from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(114))
M = H._module
chi = DirichletCharacter(H, M([76,42]))
chi.galois_orbit()
[g,chi] = znchar(Mod(39,5054))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(5054\) | |
Conductor: | \(2527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(57\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 2527.bm | 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: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
First 31 of 36 characters in Galois orbit
Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{5054}(39,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{12}{19}\right)\) |
\(\chi_{5054}(191,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{3}{19}\right)\) |
\(\chi_{5054}(305,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{1}{19}\right)\) |
\(\chi_{5054}(457,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{11}{19}\right)\) |
\(\chi_{5054}(571,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{9}{19}\right)\) |
\(\chi_{5054}(837,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{17}{19}\right)\) |
\(\chi_{5054}(989,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{8}{19}\right)\) |
\(\chi_{5054}(1103,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{6}{19}\right)\) |
\(\chi_{5054}(1255,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{16}{19}\right)\) |
\(\chi_{5054}(1369,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{14}{19}\right)\) |
\(\chi_{5054}(1521,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{5}{19}\right)\) |
\(\chi_{5054}(1635,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{3}{19}\right)\) |
\(\chi_{5054}(1787,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{13}{19}\right)\) |
\(\chi_{5054}(1901,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{11}{19}\right)\) |
\(\chi_{5054}(2053,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{2}{19}\right)\) |
\(\chi_{5054}(2319,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{10}{19}\right)\) |
\(\chi_{5054}(2433,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{8}{19}\right)\) |
\(\chi_{5054}(2585,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{18}{19}\right)\) |
\(\chi_{5054}(2699,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{16}{19}\right)\) |
\(\chi_{5054}(2851,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{7}{19}\right)\) |
\(\chi_{5054}(2965,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{5}{19}\right)\) |
\(\chi_{5054}(3117,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{15}{19}\right)\) |
\(\chi_{5054}(3231,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{13}{19}\right)\) |
\(\chi_{5054}(3383,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{43}{57}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{4}{19}\right)\) |
\(\chi_{5054}(3497,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{53}{57}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{2}{19}\right)\) |
\(\chi_{5054}(3649,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{12}{19}\right)\) |
\(\chi_{5054}(3763,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{10}{19}\right)\) |
\(\chi_{5054}(3915,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{25}{57}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{1}{19}\right)\) |
\(\chi_{5054}(4029,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{18}{19}\right)\) |
\(\chi_{5054}(4181,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{9}{19}\right)\) |
\(\chi_{5054}(4295,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{7}{19}\right)\) |