Properties

Label 1089.bf
Modulus $1089$
Conductor $1089$
Order $330$
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(1089, base_ring=CyclotomicField(330))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([275,222]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(5,1089))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1089\)
Conductor: \(1089\)
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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(13\) \(14\) \(16\) \(17\)
\(\chi_{1089}(5,\cdot)\) \(-1\) \(1\) \(e\left(\frac{167}{330}\right)\) \(e\left(\frac{2}{165}\right)\) \(e\left(\frac{313}{330}\right)\) \(e\left(\frac{7}{165}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{101}{165}\right)\) \(e\left(\frac{181}{330}\right)\) \(e\left(\frac{4}{165}\right)\) \(e\left(\frac{51}{110}\right)\)
\(\chi_{1089}(14,\cdot)\) \(-1\) \(1\) \(e\left(\frac{299}{330}\right)\) \(e\left(\frac{134}{165}\right)\) \(e\left(\frac{181}{330}\right)\) \(e\left(\frac{139}{165}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{2}{165}\right)\) \(e\left(\frac{247}{330}\right)\) \(e\left(\frac{103}{165}\right)\) \(e\left(\frac{7}{110}\right)\)
\(\chi_{1089}(20,\cdot)\) \(-1\) \(1\) \(e\left(\frac{283}{330}\right)\) \(e\left(\frac{118}{165}\right)\) \(e\left(\frac{317}{330}\right)\) \(e\left(\frac{83}{165}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{165}\right)\) \(e\left(\frac{119}{330}\right)\) \(e\left(\frac{71}{165}\right)\) \(e\left(\frac{39}{110}\right)\)
\(\chi_{1089}(38,\cdot)\) \(-1\) \(1\) \(e\left(\frac{307}{330}\right)\) \(e\left(\frac{142}{165}\right)\) \(e\left(\frac{113}{330}\right)\) \(e\left(\frac{2}{165}\right)\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{76}{165}\right)\) \(e\left(\frac{311}{330}\right)\) \(e\left(\frac{119}{165}\right)\) \(e\left(\frac{101}{110}\right)\)
\(\chi_{1089}(47,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{330}\right)\) \(e\left(\frac{19}{165}\right)\) \(e\left(\frac{251}{330}\right)\) \(e\left(\frac{149}{165}\right)\) \(e\left(\frac{19}{110}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{52}{165}\right)\) \(e\left(\frac{317}{330}\right)\) \(e\left(\frac{38}{165}\right)\) \(e\left(\frac{17}{110}\right)\)
\(\chi_{1089}(59,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{330}\right)\) \(e\left(\frac{41}{165}\right)\) \(e\left(\frac{229}{330}\right)\) \(e\left(\frac{61}{165}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{8}{165}\right)\) \(e\left(\frac{163}{330}\right)\) \(e\left(\frac{82}{165}\right)\) \(e\left(\frac{83}{110}\right)\)
\(\chi_{1089}(86,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{330}\right)\) \(e\left(\frac{23}{165}\right)\) \(e\left(\frac{217}{330}\right)\) \(e\left(\frac{163}{165}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{89}{165}\right)\) \(e\left(\frac{19}{330}\right)\) \(e\left(\frac{46}{165}\right)\) \(e\left(\frac{9}{110}\right)\)
\(\chi_{1089}(92,\cdot)\) \(-1\) \(1\) \(e\left(\frac{271}{330}\right)\) \(e\left(\frac{106}{165}\right)\) \(e\left(\frac{89}{330}\right)\) \(e\left(\frac{41}{165}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{73}{165}\right)\) \(e\left(\frac{23}{330}\right)\) \(e\left(\frac{47}{165}\right)\) \(e\left(\frac{63}{110}\right)\)
\(\chi_{1089}(104,\cdot)\) \(-1\) \(1\) \(e\left(\frac{257}{330}\right)\) \(e\left(\frac{92}{165}\right)\) \(e\left(\frac{43}{330}\right)\) \(e\left(\frac{157}{165}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{26}{165}\right)\) \(e\left(\frac{241}{330}\right)\) \(e\left(\frac{19}{165}\right)\) \(e\left(\frac{91}{110}\right)\)
