Properties

Label 3381.cl
Modulus $3381$
Conductor $3381$
Order $462$
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(3381, base_ring=CyclotomicField(462))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([231,286,42]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(2,3381))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3381\)
Conductor: \(3381\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(462\)
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: $\Q(\zeta_{231})$
Fixed field: Number field defined by a degree 462 polynomial (not computed)

First 31 of 120 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(13\) \(16\) \(17\) \(19\)
\(\chi_{3381}(2,\cdot)\) \(-1\) \(1\) \(e\left(\frac{359}{462}\right)\) \(e\left(\frac{128}{231}\right)\) \(e\left(\frac{251}{462}\right)\) \(e\left(\frac{51}{154}\right)\) \(e\left(\frac{74}{231}\right)\) \(e\left(\frac{37}{462}\right)\) \(e\left(\frac{54}{77}\right)\) \(e\left(\frac{25}{231}\right)\) \(e\left(\frac{283}{462}\right)\) \(e\left(\frac{1}{33}\right)\)
\(\chi_{3381}(32,\cdot)\) \(-1\) \(1\) \(e\left(\frac{409}{462}\right)\) \(e\left(\frac{178}{231}\right)\) \(e\left(\frac{331}{462}\right)\) \(e\left(\frac{101}{154}\right)\) \(e\left(\frac{139}{231}\right)\) \(e\left(\frac{185}{462}\right)\) \(e\left(\frac{39}{77}\right)\) \(e\left(\frac{125}{231}\right)\) \(e\left(\frac{29}{462}\right)\) \(e\left(\frac{5}{33}\right)\)
\(\chi_{3381}(95,\cdot)\) \(-1\) \(1\) \(e\left(\frac{265}{462}\right)\) \(e\left(\frac{34}{231}\right)\) \(e\left(\frac{193}{462}\right)\) \(e\left(\frac{111}{154}\right)\) \(e\left(\frac{229}{231}\right)\) \(e\left(\frac{461}{462}\right)\) \(e\left(\frac{36}{77}\right)\) \(e\left(\frac{68}{231}\right)\) \(e\left(\frac{317}{462}\right)\) \(e\left(\frac{8}{33}\right)\)
\(\chi_{3381}(170,\cdot)\) \(-1\) \(1\) \(e\left(\frac{431}{462}\right)\) \(e\left(\frac{200}{231}\right)\) \(e\left(\frac{89}{462}\right)\) \(e\left(\frac{123}{154}\right)\) \(e\left(\frac{29}{231}\right)\) \(e\left(\frac{361}{462}\right)\) \(e\left(\frac{17}{77}\right)\) \(e\left(\frac{169}{231}\right)\) \(e\left(\frac{139}{462}\right)\) \(e\left(\frac{16}{33}\right)\)
\(\chi_{3381}(179,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{462}\right)\) \(e\left(\frac{31}{231}\right)\) \(e\left(\frac{373}{462}\right)\) \(e\left(\frac{31}{154}\right)\) \(e\left(\frac{202}{231}\right)\) \(e\left(\frac{101}{462}\right)\) \(e\left(\frac{60}{77}\right)\) \(e\left(\frac{62}{231}\right)\) \(e\left(\frac{323}{462}\right)\) \(e\left(\frac{17}{33}\right)\)
\(\chi_{3381}(200,\cdot)\) \(-1\) \(1\) \(e\left(\frac{193}{462}\right)\) \(e\left(\frac{193}{231}\right)\) \(e\left(\frac{355}{462}\right)\) \(e\left(\frac{39}{154}\right)\) \(e\left(\frac{43}{231}\right)\) \(e\left(\frac{137}{462}\right)\) \(e\left(\frac{73}{77}\right)\) \(e\left(\frac{155}{231}\right)\) \(e\left(\frac{461}{462}\right)\) \(e\left(\frac{26}{33}\right)\)
