from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(961, base_ring=CyclotomicField(186))
M = H._module
chi = DirichletCharacter(H, M([125]))
chi.galois_orbit()
[g,chi] = znchar(Mod(6,961))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(961\) | |
Conductor: | \(961\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(186\) | 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: | $\Q(\zeta_{93})$ |
Fixed field: | Number field defined by a degree 186 polynomial (not computed) |
First 31 of 60 characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{961}(6,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{31}\right)\) | \(e\left(\frac{125}{186}\right)\) | \(e\left(\frac{22}{31}\right)\) | \(e\left(\frac{65}{93}\right)\) | \(e\left(\frac{5}{186}\right)\) | \(e\left(\frac{19}{93}\right)\) | \(e\left(\frac{2}{31}\right)\) | \(e\left(\frac{32}{93}\right)\) | \(e\left(\frac{5}{93}\right)\) | \(e\left(\frac{13}{186}\right)\) |
\(\chi_{961}(26,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{23}{31}\right)\) | \(e\left(\frac{19}{186}\right)\) | \(e\left(\frac{15}{31}\right)\) | \(e\left(\frac{88}{93}\right)\) | \(e\left(\frac{157}{186}\right)\) | \(e\left(\frac{20}{93}\right)\) | \(e\left(\frac{7}{31}\right)\) | \(e\left(\frac{19}{93}\right)\) | \(e\left(\frac{64}{93}\right)\) | \(e\left(\frac{185}{186}\right)\) |
\(\chi_{961}(37,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{8}{31}\right)\) | \(e\left(\frac{167}{186}\right)\) | \(e\left(\frac{16}{31}\right)\) | \(e\left(\frac{5}{93}\right)\) | \(e\left(\frac{29}{186}\right)\) | \(e\left(\frac{73}{93}\right)\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{74}{93}\right)\) | \(e\left(\frac{29}{93}\right)\) | \(e\left(\frac{1}{186}\right)\) |
\(\chi_{961}(57,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{8}{31}\right)\) | \(e\left(\frac{43}{186}\right)\) | \(e\left(\frac{16}{31}\right)\) | \(e\left(\frac{67}{93}\right)\) | \(e\left(\frac{91}{186}\right)\) | \(e\left(\frac{11}{93}\right)\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{43}{93}\right)\) | \(e\left(\frac{91}{93}\right)\) | \(e\left(\frac{125}{186}\right)\) |
\(\chi_{961}(68,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{31}\right)\) | \(e\left(\frac{23}{186}\right)\) | \(e\left(\frac{10}{31}\right)\) | \(e\left(\frac{38}{93}\right)\) | \(e\left(\frac{53}{186}\right)\) | \(e\left(\frac{34}{93}\right)\) | \(e\left(\frac{15}{31}\right)\) | \(e\left(\frac{23}{93}\right)\) | \(e\left(\frac{53}{93}\right)\) | \(e\left(\frac{175}{186}\right)\) |
\(\chi_{961}(88,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{67}{186}\right)\) | \(e\left(\frac{17}{31}\right)\) | \(e\left(\frac{46}{93}\right)\) | \(e\left(\frac{25}{186}\right)\) | \(e\left(\frac{2}{93}\right)\) | \(e\left(\frac{10}{31}\right)\) | \(e\left(\frac{67}{93}\right)\) | \(e\left(\frac{25}{93}\right)\) | \(e\left(\frac{65}{186}\right)\) |
\(\chi_{961}(99,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{31}\right)\) | \(e\left(\frac{65}{186}\right)\) | \(e\left(\frac{4}{31}\right)\) | \(e\left(\frac{71}{93}\right)\) | \(e\left(\frac{77}{186}\right)\) | \(e\left(\frac{88}{93}\right)\) | \(e\left(\frac{6}{31}\right)\) | \(e\left(\frac{65}{93}\right)\) | \(e\left(\frac{77}{93}\right)\) | \(e\left(\frac{163}{186}\right)\) |
