Properties

Label 1089.be
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([220,21]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(7,1089))
 
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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(13\) \(14\) \(16\) \(17\)
\(\chi_{1089}(7,\cdot)\) \(-1\) \(1\) \(e\left(\frac{241}{330}\right)\) \(e\left(\frac{76}{165}\right)\) \(e\left(\frac{7}{165}\right)\) \(e\left(\frac{37}{330}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{251}{330}\right)\) \(e\left(\frac{139}{165}\right)\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{13}{110}\right)\)
\(\chi_{1089}(13,\cdot)\) \(-1\) \(1\) \(e\left(\frac{83}{330}\right)\) \(e\left(\frac{83}{165}\right)\) \(e\left(\frac{101}{165}\right)\) \(e\left(\frac{251}{330}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{133}{330}\right)\) \(e\left(\frac{2}{165}\right)\) \(e\left(\frac{1}{165}\right)\) \(e\left(\frac{109}{110}\right)\)
\(\chi_{1089}(52,\cdot)\) \(-1\) \(1\) \(e\left(\frac{199}{330}\right)\) \(e\left(\frac{34}{165}\right)\) \(e\left(\frac{103}{165}\right)\) \(e\left(\frac{73}{330}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{299}{330}\right)\) \(e\left(\frac{136}{165}\right)\) \(e\left(\frac{68}{165}\right)\) \(e\left(\frac{97}{110}\right)\)
\(\chi_{1089}(61,\cdot)\) \(-1\) \(1\) \(e\left(\frac{217}{330}\right)\) \(e\left(\frac{52}{165}\right)\) \(e\left(\frac{109}{165}\right)\) \(e\left(\frac{199}{330}\right)\) \(e\left(\frac{107}{110}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{137}{330}\right)\) \(e\left(\frac{43}{165}\right)\) \(e\left(\frac{104}{165}\right)\) \(e\left(\frac{61}{110}\right)\)
\(\chi_{1089}(79,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{330}\right)\) \(e\left(\frac{13}{165}\right)\) \(e\left(\frac{151}{165}\right)\) \(e\left(\frac{91}{330}\right)\) \(e\left(\frac{13}{110}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{323}{330}\right)\) \(e\left(\frac{52}{165}\right)\) \(e\left(\frac{26}{165}\right)\) \(e\left(\frac{29}{110}\right)\)
\(\chi_{1089}(85,\cdot)\) \(-1\) \(1\) \(e\left(\frac{149}{330}\right)\) \(e\left(\frac{149}{165}\right)\) \(e\left(\frac{68}{165}\right)\) \(e\left(\frac{53}{330}\right)\) \(e\left(\frac{39}{110}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{199}{330}\right)\) \(e\left(\frac{101}{165}\right)\) \(e\left(\frac{133}{165}\right)\) \(e\left(\frac{87}{110}\right)\)
\(\chi_{1089}(106,\cdot)\) \(-1\) \(1\) \(e\left(\frac{211}{330}\right)\) \(e\left(\frac{46}{165}\right)\) \(e\left(\frac{52}{165}\right)\) \(e\left(\frac{157}{330}\right)\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{191}{330}\right)\) \(e\left(\frac{19}{165}\right)\) \(e\left(\frac{92}{165}\right)\) \(e\left(\frac{73}{110}\right)\)
\(\chi_{1089}(139,\cdot)\) \(-1\) \(1\) \(e\left(\frac{311}{330}\right)\) \(e\left(\frac{146}{165}\right)\) \(e\left(\frac{122}{165}\right)\) \(e\left(\frac{197}{330}\right)\) \(e\left(\frac{91}{110}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{61}{330}\right)\) \(e\left(\frac{89}{165}\right)\) \(e\left(\frac{127}{165}\right)\) \(e\left(\frac{93}{110}\right)\)
\(\chi_{1089}(151,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{330}\right)\) \(e\left(\frac{49}{165}\right)\) \(e\left(\frac{163}{165}\right)\) \(e\left(\frac{13}{330}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{329}{330}\right)\) \(e\left(\frac{31}{165}\right)\) \(e\left(\frac{98}{165}\right)\) \(e\left(\frac{67}{110}\right)\)
\(\chi_{1089}(160,\cdot)\) \(-1\) \(1\) \(e\left(\frac{127}{330}\right)\) \(e\left(\frac{127}{165}\right)\) \(e\left(\frac{79}{165}\right)\) \(e\left(\frac{229}{330}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{287}{330}\right)\) \(e\left(\frac{13}{165}\right)\) \(e\left(\frac{89}{165}\right)\) \(e\left(\frac{21}{110}\right)\)
