from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(953, base_ring=CyclotomicField(238))
M = H._module
chi = DirichletCharacter(H, M([12]))
chi.galois_orbit()
[g,chi] = znchar(Mod(15,953))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(953\) | |
Conductor: | \(953\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(119\) | 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: | $\Q(\zeta_{119})$ |
Fixed field: | Number field defined by a degree 119 polynomial (not computed) |
First 31 of 96 characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{953}(15,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{6}{119}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{44}{119}\right)\) | \(e\left(\frac{48}{119}\right)\) | \(e\left(\frac{64}{119}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{12}{119}\right)\) | \(e\left(\frac{86}{119}\right)\) | \(e\left(\frac{81}{119}\right)\) |
\(\chi_{953}(18,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{16}{119}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{38}{119}\right)\) | \(e\left(\frac{9}{119}\right)\) | \(e\left(\frac{12}{119}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{32}{119}\right)\) | \(e\left(\frac{31}{119}\right)\) | \(e\left(\frac{97}{119}\right)\) |
\(\chi_{953}(28,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{13}{119}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{16}{119}\right)\) | \(e\left(\frac{104}{119}\right)\) | \(e\left(\frac{99}{119}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{26}{119}\right)\) | \(e\left(\frac{107}{119}\right)\) | \(e\left(\frac{116}{119}\right)\) |
\(\chi_{953}(33,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{39}{119}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{48}{119}\right)\) | \(e\left(\frac{74}{119}\right)\) | \(e\left(\frac{59}{119}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{78}{119}\right)\) | \(e\left(\frac{83}{119}\right)\) | \(e\left(\frac{110}{119}\right)\) |
\(\chi_{953}(49,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{82}{119}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{46}{119}\right)\) | \(e\left(\frac{61}{119}\right)\) | \(e\left(\frac{2}{119}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{45}{119}\right)\) | \(e\left(\frac{25}{119}\right)\) | \(e\left(\frac{36}{119}\right)\) |
\(\chi_{953}(53,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{103}{119}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{81}{119}\right)\) | \(e\left(\frac{110}{119}\right)\) | \(e\left(\frac{107}{119}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{87}{119}\right)\) | \(e\left(\frac{88}{119}\right)\) | \(e\left(\frac{22}{119}\right)\) |
\(\chi_{953}(95,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{38}{119}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{1}{119}\right)\) | \(e\left(\frac{66}{119}\right)\) | \(e\left(\frac{88}{119}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{76}{119}\right)\) | \(e\left(\frac{29}{119}\right)\) | \(e\left(\frac{37}{119}\right)\) |
\(\chi_{953}(104,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{90}{119}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{65}{119}\right)\) | \(e\left(\frac{6}{119}\right)\) | \(e\left(\frac{8}{119}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{61}{119}\right)\) | \(e\left(\frac{100}{119}\right)\) | \(e\left(\frac{25}{119}\right)\) |
\(\chi_{953}(114,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{48}{119}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{114}{119}\right)\) | \(e\left(\frac{27}{119}\right)\) | \(e\left(\frac{36}{119}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{96}{119}\right)\) | \(e\left(\frac{93}{119}\right)\) | \(e\left(\frac{53}{119}\right)\) |
\(\chi_{953}(116,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{24}{119}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{57}{119}\right)\) | \(e\left(\frac{73}{119}\right)\) | \(e\left(\frac{18}{119}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{48}{119}\right)\) | \(e\left(\frac{106}{119}\right)\) | \(e\left(\frac{86}{119}\right)\) |
\(\chi_{953}(117,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{43}{119}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{117}{119}\right)\) | \(e\left(\frac{106}{119}\right)\) | \(e\left(\frac{62}{119}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{86}{119}\right)\) | \(e\left(\frac{61}{119}\right)\) | \(e\left(\frac{45}{119}\right)\) |
\(\chi_{953}(136,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{78}{119}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{96}{119}\right)\) | \(e\left(\frac{29}{119}\right)\) | \(e\left(\frac{118}{119}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{37}{119}\right)\) | \(e\left(\frac{47}{119}\right)\) | \(e\left(\frac{101}{119}\right)\) |
\(\chi_{953}(141,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{65}{119}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{80}{119}\right)\) | \(e\left(\frac{44}{119}\right)\) | \(e\left(\frac{19}{119}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{11}{119}\right)\) | \(e\left(\frac{59}{119}\right)\) | \(e\left(\frac{104}{119}\right)\) |
\(\chi_{953}(146,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{64}{119}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{33}{119}\right)\) | \(e\left(\frac{36}{119}\right)\) | \(e\left(\frac{48}{119}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{9}{119}\right)\) | \(e\left(\frac{5}{119}\right)\) | \(e\left(\frac{31}{119}\right)\) |
\(\chi_{953}(153,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{31}{119}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{29}{119}\right)\) | \(e\left(\frac{10}{119}\right)\) | \(e\left(\frac{53}{119}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{62}{119}\right)\) | \(e\left(\frac{8}{119}\right)\) | \(e\left(\frac{2}{119}\right)\) |
