Properties

Label 3381.ca
Modulus $3381$
Conductor $3381$
Order $154$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3381, base_ring=CyclotomicField(154))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([77,110,91]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(113,3381))
 
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: \(154\)
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: $\Q(\zeta_{77})$
Fixed field: Number field defined by a degree 154 polynomial (not computed)

First 31 of 60 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(13\) \(16\) \(17\) \(19\)
\(\chi_{3381}(113,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{154}\right)\) \(e\left(\frac{39}{77}\right)\) \(e\left(\frac{62}{77}\right)\) \(e\left(\frac{117}{154}\right)\) \(e\left(\frac{9}{154}\right)\) \(e\left(\frac{30}{77}\right)\) \(e\left(\frac{65}{77}\right)\) \(e\left(\frac{1}{77}\right)\) \(e\left(\frac{38}{77}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{3381}(134,\cdot)\) \(1\) \(1\) \(e\left(\frac{45}{154}\right)\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{36}{77}\right)\) \(e\left(\frac{135}{154}\right)\) \(e\left(\frac{117}{154}\right)\) \(e\left(\frac{5}{77}\right)\) \(e\left(\frac{75}{77}\right)\) \(e\left(\frac{13}{77}\right)\) \(e\left(\frac{32}{77}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{3381}(155,\cdot)\) \(1\) \(1\) \(e\left(\frac{65}{154}\right)\) \(e\left(\frac{65}{77}\right)\) \(e\left(\frac{52}{77}\right)\) \(e\left(\frac{41}{154}\right)\) \(e\left(\frac{15}{154}\right)\) \(e\left(\frac{50}{77}\right)\) \(e\left(\frac{57}{77}\right)\) \(e\left(\frac{53}{77}\right)\) \(e\left(\frac{12}{77}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{3381}(176,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{154}\right)\) \(e\left(\frac{29}{77}\right)\) \(e\left(\frac{54}{77}\right)\) \(e\left(\frac{87}{154}\right)\) \(e\left(\frac{137}{154}\right)\) \(e\left(\frac{46}{77}\right)\) \(e\left(\frac{74}{77}\right)\) \(e\left(\frac{58}{77}\right)\) \(e\left(\frac{48}{77}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{3381}(218,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{154}\right)\) \(e\left(\frac{27}{77}\right)\) \(e\left(\frac{37}{77}\right)\) \(e\left(\frac{81}{154}\right)\) \(e\left(\frac{101}{154}\right)\) \(e\left(\frac{3}{77}\right)\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{54}{77}\right)\) \(e\left(\frac{50}{77}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{3381}(260,\cdot)\) \(1\) \(1\) \(e\left(\frac{123}{154}\right)\) \(e\left(\frac{46}{77}\right)\) \(e\left(\frac{6}{77}\right)\) \(e\left(\frac{61}{154}\right)\) \(e\left(\frac{135}{154}\right)\) \(e\left(\frac{65}{77}\right)\) \(e\left(\frac{51}{77}\right)\) \(e\left(\frac{15}{77}\right)\) \(e\left(\frac{31}{77}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{3381}(281,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{154}\right)\) \(e\left(\frac{3}{77}\right)\) \(e\left(\frac{64}{77}\right)\) \(e\left(\frac{9}{154}\right)\) \(e\left(\frac{131}{154}\right)\) \(e\left(\frac{26}{77}\right)\) \(e\left(\frac{5}{77}\right)\) \(e\left(\frac{6}{77}\right)\) \(e\left(\frac{74}{77}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{3381}(365,\cdot)\) \(1\) \(1\) \(e\left(\frac{125}{154}\right)\) \(e\left(\frac{48}{77}\right)\) \(e\left(\frac{23}{77}\right)\) \(e\left(\frac{67}{154}\right)\) \(e\left(\frac{17}{154}\right)\) \(e\left(\frac{31}{77}\right)\) \(e\left(\frac{3}{77}\right)\) \(e\left(\frac{19}{77}\right)\) \(e\left(\frac{29}{77}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{3381}(428,\cdot)\) \(1\) \(1\) \(e\left(\frac{129}{154}\right)\) \(e\left(\frac{52}{77}\right)\) \(e\left(\frac{57}{77}\right)\) \(e\left(\frac{79}{154}\right)\) \(e\left(\frac{89}{154}\right)\) \(e\left(\frac{40}{77}\right)\) \(e\left(\frac{61}{77}\right)\) \(e\left(\frac{27}{77}\right)\) \(e\left(\frac{25}{77}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{3381}(470,\cdot)\) \(1\) \(1\) \(e\left(\frac{141}{154}\right)\) \(e