\(\chi_{1089}(178,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{330}\right)\) \(e\left(\frac{73}{165}\right)\) \(e\left(\frac{61}{165}\right)\) \(e\left(\frac{181}{330}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{113}{330}\right)\) \(e\left(\frac{127}{165}\right)\) \(e\left(\frac{146}{165}\right)\) \(e\left(\frac{19}{110}\right)\)
\(\chi_{1089}(184,\cdot)\) \(-1\) \(1\) \(e\left(\frac{329}{330}\right)\) \(e\left(\frac{164}{165}\right)\) \(e\left(\frac{128}{165}\right)\) \(e\left(\frac{323}{330}\right)\) \(e\left(\frac{109}{110}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{229}{330}\right)\) \(e\left(\frac{161}{165}\right)\) \(e\left(\frac{163}{165}\right)\) \(e\left(\frac{57}{110}\right)\)
\(\chi_{1089}(193,\cdot)\) \(-1\) \(1\) \(e\left(\frac{317}{330}\right)\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{14}{165}\right)\) \(e\left(\frac{239}{330}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{7}{330}\right)\) \(e\left(\frac{113}{165}\right)\) \(e\left(\frac{139}{165}\right)\) \(e\left(\frac{81}{110}\right)\)
\(\chi_{1089}(205,\cdot)\) \(-1\) \(1\) \(e\left(\frac{181}{330}\right)\) \(e\left(\frac{16}{165}\right)\) \(e\left(\frac{97}{165}\right)\) \(e\left(\frac{277}{330}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{131}{330}\right)\) \(e\left(\frac{64}{165}\right)\) \(e\left(\frac{32}{165}\right)\) \(e\left(\frac{23}{110}\right)\)
\(\chi_{1089}(211,\cdot)\) \(-1\) \(1\) \(e\left(\frac{203}{330}\right)\) \(e\left(\frac{38}{165}\right)\) \(e\left(\frac{86}{165}\right)\) \(e\left(\frac{101}{330}\right)\) \(e\left(\frac{93}{110}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{43}{330}\right)\) \(e\left(\frac{152}{165}\right)\) \(e\left(\frac{76}{165}\right)\) \(e\left(\frac{89}{110}\right)\)
\(\chi_{1089}(238,\cdot)\) \(-1\) \(1\) \(e\left(\frac{281}{330}\right)\) \(e\left(\frac{116}{165}\right)\) \(e\left(\frac{2}{165}\right)\) \(e\left(\frac{317}{330}\right)\) \(e\left(\frac{61}{110}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{330}\right)\) \(e\left(\frac{134}{165}\right)\) \(e\left(\frac{67}{165}\right)\) \(e\left(\frac{43}{110}\right)\)
\(\chi_{1089}(250,\cdot)\) \(-1\) \(1\) \(e\left(\frac{229}{330}\right)\) \(e\left(\frac{64}{165}\right)\) \(e\left(\frac{58}{165}\right)\) \(e\left(\frac{283}{330}\right)\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{29}{330}\right)\) \(e\left(\frac{91}{165}\right)\) \(e\left(\frac{128}{165}\right)\) \(e\left(\frac{37}{110}\right)\)
\(\chi_{1089}(259,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{330}\right)\) \(e\left(\frac{37}{165}\right)\) \(e\left(\frac{49}{165}\right)\) \(e\left(\frac{259}{330}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{107}{330}\right)\) \(e\left(\frac{148}{165}\right)\) \(e\left(\frac{74}{165}\right)\) \(e\left(\frac{91}{110}\right)\)
\(\chi_{1089}(277,\cdot)\) \(-1\) \(1\) \(e\left(\frac{133}{330}\right)\) \(e\left(\frac{133}{165}\right)\) \(e\left(\frac{136}{165}\right)\) \(e\left(\frac{271}{330}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{233}{330}\right)\) \(e\left(\frac{37}{165}\right)\) \(e\left(\frac{101}{165}\right)\) \(e\left(\frac{9}{110}\right)\)
\(\chi_{1089}(283,\cdot)\) \(-1\) \(1\) \(e\left(\frac{179}{330}\right)\) \(e\left(\frac{14}{165}\right)\) \(e\left(\frac{23}{165}\right)\) \(e\left(\frac{263}{330}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{259}{330}\right)\) \(e\left(\frac{56}{165}\right)\) \(e\left(\frac{28}{165}\right)\) \(e\left(\frac{27}{110}\right)\)
