from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, base_ring=CyclotomicField(130))
M = H._module
chi = DirichletCharacter(H, M([13,1]))
chi.galois_orbit()
[g,chi] = znchar(Mod(2,1441))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(1441\) | |
Conductor: | \(1441\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(130\) | 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: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
First 31 of 48 characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1441}(2,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{37}{65}\right)\) |
\(\chi_{1441}(8,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{41}{130}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) |
\(\chi_{1441}(90,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{97}{130}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{47}{65}\right)\) |
\(\chi_{1441}(106,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{109}{130}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{24}{65}\right)\) |
\(\chi_{1441}(118,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{16}{65}\right)\) |
\(\chi_{1441}(128,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{9}{130}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{64}{65}\right)\) |
\(\chi_{1441}(171,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{63}{130}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) |
\(\chi_{1441}(227,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{54}{65}\right)\) |
\(\chi_{1441}(255,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{77}{130}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) |
\(\chi_{1441}(292,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{48}{65}\right)\) |
\(\chi_{1441}(299,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{22}{65}\right)\) |
\(\chi_{1441}(347,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{3}{130}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{43}{65}\right)\) |
\(\chi_{1441}(349,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{121}{130}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{1}{65}\right)\) |
\(\chi_{1441}(360,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{81}{130}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{56}{65}\right)\) |
\(\chi_{1441}(403,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) |
\(\chi_{1441}(424,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{93}{130}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{33}{65}\right)\) |
\(\chi_{1441}(447,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{19}{130}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) |
\(\chi_{1441}(469,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{29}{130}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{4}{65}\right)\) |
\(\chi_{1441}(486,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{37}{130}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{32}{65}\right)\) |
\(\chi_{1441}(490,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) |
\(\chi_{1441}(497,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{62}{65}\right)\) |
\(\chi_{1441}(503,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{21}{130}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) |
\(\chi_{1441}(512,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{8}{65}\right)\) |
\(\chi_{1441}(519,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{87}{130}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) |
\(\chi_{1441}(546,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{129}{130}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{29}{65}\right)\) |
\(\chi_{1441}(547,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{6}{65}\right)\) |
\(\chi_{1441}(607,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{107}{130}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) |
\(\chi_{1441}(635,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{71}{130}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{21}{65}\right)\) |
\(\chi_{1441}(684,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{47}{130}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{2}{65}\right)\) |
\(\chi_{1441}(721,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{28}{65}\right)\) |
\(\chi_{1441}(743,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{38}{65}\right)\) |