frac{91}{330}\right)\)
\(\chi_{4235}(579,\cdot)\) \(1\) \(1\) \(e\left(\frac{98}{165}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{31}{165}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{62}{165}\right)\) \(e\left(\frac{89}{330}\right)\)
\(\chi_{4235}(684,\cdot)\) \(1\) \(1\) \(e\left(\frac{89}{165}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{165}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{26}{165}\right)\) \(e\left(\frac{197}{330}\right)\)
\(\chi_{4235}(689,\cdot)\) \(1\) \(1\) \(e\left(\frac{118}{165}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{71}{165}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{142}{165}\right)\) \(e\left(\frac{289}{330}\right)\)
\(\chi_{4235}(754,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{165}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{82}{165}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{164}{165}\right)\) \(e\left(\frac{113}{330}\right)\)
\(\chi_{4235}(789,\cdot)\) \(1\) \(1\) \(e\left(\frac{137}{165}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{109}{165}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{3}{110}\right)\) \(e\left(\frac{53}{165}\right)\) \(e\left(\frac{281}{330}\right)\)
\(\chi_{4235}(794,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{165}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{98}{165}\right)\) \(e\left(\frac{42}{55}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{91}{110}\right)\) \(e\left(\frac{31}{165}\right)\) \(e\left(\frac{127}{330}\right)\)
\(\chi_{4235}(864,\cdot)\) \(1\) \(1\) \(e\left(\frac{46}{165}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{92}{165}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{19}{165}\right)\) \(e\left(\frac{163}{330}\right)\)
\(\chi_{4235}(899,\cdot)\) \(1\) \(1\) \(e\left(\frac{127}{165}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{89}{165}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{13}{165}\right)\) \(e\left(\frac{181}{330}\right)\)
\(\chi_{4235}(964,\cdot)\) \(1\) \(1\) \(e\left(\frac{113}{165}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{61}{165}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{122}{165}\right)\) \(e\left(\frac{239}{330}\right)\)
\(\chi_{4235}(1069,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{165}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{118}{165}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{71}{165}\right)\) \(e\left(\frac{227}{330}\right)\)
\(\chi_{4235}(1074,\cdot)\) \(1\) \(1\) \(e\left(\frac{133}{165}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{101}{165}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{37}{165}\right)\) \(e\left(\frac{109}{330}\right)\)
\(\chi_{4235}(1139,\cdot)\) \(1\) \(1\) \(e\left(\frac{86}{165}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{165}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{14}{165}\right)\) \(e\left(\frac{233}{330}\right)\)
\(\chi_{4235}(1174,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{165}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{94}{165}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{23}{165}\right)\) \(e\left(\frac{41}{330}\right)\)
\(\chi_{4235}(1179,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{165}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{38}{165}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{76}{165}\right)\) \(e\left(\frac{157}{330}\right)\)
\(\chi_{4235}(1249,\cdot)\) \(1\) \(1\) \(e\left(\frac{91}{165}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{17}{165}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{59}{110}\right)\) \(e\left(\frac{34}{165}\right)\) \(e\left(\frac{283}{330}\right)\)
\(\chi_{4235}(1284,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{165}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{74}{165}\right)\) \(e\left(\frac{16}{55}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{148}{165}\right)\) \(e\left(\frac{271}{330}\right)\)
\(\chi_{4235}(1349,\cdot)\) \(1\) \(1\) \(e\left(\frac{128}{165}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{91}{165}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{17}{165}\right)\) \(e\left(\frac{59}{330}\right)\)
\(\chi_{4235}(1454,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{165}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{58}{165}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{116}{165}\right)\) \(e\left(\frac{257}{330}\right)\)
\(\chi_{4235}(1459,\cdot)\) \(1\) \(1\) \(e\left(\frac{148}{165}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{131}{165}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{97}{165}\right)\) \(e\left(\frac{259}{330}\right)\)
\(\chi_{4235}(1524,\cdot)\) \(1\) \(1\) \(e\left(\frac{131}{165}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{97}{165}\right)\) \(e\left(\frac{18}{55}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{29}{165}\right)\) \(e\left(\frac{23}{330}\right)\)