from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, base_ring=CyclotomicField(130))
M = H._module
chi = DirichletCharacter(H, M([78,48]))
chi.galois_orbit()
[g,chi] = znchar(Mod(20,1441))
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: | \(65\) | 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 65 polynomial |
First 31 of 48 characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1441}(20,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{21}{65}\right)\) |
\(\chi_{1441}(48,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) |
\(\chi_{1441}(49,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{19}{65}\right)\) |
\(\chi_{1441}(91,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) |
\(\chi_{1441}(108,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{6}{65}\right)\) |
\(\chi_{1441}(136,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) |
\(\chi_{1441}(152,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) |
\(\chi_{1441}(158,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{62}{65}\right)\) |
\(\chi_{1441}(169,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{32}{65}\right)\) |
\(\chi_{1441}(278,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{18}{65}\right)\) |
\(\chi_{1441}(295,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{56}{65}\right)\) |
\(\chi_{1441}(306,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{1}{65}\right)\) |
\(\chi_{1441}(356,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{22}{65}\right)\) |
\(\chi_{1441}(379,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{14}{65}\right)\) |
\(\chi_{1441}(400,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) |
\(\chi_{1441}(467,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{59}{65}\right)\) |
\(\chi_{1441}(498,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{53}{65}\right)\) |
\(\chi_{1441}(537,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{16}{65}\right)\) |
\(\chi_{1441}(565,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{47}{65}\right)\) |
\(\chi_{1441}(647,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) |
\(\chi_{1441}(653,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{37}{65}\right)\) |
\(\chi_{1441}(719,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{27}{65}\right)\) |
\(\chi_{1441}(764,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{29}{65}\right)\) |
\(\chi_{1441}(795,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{63}{65}\right)\) |
\(\chi_{1441}(801,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) |
\(\chi_{1441}(841,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{4}{65}\right)\) |
\(\chi_{1441}(861,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) |
\(\chi_{1441}(863,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) |
\(\chi_{1441}(867,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{61}{65}\right)\) |
\(\chi_{1441}(900,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) |
\(\chi_{1441}(907,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) |