\(\chi_{953}(155,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{89}{119}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{18}{119}\right)\) | \(e\left(\frac{117}{119}\right)\) | \(e\left(\frac{37}{119}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{59}{119}\right)\) | \(e\left(\frac{46}{119}\right)\) | \(e\left(\frac{71}{119}\right)\) |
\(\chi_{953}(182,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{40}{119}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{95}{119}\right)\) | \(e\left(\frac{82}{119}\right)\) | \(e\left(\frac{30}{119}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{80}{119}\right)\) | \(e\left(\frac{18}{119}\right)\) | \(e\left(\frac{64}{119}\right)\) |
\(\chi_{953}(186,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{99}{119}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{12}{119}\right)\) | \(e\left(\frac{78}{119}\right)\) | \(e\left(\frac{104}{119}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{79}{119}\right)\) | \(e\left(\frac{110}{119}\right)\) | \(e\left(\frac{87}{119}\right)\) |
\(\chi_{953}(200,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{59}{119}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{36}{119}\right)\) | \(e\left(\frac{115}{119}\right)\) | \(e\left(\frac{74}{119}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{118}{119}\right)\) | \(e\left(\frac{92}{119}\right)\) | \(e\left(\frac{23}{119}\right)\) |
\(\chi_{953}(203,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{93}{119}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{87}{119}\right)\) | \(e\left(\frac{30}{119}\right)\) | \(e\left(\frac{40}{119}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{67}{119}\right)\) | \(e\left(\frac{24}{119}\right)\) | \(e\left(\frac{6}{119}\right)\) |
\(\chi_{953}(209,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{71}{119}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{5}{119}\right)\) | \(e\left(\frac{92}{119}\right)\) | \(e\left(\frac{83}{119}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{23}{119}\right)\) | \(e\left(\frac{26}{119}\right)\) | \(e\left(\frac{66}{119}\right)\) |
\(\chi_{953}(225,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{12}{119}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{88}{119}\right)\) | \(e\left(\frac{96}{119}\right)\) | \(e\left(\frac{9}{119}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{24}{119}\right)\) | \(e\left(\frac{53}{119}\right)\) | \(e\left(\frac{43}{119}\right)\) |
\(\chi_{953}(226,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{110}{119}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{53}{119}\right)\) | \(e\left(\frac{47}{119}\right)\) | \(e\left(\frac{23}{119}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{101}{119}\right)\) | \(e\left(\frac{109}{119}\right)\) | \(e\left(\frac{57}{119}\right)\) |
\(\chi_{953}(230,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{67}{119}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{55}{119}\right)\) | \(e\left(\frac{60}{119}\right)\) | \(e\left(\frac{80}{119}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{15}{119}\right)\) | \(e\left(\frac{48}{119}\right)\) | \(e\left(\frac{12}{119}\right)\) |
\(\chi_{953}(240,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{69}{119}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{30}{119}\right)\) | \(e\left(\frac{76}{119}\right)\) | \(e\left(\frac{22}{119}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{19}{119}\right)\) | \(e\left(\frac{37}{119}\right)\) | \(e\left(\frac{39}{119}\right)\) |
\(\chi_{953}(270,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{22}{119}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{82}{119}\right)\) | \(e\left(\frac{57}{119}\right)\) | \(e\left(\frac{76}{119}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{44}{119}\right)\) | \(e\left(\frac{117}{119}\right)\) | \(e\left(\frac{59}{119}\right)\) |
\(\chi_{953}(288,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{79}{119}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{24}{119}\right)\) | \(e\left(\frac{37}{119}\right)\) | \(e\left(\frac{89}{119}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{39}{119}\right)\) | \(e\left(\frac{101}{119}\right)\) | \(e\left(\frac{55}{119}\right)\) |
\(\chi_{953}(296,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{108}{119}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{78}{119}\right)\) | \(e\left(\frac{31}{119}\right)\) | \(e\left(\frac{81}{119}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{97}{119}\right)\) | \(e\left(\frac{1}{119}\right)\) | \(e\left(\frac{30}{119}\right)\) |
\(\chi_{953}(324,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{32}{119}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{76}{119}\right)\) | \(e\left(\frac{18}{119}\right)\) | \(e\left(\frac{24}{119}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{64}{119}\right)\) | \(e\left(\frac{62}{119}\right)\) | \(e\left(\frac{75}{119}\right)\) |
\(\chi_{953}(328,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{83}{119}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{93}{119}\right)\) | \(e\left(\frac{69}{119}\right)\) | \(e\left(\frac{92}{119}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{47}{119}\right)\) | \(e\left(\frac{79}{119}\right)\) | \(e\left(\frac{109}{119}\right)\) |
\(\chi_{953}(331,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{53}{119}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{111}{119}\right)\) | \(e\left(\frac{67}{119}\right)\) | \(e\left(\frac{10}{119}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{106}{119}\right)\) | \(e\left(\frac{6}{119}\right)\) | \(e\left(\frac{61}{119}\right)\) |