\(\chi_{3381}(233,\cdot)\) \(-1\) \(1\) \(e\left(\frac{353}{462}\right)\) \(e\left(\frac{122}{231}\right)\) \(e\left(\frac{149}{462}\right)\) \(e\left(\frac{45}{154}\right)\) \(e\left(\frac{20}{231}\right)\) \(e\left(\frac{241}{462}\right)\) \(e\left(\frac{25}{77}\right)\) \(e\left(\frac{13}{231}\right)\) \(e\left(\frac{295}{462}\right)\) \(e\left(\frac{19}{33}\right)\)
\(\chi_{3381}(242,\cdot)\) \(-1\) \(1\) \(e\left(\frac{433}{462}\right)\) \(e\left(\frac{202}{231}\right)\) \(e\left(\frac{277}{462}\right)\) \(e\left(\frac{125}{154}\right)\) \(e\left(\frac{124}{231}\right)\) \(e\left(\frac{293}{462}\right)\) \(e\left(\frac{1}{77}\right)\) \(e\left(\frac{173}{231}\right)\) \(e\left(\frac{443}{462}\right)\) \(e\left(\frac{32}{33}\right)\)
\(\chi_{3381}(284,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{462}\right)\) \(e\left(\frac{43}{231}\right)\) \(e\left(\frac{115}{462}\right)\) \(e\left(\frac{43}{154}\right)\) \(e\left(\frac{79}{231}\right)\) \(e\left(\frac{155}{462}\right)\) \(e\left(\frac{41}{77}\right)\) \(e\left(\frac{86}{231}\right)\) \(e\left(\frac{299}{462}\right)\) \(e\left(\frac{14}{33}\right)\)
\(\chi_{3381}(305,\cdot)\) \(-1\) \(1\) \(e\left(\frac{415}{462}\right)\) \(e\left(\frac{184}{231}\right)\) \(e\left(\frac{433}{462}\right)\) \(e\left(\frac{107}{154}\right)\) \(e\left(\frac{193}{231}\right)\) \(e\left(\frac{443}{462}\right)\) \(e\left(\frac{68}{77}\right)\) \(e\left(\frac{137}{231}\right)\) \(e\left(\frac{17}{462}\right)\) \(e\left(\frac{20}{33}\right)\)
\(\chi_{3381}(317,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{462}\right)\) \(e\left(\frac{53}{231}\right)\) \(e\left(\frac{131}{462}\right)\) \(e\left(\frac{53}{154}\right)\) \(e\left(\frac{92}{231}\right)\) \(e\left(\frac{277}{462}\right)\) \(e\left(\frac{38}{77}\right)\) \(e\left(\frac{106}{231}\right)\) \(e\left(\frac{433}{462}\right)\) \(e\left(\frac{28}{33}\right)\)
\(\chi_{3381}(326,\cdot)\) \(-1\) \(1\) \(e\left(\frac{157}{462}\right)\) \(e\left(\frac{157}{231}\right)\) \(e\left(\frac{205}{462}\right)\) \(e\left(\frac{3}{154}\right)\) \(e\left(\frac{181}{231}\right)\) \(e\left(\frac{437}{462}\right)\) \(e\left(\frac{53}{77}\right)\) \(e\left(\frac{83}{231}\right)\) \(e\left(\frac{71}{462}\right)\) \(e\left(\frac{2}{33}\right)\)
\(\chi_{3381}(338,\cdot)\) \(-1\) \(1\) \(e\left(\frac{83}{462}\right)\) \(e\left(\frac{83}{231}\right)\) \(e\left(\frac{179}{462}\right)\) \(e\left(\frac{83}{154}\right)\) \(e\left(\frac{131}{231}\right)\) \(e\left(\frac{181}{462}\right)\) \(e\left(\frac{29}{77}\right)\) \(e\left(\frac{166}{231}\right)\) \(e\left(\frac{373}{462}\right)\) \(e\left(\frac{4}{33}\right)\)
\(\chi_{3381}(347,\cdot)\) \(-1\) \(1\) \(e\left(\frac{403}{462}\right)\) \(e\left(\frac{172}{231}\right)\) \(e\left(\frac{229}{462}\right)\) \(e\left(\frac{95}{154}\right)\) \(e\left(\frac{85}{231}\right)\) \(e\left(\frac{389}{462}\right)\) \(e\left(\frac{10}{77}\right)\) \(e\left(\frac{113}{231}\right)\) \(e\left(\frac{41}{462}\right)\) \(e\left(\frac{23}{33}\right)\)
\(\chi_{3381}(380,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{462}\right)\) \(e\left(\frac{59}{231}\right)\) \(e\left(\frac{233}{462}\right)\) \(e\left(\frac{59}{154}\right)\) \(e\left(\frac{146}{231}\right)\) \(e\left(\frac{73}{462}\right)\) \(e\left(\frac{67}{77}\right)\) \(e\left(\frac{118}{231}\right)\) \(e\left(\frac{421}{462}\right)\) \(e\left(\frac{10}{33}\right)\)
