from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2003, base_ring=CyclotomicField(286))
M = H._module
chi = DirichletCharacter(H, M([96]))
chi.galois_orbit()
[g,chi] = znchar(Mod(4,2003))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(2003\) | |
| Conductor: | \(2003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(143\) | 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: | $\Q(\zeta_{143})$ |
| Fixed field: | Number field defined by a degree 143 polynomial (not computed) |
First 31 of 120 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2003}(4,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{112}{143}\right)\) | \(e\left(\frac{20}{143}\right)\) | \(e\left(\frac{81}{143}\right)\) | \(e\left(\frac{48}{143}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{41}{143}\right)\) | \(e\left(\frac{50}{143}\right)\) | \(e\left(\frac{40}{143}\right)\) | \(e\left(\frac{17}{143}\right)\) | \(e\left(\frac{64}{143}\right)\) |
| \(\chi_{2003}(16,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{81}{143}\right)\) | \(e\left(\frac{40}{143}\right)\) | \(e\left(\frac{19}{143}\right)\) | \(e\left(\frac{96}{143}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{82}{143}\right)\) | \(e\left(\frac{100}{143}\right)\) | \(e\left(\frac{80}{143}\right)\) | \(e\left(\frac{34}{143}\right)\) | \(e\left(\frac{128}{143}\right)\) |
| \(\chi_{2003}(42,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{15}{143}\right)\) | \(e\left(\frac{18}{143}\right)\) | \(e\left(\frac{30}{143}\right)\) | \(e\left(\frac{129}{143}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{137}{143}\right)\) | \(e\left(\frac{45}{143}\right)\) | \(e\left(\frac{36}{143}\right)\) | \(e\left(\frac{1}{143}\right)\) | \(e\left(\frac{29}{143}\right)\) |
| \(\chi_{2003}(46,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{143}\right)\) | \(e\left(\frac{64}{143}\right)\) | \(e\left(\frac{59}{143}\right)\) | \(e\left(\frac{125}{143}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{74}{143}\right)\) | \(e\left(\frac{17}{143}\right)\) | \(e\left(\frac{128}{143}\right)\) | \(e\left(\frac{83}{143}\right)\) | \(e\left(\frac{119}{143}\right)\) |
| \(\chi_{2003}(64,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{50}{143}\right)\) | \(e\left(\frac{60}{143}\right)\) | \(e\left(\frac{100}{143}\right)\) | \(e\left(\frac{1}{143}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{123}{143}\right)\) | \(e\left(\frac{7}{143}\right)\) | \(e\left(\frac{120}{143}\right)\) | \(e\left(\frac{51}{143}\right)\) | \(e\left(\frac{49}{143}\right)\) |
| \(\chi_{2003}(88,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{143}\right)\) | \(e\left(\frac{97}{143}\right)\) | \(e\left(\frac{114}{143}\right)\) | \(e\left(\frac{4}{143}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{63}{143}\right)\) | \(e\left(\frac{28}{143}\right)\) | \(e\left(\frac{51}{143}\right)\) | \(e\left(\frac{61}{143}\right)\) | \(e\left(\frac{53}{143}\right)\) |
| \(\chi_{2003}(90,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{100}{143}\right)\) | \(e\left(\frac{120}{143}\right)\) | \(e\left(\frac{57}{143}\right)\) | \(e\left(\frac{2}{143}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{103}{143}\right)\) | \(e\left(\frac{14}{143}\right)\) | \(e\left(\frac{97}{143}\right)\) | \(e\left(\frac{102}{143}\right)\) | \(e\left(\frac{98}{143}\right)\) |
| \(\chi_{2003}(113,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{143}\right)\) | \(e\left(\frac{128}{143}\right)\) | \(e\left(\frac{118}{143}\right)\) | \(e\left(\frac{107}{143}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{5}{143}\right)\) | \(e\left(\frac{34}{143}\right)\) | \(e\left(\frac{113}{143}\right)\) | \(e\left(\frac{23}{143}\right)\) | \(e\left(\frac{95}{143}\right)\) |
| \(\chi_{2003}(121,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{64}{143}\right)\) | \(e\left(\frac{134}{143}\right)\) | \(e\left(\frac{128}{143}\right)\) | \(e\left(\frac{7}{143}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{3}{143}\right)\) | \(e\left(\frac{49}{143}\right)\) | \(e\left(\frac{125}{143}\right)\) | \(e\left(\frac{71}{143}\right)\) | \(e\left(\frac{57}{143}\right)\) |