\left(\frac{64}{77}\right)\) \(e\left(\frac{5}{77}\right)\) \(e\left(\frac{115}{154}\right)\) \(e\left(\frac{151}{154}\right)\) \(e\left(\frac{67}{77}\right)\) \(e\left(\frac{4}{77}\right)\) \(e\left(\frac{51}{77}\right)\) \(e\left(\frac{13}{77}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{3381}(596,\cdot)\) \(1\) \(1\) \(e\left(\frac{149}{154}\right)\) \(e\left(\frac{72}{77}\right)\) \(e\left(\frac{73}{77}\right)\) \(e\left(\frac{139}{154}\right)\) \(e\left(\frac{141}{154}\right)\) \(e\left(\frac{8}{77}\right)\) \(e\left(\frac{43}{77}\right)\) \(e\left(\frac{67}{77}\right)\) \(e\left(\frac{5}{77}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{3381}(617,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{154}\right)\) \(e\left(\frac{1}{77}\right)\) \(e\left(\frac{47}{77}\right)\) \(e\left(\frac{3}{154}\right)\) \(e\left(\frac{95}{154}\right)\) \(e\left(\frac{60}{77}\right)\) \(e\left(\frac{53}{77}\right)\) \(e\left(\frac{2}{77}\right)\) \(e\left(\frac{76}{77}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{3381}(659,\cdot)\) \(1\) \(1\) \(e\left(\frac{139}{154}\right)\) \(e\left(\frac{62}{77}\right)\) \(e\left(\frac{65}{77}\right)\) \(e\left(\frac{109}{154}\right)\) \(e\left(\frac{115}{154}\right)\) \(e\left(\frac{24}{77}\right)\) \(e\left(\frac{52}{77}\right)\) \(e\left(\frac{47}{77}\right)\) \(e\left(\frac{15}{77}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{3381}(701,\cdot)\) \(1\) \(1\) \(e\left(\frac{137}{154}\right)\) \(e\left(\frac{60}{77}\right)\) \(e\left(\frac{48}{77}\right)\) \(e\left(\frac{103}{154}\right)\) \(e\left(\frac{79}{154}\right)\) \(e\left(\frac{58}{77}\right)\) \(e\left(\frac{23}{77}\right)\) \(e\left(\frac{43}{77}\right)\) \(e\left(\frac{17}{77}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{3381}(743,\cdot)\) \(1\) \(1\) \(e\left(\frac{79}{154}\right)\) \(e\left(\frac{2}{77}\right)\) \(e\left(\frac{17}{77}\right)\) \(e\left(\frac{83}{154}\right)\) \(e\left(\frac{113}{154}\right)\) \(e\left(\frac{43}{77}\right)\) \(e\left(\frac{29}{77}\right)\) \(e\left(\frac{4}{77}\right)\) \(e\left(\frac{75}{77}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{3381}(764,\cdot)\) \(1\) \(1\) \(e\left(\frac{113}{154}\right)\) \(e\left(\frac{36}{77}\right)\) \(e\left(\frac{75}{77}\right)\) \(e\left(\frac{31}{154}\right)\) \(e\left(\frac{109}{154}\right)\) \(e\left(\frac{4}{77}\right)\) \(e\left(\frac{60}{77}\right)\) \(e\left(\frac{72}{77}\right)\) \(e\left(\frac{41}{77}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{3381}(848,\cdot)\) \(1\) \(1\) \(e\left(\frac{81}{154}\right)\) \(e\left(\frac{4}{77}\right)\) \(e\left(\frac{34}{77}\right)\) \(e\left(\frac{89}{154}\right)\) \(e\left(\frac{149}{154}\right)\) \(e\left(\frac{9}{77}\right)\) \(e\left(\frac{58}{77}\right)\) \(e\left(\frac{8}{77}\right)\) \(e\left(\frac{73}{77}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{3381}(911,\cdot)\) \(1\) \(1\) \(e\left(\frac{85}{154}\right)\) \(e\left(\frac{8}{77}\right)\) \(e\left(\frac{68}{77}\right)\) \(e\left(\frac{101}{154}\right)\) \(e\left(\frac{67}{154}\right)\) \(e\left(\frac{18}{77}\right)\) \(e\left(\frac{39}{77}\right)\) \(e\left(\frac{16}{77}\right)\) \(e\left(\frac{69}{77}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{3381}(953,\cdot)\) \(1\) \(1\) \(e\left(\frac{97}{154}\right)\) \(e\left(\frac{20}{77}\right)\) \(e\left(\frac{16}{77}\right)\) \(e\left(\frac{137}{154}\right)\) \(e\left(\frac{129}{154}\right)\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{59}{77}\right)\) \(e\left(\frac{40}{77}\right)\) \(e\left(\frac{57}{77}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{3381}(1100,\cdot)\) \(1\) \(1\) \(e\left(\frac{111}{154}\right)\) \(e\left(\frac{34}{77}\right)\) \(e\left(\frac{58}{77}\right)\) \(e\left(\frac{25}{154}\right)\) \(e\left(\frac{73}{154}\right)\) \(e\left(\frac{38}{77}\right)\) \(e\left(\frac{31}{77}\right)\) \(e\left(\frac{68}{77}\right)\) \(e\left(\frac{43}{77}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{3381}(1121,\cdot)\) \(1\) \(1\) \(e\left(\frac{131}