from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(683, base_ring=CyclotomicField(62))
M = H._module
chi = DirichletCharacter(H, M([30]))
chi.galois_orbit()
[g,chi] = znchar(Mod(3,683))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(683\) | |
Conductor: | \(683\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(31\) | 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: | $\Q(\zeta_{31})$ |
Fixed field: | Number field defined by a degree 31 polynomial |
First 30 of 30 characters in Galois orbit
Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{683}(3,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{21}{31}\right)\) | \(1\) | \(e\left(\frac{15}{31}\right)\) | \(e\left(\frac{21}{31}\right)\) | \(e\left(\frac{7}{31}\right)\) | \(1\) | \(e\left(\frac{11}{31}\right)\) | \(e\left(\frac{15}{31}\right)\) | \(e\left(\frac{28}{31}\right)\) |
\(\chi_{683}(9,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{11}{31}\right)\) | \(1\) | \(e\left(\frac{30}{31}\right)\) | \(e\left(\frac{11}{31}\right)\) | \(e\left(\frac{14}{31}\right)\) | \(1\) | \(e\left(\frac{22}{31}\right)\) | \(e\left(\frac{30}{31}\right)\) | \(e\left(\frac{25}{31}\right)\) |
\(\chi_{683}(27,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{31}\right)\) | \(1\) | \(e\left(\frac{14}{31}\right)\) | \(e\left(\frac{1}{31}\right)\) | \(e\left(\frac{21}{31}\right)\) | \(1\) | \(e\left(\frac{2}{31}\right)\) | \(e\left(\frac{14}{31}\right)\) | \(e\left(\frac{22}{31}\right)\) |
\(\chi_{683}(46,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{31}\right)\) | \(1\) | \(e\left(\frac{28}{31}\right)\) | \(e\left(\frac{2}{31}\right)\) | \(e\left(\frac{11}{31}\right)\) | \(1\) | \(e\left(\frac{4}{31}\right)\) | \(e\left(\frac{28}{31}\right)\) | \(e\left(\frac{13}{31}\right)\) |
\(\chi_{683}(67,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{4}{31}\right)\) | \(1\) | \(e\left(\frac{25}{31}\right)\) | \(e\left(\frac{4}{31}\right)\) | \(e\left(\frac{22}{31}\right)\) | \(1\) | \(e\left(\frac{8}{31}\right)\) | \(e\left(\frac{25}{31}\right)\) | \(e\left(\frac{26}{31}\right)\) |
\(\chi_{683}(76,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{20}{31}\right)\) | \(1\) | \(e\left(\frac{1}{31}\right)\) | \(e\left(\frac{20}{31}\right)\) | \(e\left(\frac{17}{31}\right)\) | \(1\) | \(e\left(\frac{9}{31}\right)\) | \(e\left(\frac{1}{31}\right)\) | \(e\left(\frac{6}{31}\right)\) |
\(\chi_{683}(81,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{22}{31}\right)\) | \(1\) | \(e\left(\frac{29}{31}\right)\) | \(e\left(\frac{22}{31}\right)\) | \(e\left(\frac{28}{31}\right)\) | \(1\) | \(e\left(\frac{13}{31}\right)\) | \(e\left(\frac{29}{31}\right)\) | \(e\left(\frac{19}{31}\right)\) |
\(\chi_{683}(104,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{19}{31}\right)\) | \(1\) | \(e\left(\frac{18}{31}\right)\) | \(e\left(\frac{19}{31}\right)\) | \(e\left(\frac{27}{31}\right)\) | \(1\) | \(e\left(\frac{7}{31}\right)\) | \(e\left(\frac{18}{31}\right)\) | \(e\left(\frac{15}{31}\right)\) |
\(\chi_{683}(138,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{23}{31}\right)\) | \(1\) | \(e\left(\frac{12}{31}\right)\) | \(e\left(\frac{23}{31}\right)\) | \(e\left(\frac{18}{31}\right)\) | \(1\) | \(e\left(\frac{15}{31}\right)\) | \(e\left(\frac{12}{31}\right)\) | \(e\left(\frac{10}{31}\right)\) |
\(\chi_{683}(201,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{25}{31}\right)\) | \(1\) | \(e\left(\frac{9}{31}\right)\) | \(e\left(\frac{25}{31}\right)\) | \(e\left(\frac{29}{31}\right)\) | \(1\) | \(e\left(\frac{19}{31}\right)\) | \(e\left(\frac{9}{31}\right)\) | \(e\left(\frac{23}{31}\right)\) |
\(\chi_{683}(228,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{10}{31}\right)\) | \(1\) | \(e\left(\frac{16}{31}\right)\) | \(e\left(\frac{10}{31}\right)\) | \(e\left(\frac{24}{31}\right)\) | \(1\) | \(e\left(\frac{20}{31}\right)\) | \(e\left(\frac{16}{31}\right)\) | \(e\left(\frac{3}{31}\right)\) |