\(\chi_{961}(119,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{31}\right)\) | \(e\left(\frac{91}{186}\right)\) | \(e\left(\frac{18}{31}\right)\) | \(e\left(\frac{25}{93}\right)\) | \(e\left(\frac{145}{186}\right)\) | \(e\left(\frac{86}{93}\right)\) | \(e\left(\frac{27}{31}\right)\) | \(e\left(\frac{91}{93}\right)\) | \(e\left(\frac{52}{93}\right)\) | \(e\left(\frac{5}{186}\right)\) |
\(\chi_{961}(130,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{30}{31}\right)\) | \(e\left(\frac{107}{186}\right)\) | \(e\left(\frac{29}{31}\right)\) | \(e\left(\frac{11}{93}\right)\) | \(e\left(\frac{101}{186}\right)\) | \(e\left(\frac{49}{93}\right)\) | \(e\left(\frac{28}{31}\right)\) | \(e\left(\frac{14}{93}\right)\) | \(e\left(\frac{8}{93}\right)\) | \(e\left(\frac{151}{186}\right)\) |
\(\chi_{961}(150,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{25}{31}\right)\) | \(e\left(\frac{115}{186}\right)\) | \(e\left(\frac{19}{31}\right)\) | \(e\left(\frac{4}{93}\right)\) | \(e\left(\frac{79}{186}\right)\) | \(e\left(\frac{77}{93}\right)\) | \(e\left(\frac{13}{31}\right)\) | \(e\left(\frac{22}{93}\right)\) | \(e\left(\frac{79}{93}\right)\) | \(e\left(\frac{131}{186}\right)\) |
\(\chi_{961}(161,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{27}{31}\right)\) | \(e\left(\frac{149}{186}\right)\) | \(e\left(\frac{23}{31}\right)\) | \(e\left(\frac{44}{93}\right)\) | \(e\left(\frac{125}{186}\right)\) | \(e\left(\frac{10}{93}\right)\) | \(e\left(\frac{19}{31}\right)\) | \(e\left(\frac{56}{93}\right)\) | \(e\left(\frac{32}{93}\right)\) | \(e\left(\frac{139}{186}\right)\) |
\(\chi_{961}(181,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{10}{31}\right)\) | \(e\left(\frac{139}{186}\right)\) | \(e\left(\frac{20}{31}\right)\) | \(e\left(\frac{76}{93}\right)\) | \(e\left(\frac{13}{186}\right)\) | \(e\left(\frac{68}{93}\right)\) | \(e\left(\frac{30}{31}\right)\) | \(e\left(\frac{46}{93}\right)\) | \(e\left(\frac{13}{93}\right)\) | \(e\left(\frac{71}{186}\right)\) |
\(\chi_{961}(192,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{5}{186}\right)\) | \(e\left(\frac{17}{31}\right)\) | \(e\left(\frac{77}{93}\right)\) | \(e\left(\frac{149}{186}\right)\) | \(e\left(\frac{64}{93}\right)\) | \(e\left(\frac{10}{31}\right)\) | \(e\left(\frac{5}{93}\right)\) | \(e\left(\frac{56}{93}\right)\) | \(e\left(\frac{127}{186}\right)\) |
\(\chi_{961}(212,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{26}{31}\right)\) | \(e\left(\frac{163}{186}\right)\) | \(e\left(\frac{21}{31}\right)\) | \(e\left(\frac{55}{93}\right)\) | \(e\left(\frac{133}{186}\right)\) | \(e\left(\frac{59}{93}\right)\) | \(e\left(\frac{16}{31}\right)\) | \(e\left(\frac{70}{93}\right)\) | \(e\left(\frac{40}{93}\right)\) | \(e\left(\frac{11}{186}\right)\) |
\(\chi_{961}(223,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{21}{31}\right)\) | \(e\left(\frac{47}{186}\right)\) | \(e\left(\frac{11}{31}\right)\) | \(e\left(\frac{17}{93}\right)\) | \(e\left(\frac{173}{186}\right)\) | \(e\left(\frac{25}{93}\right)\) | \(e\left(\frac{1}{31}\right)\) | \(e\left(\frac{47}{93}\right)\) | \(e\left(\frac{80}{93}\right)\) | \(e\left(\frac{115}{186}\right)\) |