{154}\right)\) \(e\left(\frac{54}{77}\right)\) \(e\left(\frac{74}{77}\right)\) \(e\left(\frac{85}{154}\right)\) \(e\left(\frac{125}{154}\right)\) \(e\left(\frac{6}{77}\right)\) \(e\left(\frac{13}{77}\right)\) \(e\left(\frac{31}{77}\right)\) \(e\left(\frac{23}{77}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{3381}(1142,\cdot)\) \(1\) \(1\) \(e\left(\frac{95}{154}\right)\) \(e\left(\frac{18}{77}\right)\) \(e\left(\frac{76}{77}\right)\) \(e\left(\frac{131}{154}\right)\) \(e\left(\frac{93}{154}\right)\) \(e\left(\frac{2}{77}\right)\) \(e\left(\frac{30}{77}\right)\) \(e\left(\frac{36}{77}\right)\) \(e\left(\frac{59}{77}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{3381}(1184,\cdot)\) \(1\) \(1\) \(e\left(\frac{93}{154}\right)\) \(e\left(\frac{16}{77}\right)\) \(e\left(\frac{59}{77}\right)\) \(e\left(\frac{125}{154}\right)\) \(e\left(\frac{57}{154}\right)\) \(e\left(\frac{36}{77}\right)\) \(e\left(\frac{1}{77}\right)\) \(e\left(\frac{32}{77}\right)\) \(e\left(\frac{61}{77}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{3381}(1247,\cdot)\) \(1\) \(1\) \(e\left(\frac{69}{154}\right)\) \(e\left(\frac{69}{77}\right)\) \(e\left(\frac{9}{77}\right)\) \(e\left(\frac{53}{154}\right)\) \(e\left(\frac{87}{154}\right)\) \(e\left(\frac{59}{77}\right)\) \(e\left(\frac{38}{77}\right)\) \(e\left(\frac{61}{77}\right)\) \(e\left(\frac{8}{77}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{3381}(1331,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{154}\right)\) \(e\left(\frac{37}{77}\right)\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{111}{154}\right)\) \(e\left(\frac{127}{154}\right)\) \(e\left(\frac{64}{77}\right)\) \(e\left(\frac{36}{77}\right)\) \(e\left(\frac{74}{77}\right)\) \(e\left(\frac{40}{77}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{3381}(1394,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{154}\right)\) \(e\left(\frac{41}{77}\right)\) \(e\left(\frac{2}{77}\right)\) \(e\left(\frac{123}{154}\right)\) \(e\left(\frac{45}{154}\right)\) \(e\left(\frac{73}{77}\right)\) \(e\left(\frac{17}{77}\right)\) \(e\left(\frac{5}{77}\right)\) \(e\left(\frac{36}{77}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{3381}(1436,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{154}\right)\) \(e\left(\frac{53}{77}\right)\) \(e\left(\frac{27}{77}\right)\) \(e\left(\frac{5}{154}\right)\) \(e\left(\frac{107}{154}\right)\) \(e\left(\frac{23}{77}\right)\) \(e\left(\frac{37}{77}\right)\) \(e\left(\frac{29}{77}\right)\) \(e\left(\frac{24}{77}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{3381}(1562,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{154}\right)\) \(e\left(\frac{61}{77}\right)\) \(e\left(\frac{18}{77}\right)\) \(e\left(\frac{29}{154}\right)\) \(e\left(\frac{97}{154}\right)\) \(e\left(\frac{41}{77}\right)\) \(e\left(\frac{76}{77}\right)\) \(e\left(\frac{45}{77}\right)\) \(e\left(\frac{16}{77}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{3381}(1583,\cdot)\) \(1\) \(1\) \(e\left(\frac{67}{154}\right)\) \(e\left(\frac{67}{77}\right)\) \(e\left(\frac{69}{77}\right)\) \(e\left(\frac{47}{154}\right)\) \(e\left(\frac{51}{154}\right)\) \(e\left(\frac{16}{77}\right)\) \(e\left(\frac{9}{77}\right)\) \(e\left(\frac{57}{77}\right)\) \(e\left(\frac{10}{77}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{3381}(1604,\cdot)\) \(1\) \(1\) \(e\left(\frac{87}{154}\right)\) \(e\left(\frac{10}{77}\right)\) \(e\left(\frac{8}{77}\right)\) \(e\left(\frac{107}{154}\right)\) \(e\left(\frac{103}{154}\right)\) \(e\left(\frac{61}{77}\right)\) \(e\left(\frac{68}{77}\right)\) \(e\left(\frac{20}{77}\right)\) \(e\left(\frac{67}{77}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{3381}(1625,\cdot)\) \(1\) \(1\) \(e\left(\frac{51}{154}\right)\) \(e\left(\frac{51}{77}\right)\) \(e\left(\frac{10}{77}\right)\) \(e\left(\frac{153}{154}\right)\) \(e\left(\frac{71}{154}\right)\) \(e\left(\frac{57}{77}\right)\) \(e\left(\frac{8}{77}\right)\) \(e\left(\frac{25}{77}\right)\) \(e\left(\frac{26}{77}\right)\) \(e\left(\frac{13}{22}\right)\)