| \(\chi_{2003}(134,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{58}{143}\right)\) | \(e\left(\frac{41}{143}\right)\) | \(e\left(\frac{116}{143}\right)\) | \(e\left(\frac{127}{143}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{34}{143}\right)\) | \(e\left(\frac{31}{143}\right)\) | \(e\left(\frac{82}{143}\right)\) | \(e\left(\frac{42}{143}\right)\) | \(e\left(\frac{74}{143}\right)\) |
| \(\chi_{2003}(141,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{139}{143}\right)\) | \(e\left(\frac{81}{143}\right)\) | \(e\left(\frac{135}{143}\right)\) | \(e\left(\frac{80}{143}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{116}{143}\right)\) | \(e\left(\frac{131}{143}\right)\) | \(e\left(\frac{19}{143}\right)\) | \(e\left(\frac{76}{143}\right)\) | \(e\left(\frac{59}{143}\right)\) |
| \(\chi_{2003}(142,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{143}\right)\) | \(e\left(\frac{92}{143}\right)\) | \(e\left(\frac{58}{143}\right)\) | \(e\left(\frac{135}{143}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{17}{143}\right)\) | \(e\left(\frac{87}{143}\right)\) | \(e\left(\frac{41}{143}\right)\) | \(e\left(\frac{21}{143}\right)\) | \(e\left(\frac{37}{143}\right)\) |
| \(\chi_{2003}(155,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{143}\right)\) | \(e\left(\frac{105}{143}\right)\) | \(e\left(\frac{32}{143}\right)\) | \(e\left(\frac{109}{143}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{108}{143}\right)\) | \(e\left(\frac{48}{143}\right)\) | \(e\left(\frac{67}{143}\right)\) | \(e\left(\frac{125}{143}\right)\) | \(e\left(\frac{50}{143}\right)\) |
| \(\chi_{2003}(168,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{143}\right)\) | \(e\left(\frac{38}{143}\right)\) | \(e\left(\frac{111}{143}\right)\) | \(e\left(\frac{34}{143}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{35}{143}\right)\) | \(e\left(\frac{95}{143}\right)\) | \(e\left(\frac{76}{143}\right)\) | \(e\left(\frac{18}{143}\right)\) | \(e\left(\frac{93}{143}\right)\) |
| \(\chi_{2003}(174,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{143}\right)\) | \(e\left(\frac{109}{143}\right)\) | \(e\left(\frac{134}{143}\right)\) | \(e\left(\frac{90}{143}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{59}{143}\right)\) | \(e\left(\frac{58}{143}\right)\) | \(e\left(\frac{75}{143}\right)\) | \(e\left(\frac{14}{143}\right)\) | \(e\left(\frac{120}{143}\right)\) |
| \(\chi_{2003}(182,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{111}{143}\right)\) | \(e\left(\frac{76}{143}\right)\) | \(e\left(\frac{79}{143}\right)\) | \(e\left(\frac{68}{143}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{70}{143}\right)\) | \(e\left(\frac{47}{143}\right)\) | \(e\left(\frac{9}{143}\right)\) | \(e\left(\frac{36}{143}\right)\) | \(e\left(\frac{43}{143}\right)\) |
| \(\chi_{2003}(184,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{70}{143}\right)\) | \(e\left(\frac{84}{143}\right)\) | \(e\left(\frac{140}{143}\right)\) | \(e\left(\frac{30}{143}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{115}{143}\right)\) | \(e\left(\frac{67}{143}\right)\) | \(e\left(\frac{25}{143}\right)\) | \(e\left(\frac{100}{143}\right)\) | \(e\left(\frac{40}{143}\right)\) |
| \(\chi_{2003}(185,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{105}{143}\right)\) | \(e\left(\frac{126}{143}\right)\) | \(e\left(\frac{67}{143}\right)\) | \(e\left(\frac{45}{143}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{101}{143}\right)\) | \(e\left(\frac{29}{143}\right)\) | \(e\left(\frac{109}{143}\right)\) | \(e\left(\frac{7}{143}\right)\) | \(e\left(\frac{60}{143}\right)\) |
| \(\chi_{2003}(190,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{122}{143}\right)\) | \(e\left(\frac{32}{143}\right)\) | \(e\left(\frac{101}{143}\right)\) | \(e\left(\frac{134}{143}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{37}{143}\right)\) | \(e\left(\frac{80}{143}\right)\) | \(e\left(\frac{64}{143}\right)\) | \(e\left(\frac{113}{143}\right)\) | \(e\left(\frac{131}{143}\right)\) |
| \(\chi_{2003}(231,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{134}{143}\right)\) | \(e\left(\frac{75}{143}\right)\) | \(e\left(\frac{125}{143}\right)\) | \(e\left(\frac{37}{143}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{118}{143}\right)\) | \(e\left(\frac{116}{143}\right)\) | \(e\left(\frac{7}{143}\right)\) | \(e\left(\frac{28}{143}\right)\) | \(e\left(\frac{97}{143}\right)\) |
