Properties

Label 927.bf
Modulus $927$
Conductor $927$
Order $102$
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(927, base_ring=CyclotomicField(102))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([85,48]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(14,927))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(927\)
Conductor: \(927\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(102\)
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: $\Q(\zeta_{51})$
Fixed field: Number field defined by a degree 102 polynomial (not computed)

First 31 of 32 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{927}(14,\cdot)\) \(-1\) \(1\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{77}{102}\right)\) \(e\left(\frac{8}{51}\right)\)
\(\chi_{927}(23,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{102}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{41}{102}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{19}{102}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{47}{102}\right)\) \(e\left(\frac{38}{51}\right)\)
\(\chi_{927}(137,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{102}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{97}{102}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{35}{102}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{49}{102}\right)\) \(e\left(\frac{19}{51}\right)\)
\(\chi_{927}(164,\cdot)\) \(-1\) \(1\) \(e\left(\frac{71}{102}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{19}{102}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{71}{102}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{79}{102}\right)\) \(e\left(\frac{40}{51}\right)\)
\(\chi_{927}(167,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{102}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{77}{102}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{73}{102}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{41}{102}\right)\) \(e\left(\frac{44}{51}\right)\)
\(\chi_{927}(182,\cdot)\) \(-1\) \(1\) \(e\left(\frac{95}{102}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{1}{102}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{95}{102}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{31}{102}\right)\) \(e\left(\frac{37}{51}\right)\)
\(\chi_{927}(203,\cdot)\) \(-1\) \(1\) \(e\left(\frac{67}{102}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{5}{102}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{67}{102}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{53}{102}\right)\) \(e\left(\frac{32}{51}\right)\)
\(\chi_{927}(236,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{102}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{67}{102}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{41}{102}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{37}{102}\right)\) \(e\left(\frac{31}{51}\right)\)
\(\chi_{927}(272,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{102}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{25}{102}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{29}{102}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{61}{102}\right)\) \(e\left(\frac{7}{51}\right)\)
\(\chi_{927}(299,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{102}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{79}{102}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{59}{102}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{1}{102}\right)\) \(e\left(\frac{16}{51}\right)\)
\(\chi_{927}(317,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{102}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{13}{102}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{11}{102}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{97}{102}\right)\) \(e\left(\frac{22}{51}\right)\)
\(\chi_{927}(425,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{102}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{23}{102}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{73}{102}\right)\) \(e\left(\frac{46}{51}\right)\)
\(\chi_{927}(446,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{102}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{29}{102}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{1}{102}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{83}{102}\right)\) \(e\left(\frac{2}{51}\right)\)
\(\chi_{927}(473,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{102}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{53}{102}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{37}{102}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{11}{102}\right)\) \(e\left(\frac{23}{51}\right)\)
\(\chi_{927}(488,\cdot)\) \(-1\) \(1\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{49}{102}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{91}{102}\right)\) \(e\left(\frac{28}{51}\right)\)
\(\chi_{927}(491,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{102}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{35}{102}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{61}{102}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{20}{51}\right)\)
\(\chi_{927}(524,\cdot)\) \(-1\) \(1\) \(e\left(\frac{83}{102}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{61}{102}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{83}{102}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{13}{51}\right)\)
\(\chi_{927}(545,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{102}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{101}{102}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{7}{102}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{71}{102}\right)\) \(e\left(\frac{14}{51}\right)\)
\(\chi_{927}(581,\cdot)\) \(-1\) \(1\) \(e\left(\frac{97}{102}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{59}{102}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{97}{102}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{95}{102}\right)\) \(e\left(\frac{41}{51}\right)\)
\(\chi_{927}(587,\cdot)\) \(-1\) \(1\) \(e\left(\frac{77}{102}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{91}{102}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{77}{102}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{67}{102}\right)\) \(e\left(\frac{1}{51}\right)\)
\(\chi_{927}(596,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{102}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{37}{102}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{47}{102}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{25}{102}\right)\) \(e\left(\frac{43}{51}\right)\)
\(\chi_{927}(608,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{102}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{11}{102}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{25}{102}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{35}{102}\right)\) \(e\left(\frac{50}{51}\right)\)
\(\chi_{927}(626,\cdot)\) \(-1\) \(1\) \(e\left(\frac{79}{102}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{47}{102}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{79}{102}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{29}{102}\right)\) \(e\left(\frac{5}{51}\right)\)
\(\chi_{927}(632,\cdot)\) \(-1\) \(1\) \(e\left(\frac{89}{102}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{31}{102}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{89}{102}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{43}{102}\right)\) \(e\left(\frac{25}{51}\right)\)
\(\chi_{927}(641,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{102}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{7}{102}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{53}{102}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{13}{102}\right)\) \(e\left(\frac{4}{51}\right)\)
\(\chi_{927}(734,\cdot)\) \(-1\) \(1\) \(e\left(\frac{91}{102}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{89}{102}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{91}{102}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{5}{102}\right)\) \(e\left(\frac{29}{51}\right)\)
\(\chi_{927}(785,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{102}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{43}{102}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{5}{102}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{7}{102}\right)\) \(e\left(\frac{10}{51}\right)\)
\(\chi_{927}(797,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{102}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{83}{102}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{31}{102}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{23}{102}\right)\) \(e\left(\frac{11}{51}\right)\)
\(\chi_{927}(821,\cdot)\) \(-1\) \(1\) \(e\left(\frac{101}{102}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{73}{102}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{101}{102}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{19}{102}\right)\) \(e\left(\frac{49}{51}\right)\)
\(\chi_{927}(833,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{102}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{95}{102}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{49}{102}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{89}{102}\right)\) \(e\left(\frac{47}{51}\right)\)
\(\chi_{927}(896,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{102}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{23}{102}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{43}{102}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{101}{102}\right)\) \(e\left(\frac{35}{51}\right)\)