\(\chi_{1089}(292,\cdot)\) \(-1\) \(1\) \(e\left(\frac{227}{330}\right)\) \(e\left(\frac{62}{165}\right)\) \(e\left(\frac{149}{165}\right)\) \(e\left(\frac{269}{330}\right)\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{157}{330}\right)\) \(e\left(\frac{83}{165}\right)\) \(e\left(\frac{124}{165}\right)\) \(e\left(\frac{41}{110}\right)\)
\(\chi_{1089}(304,\cdot)\) \(-1\) \(1\) \(e\left(\frac{151}{330}\right)\) \(e\left(\frac{151}{165}\right)\) \(e\left(\frac{142}{165}\right)\) \(e\left(\frac{67}{330}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{71}{330}\right)\) \(e\left(\frac{109}{165}\right)\) \(e\left(\frac{137}{165}\right)\) \(e\left(\frac{83}{110}\right)\)
\(\chi_{1089}(310,\cdot)\) \(-1\) \(1\) \(e\left(\frac{263}{330}\right)\) \(e\left(\frac{98}{165}\right)\) \(e\left(\frac{161}{165}\right)\) \(e\left(\frac{191}{330}\right)\) \(e\left(\frac{43}{110}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{163}{330}\right)\) \(e\left(\frac{62}{165}\right)\) \(e\left(\frac{31}{165}\right)\) \(e\left(\frac{79}{110}\right)\)
\(\chi_{1089}(337,\cdot)\) \(-1\) \(1\) \(e\left(\frac{251}{330}\right)\) \(e\left(\frac{86}{165}\right)\) \(e\left(\frac{47}{165}\right)\) \(e\left(\frac{107}{330}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{271}{330}\right)\) \(e\left(\frac{14}{165}\right)\) \(e\left(\frac{7}{165}\right)\) \(e\left(\frac{103}{110}\right)\)
\(\chi_{1089}(349,\cdot)\) \(-1\) \(1\) \(e\left(\frac{79}{330}\right)\) \(e\left(\frac{79}{165}\right)\) \(e\left(\frac{118}{165}\right)\) \(e\left(\frac{223}{330}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{59}{330}\right)\) \(e\left(\frac{151}{165}\right)\) \(e\left(\frac{158}{165}\right)\) \(e\left(\frac{7}{110}\right)\)
\(\chi_{1089}(358,\cdot)\) \(-1\) \(1\) \(e\left(\frac{277}{330}\right)\) \(e\left(\frac{112}{165}\right)\) \(e\left(\frac{19}{165}\right)\) \(e\left(\frac{289}{330}\right)\) \(e\left(\frac{57}{110}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{257}{330}\right)\) \(e\left(\frac{118}{165}\right)\) \(e\left(\frac{59}{165}\right)\) \(e\left(\frac{51}{110}\right)\)
\(\chi_{1089}(376,\cdot)\) \(-1\) \(1\) \(e\left(\frac{193}{330}\right)\) \(e\left(\frac{28}{165}\right)\) \(e\left(\frac{46}{165}\right)\) \(e\left(\frac{31}{330}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{23}{330}\right)\) \(e\left(\frac{112}{165}\right)\) \(e\left(\frac{56}{165}\right)\) \(e\left(\frac{109}{110}\right)\)
\(\chi_{1089}(382,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{330}\right)\) \(e\left(\frac{29}{165}\right)\) \(e\left(\frac{83}{165}\right)\) \(e\left(\frac{203}{330}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{289}{330}\right)\) \(e\left(\frac{116}{165}\right)\) \(e\left(\frac{58}{165}\right)\) \(e\left(\frac{107}{110}\right)\)
\(\chi_{1089}(391,\cdot)\) \(-1\) \(1\) \(e\left(\frac{137}{330}\right)\) \(e\left(\frac{137}{165}\right)\) \(e\left(\frac{119}{165}\right)\) \(e\left(\frac{299}{330}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{307}{330}\right)\) \(e\left(\frac{53}{165}\right)\) \(e\left(\frac{109}{165}\right)\) \(e\left(\frac{1}{110}\right)\)
\(\chi_{1089}(409,\cdot)\) \(-1\) \(1\) \(e\left(\frac{323}{330}\right)\) \(e\left(\frac{158}{165}\right)\) \(e\left(\frac{71}{165}\right)\) \(e\left(\frac{281}{330}\right)\) \(e\left(\frac{103}{110}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{283}{330}\right)\) \(e\left(\frac{137}{165}\right)\) \(e\left(\frac{151}{165}\right)\) \(e\left(\frac{69}{110}\right)\)
\(\chi_{1089}(436,\cdot)\) \(-1\) \(1\) \(e\left(\frac{221}{330}\right)\) \(e\left(\frac{56}{165}\right)\) \(e\left(\frac{92}{165}\right)\) \(e\left(\frac{227}{330}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{211}{330}\right)\) \(e\left(\frac{59}{165}\right)\) \(e\left(\frac{112}{165}\right)\) \(e\left(\frac{53}{110}\right)\)