\(\chi_{1089}(113,\cdot)\) \(-1\) \(1\) \(e\left(\frac{119}{330}\right)\) \(e\left(\frac{119}{165}\right)\) \(e\left(\frac{61}{330}\right)\) \(e\left(\frac{4}{165}\right)\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{127}{330}\right)\) \(e\left(\frac{73}{165}\right)\) \(e\left(\frac{37}{110}\right)\)
\(\chi_{1089}(119,\cdot)\) \(-1\) \(1\) \(e\left(\frac{223}{330}\right)\) \(e\left(\frac{58}{165}\right)\) \(e\left(\frac{167}{330}\right)\) \(e\left(\frac{38}{165}\right)\) \(e\left(\frac{3}{110}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{124}{165}\right)\) \(e\left(\frac{299}{330}\right)\) \(e\left(\frac{116}{165}\right)\) \(e\left(\frac{49}{110}\right)\)
\(\chi_{1089}(137,\cdot)\) \(-1\) \(1\) \(e\left(\frac{67}{330}\right)\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{173}{330}\right)\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{67}{110}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{41}{330}\right)\) \(e\left(\frac{134}{165}\right)\) \(e\left(\frac{31}{110}\right)\)
\(\chi_{1089}(146,\cdot)\) \(-1\) \(1\) \(e\left(\frac{169}{330}\right)\) \(e\left(\frac{4}{165}\right)\) \(e\left(\frac{131}{330}\right)\) \(e\left(\frac{14}{165}\right)\) \(e\left(\frac{59}{110}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{37}{165}\right)\) \(e\left(\frac{197}{330}\right)\) \(e\left(\frac{8}{165}\right)\) \(e\left(\frac{47}{110}\right)\)
\(\chi_{1089}(158,\cdot)\) \(-1\) \(1\) \(e\left(\frac{71}{330}\right)\) \(e\left(\frac{71}{165}\right)\) \(e\left(\frac{139}{330}\right)\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{38}{165}\right)\) \(e\left(\frac{73}{330}\right)\) \(e\left(\frac{142}{165}\right)\) \(e\left(\frac{23}{110}\right)\)
\(\chi_{1089}(185,\cdot)\) \(-1\) \(1\) \(e\left(\frac{293}{330}\right)\) \(e\left(\frac{128}{165}\right)\) \(e\left(\frac{67}{330}\right)\) \(e\left(\frac{118}{165}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{29}{165}\right)\) \(e\left(\frac{199}{330}\right)\) \(e\left(\frac{91}{165}\right)\) \(e\left(\frac{19}{110}\right)\)
\(\chi_{1089}(191,\cdot)\) \(-1\) \(1\) \(e\left(\frac{301}{330}\right)\) \(e\left(\frac{136}{165}\right)\) \(e\left(\frac{329}{330}\right)\) \(e\left(\frac{146}{165}\right)\) \(e\left(\frac{81}{110}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{103}{165}\right)\) \(e\left(\frac{263}{330}\right)\) \(e\left(\frac{107}{165}\right)\) \(e\left(\frac{3}{110}\right)\)
\(\chi_{1089}(203,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{330}\right)\) \(e\left(\frac{17}{165}\right)\) \(e\left(\frac{103}{330}\right)\) \(e\left(\frac{142}{165}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{116}{165}\right)\) \(e\left(\frac{301}{330}\right)\) \(e\left(\frac{34}{165}\right)\) \(e\left(\frac{21}{110}\right)\)
\(\chi_{1089}(212,\cdot)\) \(-1\) \(1\) \(e\left(\frac{269}{330}\right)\) \(e\left(\frac{104}{165}\right)\) \(e\left(\frac{271}{330}\right)\) \(e\left(\frac{34}{165}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{137}{165}\right)\) \(e\left(\frac{7}{330}\right)\) \(e\left(\frac{43}{165}\right)\) \(e\left(\frac{67}{110}\right)\)
\(\chi_{1089}(218,\cdot)\) \(-1\) \(1\) \(e\left(\frac{163}{330}\right)\) \(e\left(\frac{163}{165}\right)\) \(e\left(\frac{17}{330}\right)\) \(e\left(\frac{158}{165}\right)\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{64}{165}\right)\) \(e\left(\frac{149}{330}\right)\) \(e\left(\frac{161}{165}\right)\) \(e\left(\frac{59}{110}\right)\)
\(\chi_{1089}(236,\cdot)\) \(-1\) \(1\) \(e\left(\frac{157}{330}\right)\) \(e\left(\frac{157}{165}\right)\) \(e\left(\frac{233}{330}\right)\) \(e\left(\frac{137}{165}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{91}{165}\right)\) \(e\left(\frac{101}{330}\right)\) \(e\left(\frac{149}{165}\right)\) \(e\left(\frac{71}{110}\right)\)