\(\chi_{961}(243,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{31}\right)\) | \(e\left(\frac{1}{186}\right)\) | \(e\left(\frac{22}{31}\right)\) | \(e\left(\frac{34}{93}\right)\) | \(e\left(\frac{67}{186}\right)\) | \(e\left(\frac{50}{93}\right)\) | \(e\left(\frac{2}{31}\right)\) | \(e\left(\frac{1}{93}\right)\) | \(e\left(\frac{67}{93}\right)\) | \(e\left(\frac{137}{186}\right)\) |
\(\chi_{961}(254,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{18}{31}\right)\) | \(e\left(\frac{89}{186}\right)\) | \(e\left(\frac{5}{31}\right)\) | \(e\left(\frac{50}{93}\right)\) | \(e\left(\frac{11}{186}\right)\) | \(e\left(\frac{79}{93}\right)\) | \(e\left(\frac{23}{31}\right)\) | \(e\left(\frac{89}{93}\right)\) | \(e\left(\frac{11}{93}\right)\) | \(e\left(\frac{103}{186}\right)\) |
\(\chi_{961}(274,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{27}{31}\right)\) | \(e\left(\frac{25}{186}\right)\) | \(e\left(\frac{23}{31}\right)\) | \(e\left(\frac{13}{93}\right)\) | \(e\left(\frac{1}{186}\right)\) | \(e\left(\frac{41}{93}\right)\) | \(e\left(\frac{19}{31}\right)\) | \(e\left(\frac{25}{93}\right)\) | \(e\left(\frac{1}{93}\right)\) | \(e\left(\frac{77}{186}\right)\) |
\(\chi_{961}(285,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{15}{31}\right)\) | \(e\left(\frac{131}{186}\right)\) | \(e\left(\frac{30}{31}\right)\) | \(e\left(\frac{83}{93}\right)\) | \(e\left(\frac{35}{186}\right)\) | \(e\left(\frac{40}{93}\right)\) | \(e\left(\frac{14}{31}\right)\) | \(e\left(\frac{38}{93}\right)\) | \(e\left(\frac{35}{93}\right)\) | \(e\left(\frac{91}{186}\right)\) |
\(\chi_{961}(305,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{12}{31}\right)\) | \(e\left(\frac{49}{186}\right)\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{85}{93}\right)\) | \(e\left(\frac{121}{186}\right)\) | \(e\left(\frac{32}{93}\right)\) | \(e\left(\frac{5}{31}\right)\) | \(e\left(\frac{49}{93}\right)\) | \(e\left(\frac{28}{93}\right)\) | \(e\left(\frac{17}{186}\right)\) |
\(\chi_{961}(316,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{12}{31}\right)\) | \(e\left(\frac{173}{186}\right)\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{23}{93}\right)\) | \(e\left(\frac{59}{186}\right)\) | \(e\left(\frac{1}{93}\right)\) | \(e\left(\frac{5}{31}\right)\) | \(e\left(\frac{80}{93}\right)\) | \(e\left(\frac{59}{93}\right)\) | \(e\left(\frac{79}{186}\right)\) |
\(\chi_{961}(336,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{28}{31}\right)\) | \(e\left(\frac{73}{186}\right)\) | \(e\left(\frac{25}{31}\right)\) | \(e\left(\frac{64}{93}\right)\) | \(e\left(\frac{55}{186}\right)\) | \(e\left(\frac{23}{93}\right)\) | \(e\left(\frac{22}{31}\right)\) | \(e\left(\frac{73}{93}\right)\) | \(e\left(\frac{55}{93}\right)\) | \(e\left(\frac{143}{186}\right)\) |
\(\chi_{961}(347,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{31}\right)\) | \(e\left(\frac{29}{186}\right)\) | \(e\left(\frac{18}{31}\right)\) | \(e\left(\frac{56}{93}\right)\) | \(e\left(\frac{83}{186}\right)\) | \(e\left(\frac{55}{93}\right)\) | \(e\left(\frac{27}{31}\right)\) | \(e\left(\frac{29}{93}\right)\) | \(e\left(\frac{83}{93}\right)\) | \(e\left(\frac{67}{186}\right)\) |