\(\chi_{3381}(443,\cdot)\) \(-1\) \(1\) \(e\left(\frac{107}{462}\right)\) \(e\left(\frac{107}{231}\right)\) \(e\left(\frac{125}{462}\right)\) \(e\left(\frac{107}{154}\right)\) \(e\left(\frac{116}{231}\right)\) \(e\left(\frac{289}{462}\right)\) \(e\left(\frac{68}{77}\right)\) \(e\left(\frac{214}{231}\right)\) \(e\left(\frac{325}{462}\right)\) \(e\left(\frac{31}{33}\right)\)
\(\chi_{3381}(464,\cdot)\) \(-1\) \(1\) \(e\left(\frac{179}{462}\right)\) \(e\left(\frac{179}{231}\right)\) \(e\left(\frac{425}{462}\right)\) \(e\left(\frac{25}{154}\right)\) \(e\left(\frac{71}{231}\right)\) \(e\left(\frac{151}{462}\right)\) \(e\left(\frac{31}{77}\right)\) \(e\left(\frac{127}{231}\right)\) \(e\left(\frac{181}{462}\right)\) \(e\left(\frac{13}{33}\right)\)
\(\chi_{3381}(473,\cdot)\) \(-1\) \(1\) \(e\left(\frac{115}{462}\right)\) \(e\left(\frac{115}{231}\right)\) \(e\left(\frac{415}{462}\right)\) \(e\left(\frac{115}{154}\right)\) \(e\left(\frac{34}{231}\right)\) \(e\left(\frac{17}{462}\right)\) \(e\left(\frac{4}{77}\right)\) \(e\left(\frac{230}{231}\right)\) \(e\left(\frac{155}{462}\right)\) \(e\left(\frac{29}{33}\right)\)
\(\chi_{3381}(485,\cdot)\) \(-1\) \(1\) \(e\left(\frac{293}{462}\right)\) \(e\left(\frac{62}{231}\right)\) \(e\left(\frac{53}{462}\right)\) \(e\left(\frac{139}{154}\right)\) \(e\left(\frac{173}{231}\right)\) \(e\left(\frac{433}{462}\right)\) \(e\left(\frac{43}{77}\right)\) \(e\left(\frac{124}{231}\right)\) \(e\left(\frac{415}{462}\right)\) \(e\left(\frac{1}{33}\right)\)
\(\chi_{3381}(515,\cdot)\) \(-1\) \(1\) \(e\left(\frac{145}{462}\right)\) \(e\left(\frac{145}{231}\right)\) \(e\left(\frac{1}{462}\right)\) \(e\left(\frac{145}{154}\right)\) \(e\left(\frac{73}{231}\right)\) \(e\left(\frac{383}{462}\right)\) \(e\left(\frac{72}{77}\right)\) \(e\left(\frac{59}{231}\right)\) \(e\left(\frac{95}{462}\right)\) \(e\left(\frac{5}{33}\right)\)
\(\chi_{3381}(578,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{462}\right)\) \(e\left(\frac{1}{231}\right)\) \(e\left(\frac{325}{462}\right)\) \(e\left(\frac{1}{154}\right)\) \(e\left(\frac{163}{231}\right)\) \(e\left(\frac{197}{462}\right)\) \(e\left(\frac{69}{77}\right)\) \(e\left(\frac{2}{231}\right)\) \(e\left(\frac{383}{462}\right)\) \(e\left(\frac{8}{33}\right)\)
\(\chi_{3381}(611,\cdot)\) \(-1\) \(1\) \(e\left(\frac{137}{462}\right)\) \(e\left(\frac{137}{231}\right)\) \(e\left(\frac{173}{462}\right)\) \(e\left(\frac{137}{154}\right)\) \(e\left(\frac{155}{231}\right)\) \(e\left(\frac{193}{462}\right)\) \(e\left(\frac{59}{77}\right)\) \(e\left(\frac{43}{231}\right)\) \(e\left(\frac{265}{462}\right)\) \(e\left(\frac{7}{33}\right)\)
\(\chi_{3381}(653,\cdot)\) \(-1\) \(1\) \(e\left(\frac{365}{462}\right)\) \(e\left(\frac{134}{231}\right)\) \(e\left(\frac{353}{462}\right)\) \(e\left(\frac{57}{154}\right)\) \(e\left(\frac{128}{231}\right)\) \(e\left(\frac{295}{462}\right)\) \(e\left(\frac{6}{77}\right)\) \(e\left(\frac{37}{231}\right)\) \(e\left(\frac{271}{462}\right)\) \(e\left(\frac{16}{33}\right)\)