\(\chi_{1089}(257,\cdot)\) \(-1\) \(1\) \(e\left(\frac{101}{330}\right)\) \(e\left(\frac{101}{165}\right)\) \(e\left(\frac{49}{330}\right)\) \(e\left(\frac{106}{165}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{68}{165}\right)\) \(e\left(\frac{313}{330}\right)\) \(e\left(\frac{37}{165}\right)\) \(e\left(\frac{73}{110}\right)\)
\(\chi_{1089}(284,\cdot)\) \(-1\) \(1\) \(e\left(\frac{233}{330}\right)\) \(e\left(\frac{68}{165}\right)\) \(e\left(\frac{247}{330}\right)\) \(e\left(\frac{73}{165}\right)\) \(e\left(\frac{13}{110}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{134}{165}\right)\) \(e\left(\frac{49}{330}\right)\) \(e\left(\frac{136}{165}\right)\) \(e\left(\frac{29}{110}\right)\)
\(\chi_{1089}(290,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{330}\right)\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{239}{330}\right)\) \(e\left(\frac{86}{165}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{133}{165}\right)\) \(e\left(\frac{173}{330}\right)\) \(e\left(\frac{2}{165}\right)\) \(e\left(\frac{53}{110}\right)\)
\(\chi_{1089}(302,\cdot)\) \(-1\) \(1\) \(e\left(\frac{107}{330}\right)\) \(e\left(\frac{107}{165}\right)\) \(e\left(\frac{163}{330}\right)\) \(e\left(\frac{127}{165}\right)\) \(e\left(\frac{107}{110}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{41}{165}\right)\) \(e\left(\frac{31}{330}\right)\) \(e\left(\frac{49}{165}\right)\) \(e\left(\frac{61}{110}\right)\)
\(\chi_{1089}(311,\cdot)\) \(-1\) \(1\) \(e\left(\frac{89}{330}\right)\) \(e\left(\frac{89}{165}\right)\) \(e\left(\frac{151}{330}\right)\) \(e\left(\frac{64}{165}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{122}{165}\right)\) \(e\left(\frac{217}{330}\right)\) \(e\left(\frac{13}{165}\right)\) \(e\left(\frac{97}{110}\right)\)
\(\chi_{1089}(317,\cdot)\) \(-1\) \(1\) \(e\left(\frac{103}{330}\right)\) \(e\left(\frac{103}{165}\right)\) \(e\left(\frac{197}{330}\right)\) \(e\left(\frac{113}{165}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{4}{165}\right)\) \(e\left(\frac{329}{330}\right)\) \(e\left(\frac{41}{165}\right)\) \(e\left(\frac{69}{110}\right)\)
\(\chi_{1089}(335,\cdot)\) \(-1\) \(1\) \(e\left(\frac{247}{330}\right)\) \(e\left(\frac{82}{165}\right)\) \(e\left(\frac{293}{330}\right)\) \(e\left(\frac{122}{165}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{16}{165}\right)\) \(e\left(\frac{161}{330}\right)\) \(e\left(\frac{164}{165}\right)\) \(e\left(\frac{1}{110}\right)\)
\(\chi_{1089}(344,\cdot)\) \(-1\) \(1\) \(e\left(\frac{139}{330}\right)\) \(e\left(\frac{139}{165}\right)\) \(e\left(\frac{221}{330}\right)\) \(e\left(\frac{74}{165}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{165}\right)\) \(e\left(\frac{287}{330}\right)\) \(e\left(\frac{113}{165}\right)\) \(e\left(\frac{107}{110}\right)\)
\(\chi_{1089}(356,\cdot)\) \(-1\) \(1\) \(e\left(\frac{131}{330}\right)\) \(e\left(\frac{131}{165}\right)\) \(e\left(\frac{289}{330}\right)\) \(e\left(\frac{46}{165}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{98}{165}\right)\) \(e\left(\frac{223}{330}\right)\) \(e\left(\frac{97}{165}\right)\) \(e\left(\frac{13}{110}\right)\)
\(\chi_{1089}(383,\cdot)\) \(-1\) \(1\) \(e\left(\frac{173}{330}\right)\) \(e\left(\frac{8}{165}\right)\) \(e\left(\frac{97}{330}\right)\) \(e\left(\frac{28}{165}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{74}{165}\right)\) \(e\left(\frac{229}{330}\right)\) \(e\left(\frac{16}{165}\right)\) \(e\left(\frac{39}{110}\right)\)
\(\chi_{1089}(389,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{330}\right)\) \(e\left(\frac{31}{165}\right)\) \(e\left(\frac{149}{330}\right)\) \(e\left(\frac{26}{165}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{163}{165}\right)\) \(e\left(\frac{83}{330}\right)\) \(e\left(\frac{62}{165}\right)\) \(e\left(\frac{103}{110}\right)\)