| \(\chi_{2003}(256,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{143}\right)\) | \(e\left(\frac{80}{143}\right)\) | \(e\left(\frac{38}{143}\right)\) | \(e\left(\frac{49}{143}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{21}{143}\right)\) | \(e\left(\frac{57}{143}\right)\) | \(e\left(\frac{17}{143}\right)\) | \(e\left(\frac{68}{143}\right)\) | \(e\left(\frac{113}{143}\right)\) |
| \(\chi_{2003}(298,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{48}{143}\right)\) | \(e\left(\frac{29}{143}\right)\) | \(e\left(\frac{96}{143}\right)\) | \(e\left(\frac{41}{143}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{38}{143}\right)\) | \(e\left(\frac{1}{143}\right)\) | \(e\left(\frac{58}{143}\right)\) | \(e\left(\frac{89}{143}\right)\) | \(e\left(\frac{7}{143}\right)\) |
| \(\chi_{2003}(356,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{68}{143}\right)\) | \(e\left(\frac{53}{143}\right)\) | \(e\left(\frac{136}{143}\right)\) | \(e\left(\frac{70}{143}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{30}{143}\right)\) | \(e\left(\frac{61}{143}\right)\) | \(e\left(\frac{106}{143}\right)\) | \(e\left(\frac{138}{143}\right)\) | \(e\left(\frac{141}{143}\right)\) |
| \(\chi_{2003}(360,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{69}{143}\right)\) | \(e\left(\frac{140}{143}\right)\) | \(e\left(\frac{138}{143}\right)\) | \(e\left(\frac{50}{143}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{1}{143}\right)\) | \(e\left(\frac{64}{143}\right)\) | \(e\left(\frac{137}{143}\right)\) | \(e\left(\frac{119}{143}\right)\) | \(e\left(\frac{19}{143}\right)\) |
| \(\chi_{2003}(390,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{143}\right)\) | \(e\left(\frac{35}{143}\right)\) | \(e\left(\frac{106}{143}\right)\) | \(e\left(\frac{84}{143}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{36}{143}\right)\) | \(e\left(\frac{16}{143}\right)\) | \(e\left(\frac{70}{143}\right)\) | \(e\left(\frac{137}{143}\right)\) | \(e\left(\frac{112}{143}\right)\) |
| \(\chi_{2003}(441,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{143}\right)\) | \(e\left(\frac{16}{143}\right)\) | \(e\left(\frac{122}{143}\right)\) | \(e\left(\frac{67}{143}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{90}{143}\right)\) | \(e\left(\frac{40}{143}\right)\) | \(e\left(\frac{32}{143}\right)\) | \(e\left(\frac{128}{143}\right)\) | \(e\left(\frac{137}{143}\right)\) |
| \(\chi_{2003}(452,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{28}{143}\right)\) | \(e\left(\frac{5}{143}\right)\) | \(e\left(\frac{56}{143}\right)\) | \(e\left(\frac{12}{143}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{46}{143}\right)\) | \(e\left(\frac{84}{143}\right)\) | \(e\left(\frac{10}{143}\right)\) | \(e\left(\frac{40}{143}\right)\) | \(e\left(\frac{16}{143}\right)\) |
| \(\chi_{2003}(477,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{143}\right)\) | \(e\left(\frac{2}{143}\right)\) | \(e\left(\frac{51}{143}\right)\) | \(e\left(\frac{62}{143}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{47}{143}\right)\) | \(e\left(\frac{5}{143}\right)\) | \(e\left(\frac{4}{143}\right)\) | \(e\left(\frac{16}{143}\right)\) | \(e\left(\frac{35}{143}\right)\) |
| \(\chi_{2003}(478,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{86}{143}\right)\) | \(e\left(\frac{46}{143}\right)\) | \(e\left(\frac{29}{143}\right)\) | \(e\left(\frac{139}{143}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{80}{143}\right)\) | \(e\left(\frac{115}{143}\right)\) | \(e\left(\frac{92}{143}\right)\) | \(e\left(\frac{82}{143}\right)\) | \(e\left(\frac{90}{143}\right)\) |
| \(\chi_{2003}(479,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{42}{143}\right)\) | \(e\left(\frac{79}{143}\right)\) | \(e\left(\frac{84}{143}\right)\) | \(e\left(\frac{18}{143}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{69}{143}\right)\) | \(e\left(\frac{126}{143}\right)\) | \(e\left(\frac{15}{143}\right)\) | \(e\left(\frac{60}{143}\right)\) | \(e\left(\frac{24}{143}\right)\) |
| \(\chi_{2003}(483,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{143}\right)\) | \(e\left(\frac{62}{143}\right)\) | \(e\left(\frac{8}{143}\right)\) | \(e\left(\frac{63}{143}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{27}{143}\right)\) | \(e\left(\frac{12}{143}\right)\) | \(e\left(\frac{124}{143}\right)\) | \(e\left(\frac{67}{143}\right)\) | \(e\left(\frac{84}{143}\right)\) |