\(\chi_{961}(367,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{31}\right)\) | \(e\left(\frac{97}{186}\right)\) | \(e\left(\frac{26}{31}\right)\) | \(e\left(\frac{43}{93}\right)\) | \(e\left(\frac{175}{186}\right)\) | \(e\left(\frac{14}{93}\right)\) | \(e\left(\frac{8}{31}\right)\) | \(e\left(\frac{4}{93}\right)\) | \(e\left(\frac{82}{93}\right)\) | \(e\left(\frac{83}{186}\right)\) |
\(\chi_{961}(378,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{6}{31}\right)\) | \(e\left(\frac{71}{186}\right)\) | \(e\left(\frac{12}{31}\right)\) | \(e\left(\frac{89}{93}\right)\) | \(e\left(\frac{107}{186}\right)\) | \(e\left(\frac{16}{93}\right)\) | \(e\left(\frac{18}{31}\right)\) | \(e\left(\frac{71}{93}\right)\) | \(e\left(\frac{14}{93}\right)\) | \(e\left(\frac{55}{186}\right)\) |
\(\chi_{961}(398,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{31}\right)\) | \(e\left(\frac{121}{186}\right)\) | \(e\left(\frac{27}{31}\right)\) | \(e\left(\frac{22}{93}\right)\) | \(e\left(\frac{109}{186}\right)\) | \(e\left(\frac{5}{93}\right)\) | \(e\left(\frac{25}{31}\right)\) | \(e\left(\frac{28}{93}\right)\) | \(e\left(\frac{16}{93}\right)\) | \(e\left(\frac{23}{186}\right)\) |
\(\chi_{961}(409,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{31}\right)\) | \(e\left(\frac{113}{186}\right)\) | \(e\left(\frac{6}{31}\right)\) | \(e\left(\frac{29}{93}\right)\) | \(e\left(\frac{131}{186}\right)\) | \(e\left(\frac{70}{93}\right)\) | \(e\left(\frac{9}{31}\right)\) | \(e\left(\frac{20}{93}\right)\) | \(e\left(\frac{38}{93}\right)\) | \(e\left(\frac{43}{186}\right)\) |
\(\chi_{961}(429,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{14}{31}\right)\) | \(e\left(\frac{145}{186}\right)\) | \(e\left(\frac{28}{31}\right)\) | \(e\left(\frac{1}{93}\right)\) | \(e\left(\frac{43}{186}\right)\) | \(e\left(\frac{89}{93}\right)\) | \(e\left(\frac{11}{31}\right)\) | \(e\left(\frac{52}{93}\right)\) | \(e\left(\frac{43}{93}\right)\) | \(e\left(\frac{149}{186}\right)\) |
\(\chi_{961}(460,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{30}{31}\right)\) | \(e\left(\frac{169}{186}\right)\) | \(e\left(\frac{29}{31}\right)\) | \(e\left(\frac{73}{93}\right)\) | \(e\left(\frac{163}{186}\right)\) | \(e\left(\frac{80}{93}\right)\) | \(e\left(\frac{28}{31}\right)\) | \(e\left(\frac{76}{93}\right)\) | \(e\left(\frac{70}{93}\right)\) | \(e\left(\frac{89}{186}\right)\) |
\(\chi_{961}(471,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{28}{31}\right)\) | \(e\left(\frac{11}{186}\right)\) | \(e\left(\frac{25}{31}\right)\) | \(e\left(\frac{2}{93}\right)\) | \(e\left(\frac{179}{186}\right)\) | \(e\left(\frac{85}{93}\right)\) | \(e\left(\frac{22}{31}\right)\) | \(e\left(\frac{11}{93}\right)\) | \(e\left(\frac{86}{93}\right)\) | \(e\left(\frac{19}{186}\right)\) |
\(\chi_{961}(491,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{15}{31}\right)\) | \(e\left(\frac{7}{186}\right)\) | \(e\left(\frac{30}{31}\right)\) | \(e\left(\frac{52}{93}\right)\) | \(e\left(\frac{97}{186}\right)\) | \(e\left(\frac{71}{93}\right)\) | \(e\left(\frac{14}{31}\right)\) | \(e\left(\frac{7}{93}\right)\) | \(e\left(\frac{4}{93}\right)\) | \(e\left(\frac{29}{186}\right)\) |