\(\chi_{3381}(662,\cdot)\) \(-1\) \(1\) \(e\left(\frac{229}{462}\right)\) \(e\left(\frac{229}{231}\right)\) \(e\left(\frac{43}{462}\right)\) \(e\left(\frac{75}{154}\right)\) \(e\left(\frac{136}{231}\right)\) \(e\left(\frac{299}{462}\right)\) \(e\left(\frac{16}{77}\right)\) \(e\left(\frac{227}{231}\right)\) \(e\left(\frac{389}{462}\right)\) \(e\left(\frac{17}{33}\right)\)
\(\chi_{3381}(683,\cdot)\) \(-1\) \(1\) \(e\left(\frac{391}{462}\right)\) \(e\left(\frac{160}{231}\right)\) \(e\left(\frac{25}{462}\right)\) \(e\left(\frac{83}{154}\right)\) \(e\left(\frac{208}{231}\right)\) \(e\left(\frac{335}{462}\right)\) \(e\left(\frac{29}{77}\right)\) \(e\left(\frac{89}{231}\right)\) \(e\left(\frac{65}{462}\right)\) \(e\left(\frac{26}{33}\right)\)
\(\chi_{3381}(725,\cdot)\) \(-1\) \(1\) \(e\left(\frac{169}{462}\right)\) \(e\left(\frac{169}{231}\right)\) \(e\left(\frac{409}{462}\right)\) \(e\left(\frac{15}{154}\right)\) \(e\left(\frac{58}{231}\right)\) \(e\left(\frac{29}{462}\right)\) \(e\left(\frac{34}{77}\right)\) \(e\left(\frac{107}{231}\right)\) \(e\left(\frac{47}{462}\right)\) \(e\left(\frac{32}{33}\right)\)
\(\chi_{3381}(767,\cdot)\) \(-1\) \(1\) \(e\left(\frac{241}{462}\right)\) \(e\left(\frac{10}{231}\right)\) \(e\left(\frac{247}{462}\right)\) \(e\left(\frac{87}{154}\right)\) \(e\left(\frac{13}{231}\right)\) \(e\left(\frac{353}{462}\right)\) \(e\left(\frac{74}{77}\right)\) \(e\left(\frac{20}{231}\right)\) \(e\left(\frac{365}{462}\right)\) \(e\left(\frac{14}{33}\right)\)
\(\chi_{3381}(788,\cdot)\) \(-1\) \(1\) \(e\left(\frac{151}{462}\right)\) \(e\left(\frac{151}{231}\right)\) \(e\left(\frac{103}{462}\right)\) \(e\left(\frac{151}{154}\right)\) \(e\left(\frac{127}{231}\right)\) \(e\left(\frac{179}{462}\right)\) \(e\left(\frac{24}{77}\right)\) \(e\left(\frac{71}{231}\right)\) \(e\left(\frac{83}{462}\right)\) \(e\left(\frac{20}{33}\right)\)
\(\chi_{3381}(800,\cdot)\) \(-1\) \(1\) \(e\left(\frac{449}{462}\right)\) \(e\left(\frac{218}{231}\right)\) \(e\left(\frac{395}{462}\right)\) \(e\left(\frac{141}{154}\right)\) \(e\left(\frac{191}{231}\right)\) \(e\left(\frac{211}{462}\right)\) \(e\left(\frac{27}{77}\right)\) \(e\left(\frac{205}{231}\right)\) \(e\left(\frac{103}{462}\right)\) \(e\left(\frac{28}{33}\right)\)
\(\chi_{3381}(809,\cdot)\) \(-1\) \(1\) \(e\left(\frac{355}{462}\right)\) \(e\left(\frac{124}{231}\right)\) \(e\left(\frac{337}{462}\right)\) \(e\left(\frac{47}{154}\right)\) \(e\left(\frac{115}{231}\right)\) \(e\left(\frac{173}{462}\right)\) \(e\left(\frac{9}{77}\right)\) \(e\left(\frac{17}{231}\right)\) \(e\left(\frac{137}{462}\right)\) \(e\left(\frac{2}{33}\right)\)
\(\chi_{3381}(821,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{462}\right)\) \(e\left(\frac{17}{231}\right)\) \(e\left(\frac{443}{462}\right)\) \(e\left(\frac{17}{154}\right)\) \(e\left(\frac{230}{231}\right)\) \(e\left(\frac{115}{462}\right)\) \(e\left(\frac{18}{77}\right)\) \(e\left(\frac{34}{231}\right)\) \(e\left(\frac{43}{462}\right)\) \(e\left(\frac{4}{33}\right)\)