\(\chi_{683}(243,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{12}{31}\right)\) | \(1\) | \(e\left(\frac{13}{31}\right)\) | \(e\left(\frac{12}{31}\right)\) | \(e\left(\frac{4}{31}\right)\) | \(1\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{13}{31}\right)\) | \(e\left(\frac{16}{31}\right)\) |
\(\chi_{683}(250,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{14}{31}\right)\) | \(1\) | \(e\left(\frac{10}{31}\right)\) | \(e\left(\frac{14}{31}\right)\) | \(e\left(\frac{15}{31}\right)\) | \(1\) | \(e\left(\frac{28}{31}\right)\) | \(e\left(\frac{10}{31}\right)\) | \(e\left(\frac{29}{31}\right)\) |
\(\chi_{683}(253,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{30}{31}\right)\) | \(1\) | \(e\left(\frac{17}{31}\right)\) | \(e\left(\frac{30}{31}\right)\) | \(e\left(\frac{10}{31}\right)\) | \(1\) | \(e\left(\frac{29}{31}\right)\) | \(e\left(\frac{17}{31}\right)\) | \(e\left(\frac{9}{31}\right)\) |
\(\chi_{683}(311,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{24}{31}\right)\) | \(1\) | \(e\left(\frac{26}{31}\right)\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{8}{31}\right)\) | \(1\) | \(e\left(\frac{17}{31}\right)\) | \(e\left(\frac{26}{31}\right)\) | \(e\left(\frac{1}{31}\right)\) |
\(\chi_{683}(312,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{9}{31}\right)\) | \(1\) | \(e\left(\frac{2}{31}\right)\) | \(e\left(\frac{9}{31}\right)\) | \(e\left(\frac{3}{31}\right)\) | \(1\) | \(e\left(\frac{18}{31}\right)\) | \(e\left(\frac{2}{31}\right)\) | \(e\left(\frac{12}{31}\right)\) |
\(\chi_{683}(347,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{28}{31}\right)\) | \(1\) | \(e\left(\frac{20}{31}\right)\) | \(e\left(\frac{28}{31}\right)\) | \(e\left(\frac{30}{31}\right)\) | \(1\) | \(e\left(\frac{25}{31}\right)\) | \(e\left(\frac{20}{31}\right)\) | \(e\left(\frac{27}{31}\right)\) |
\(\chi_{683}(350,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{6}{31}\right)\) | \(1\) | \(e\left(\frac{22}{31}\right)\) | \(e\left(\frac{6}{31}\right)\) | \(e\left(\frac{2}{31}\right)\) | \(1\) | \(e\left(\frac{12}{31}\right)\) | \(e\left(\frac{22}{31}\right)\) | \(e\left(\frac{8}{31}\right)\) |
\(\chi_{683}(358,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{18}{31}\right)\) | \(1\) | \(e\left(\frac{4}{31}\right)\) | \(e\left(\frac{18}{31}\right)\) | \(e\left(\frac{6}{31}\right)\) | \(1\) | \(e\left(\frac{5}{31}\right)\) | \(e\left(\frac{4}{31}\right)\) | \(e\left(\frac{24}{31}\right)\) |
\(\chi_{683}(367,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{27}{31}\right)\) | \(1\) | \(e\left(\frac{6}{31}\right)\) | \(e\left(\frac{27}{31}\right)\) | \(e\left(\frac{9}{31}\right)\) | \(1\) | \(e\left(\frac{23}{31}\right)\) | \(e\left(\frac{6}{31}\right)\) | \(e\left(\frac{5}{31}\right)\) |
\(\chi_{683}(391,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{8}{31}\right)\) | \(1\) | \(e\left(\frac{19}{31}\right)\) | \(e\left(\frac{8}{31}\right)\) | \(e\left(\frac{13}{31}\right)\) | \(1\) | \(e\left(\frac{16}{31}\right)\) | \(e\left(\frac{19}{31}\right)\) | \(e\left(\frac{21}{31}\right)\) |
\(\chi_{683}(414,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{13}{31}\right)\) | \(1\) | \(e\left(\frac{27}{31}\right)\) | \(e\left(\frac{13}{31}\right)\) | \(e\left(\frac{25}{31}\right)\) | \(1\) | \(e\left(\frac{26}{31}\right)\) | \(e\left(\frac{27}{31}\right)\) | \(e\left(\frac{7}{31}\right)\) |
\(\chi_{683}(418,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{17}{31}\right)\) | \(1\) | \(e\left(\frac{21}{31}\right)\) | \(e\left(\frac{17}{31}\right)\) | \(e\left(\frac{16}{31}\right)\) | \(1\) | \(e\left(\frac{3}{31}\right)\) | \(e\left(\frac{21}{31}\right)\) | \(e\left(\frac{2}{31}\right)\) |
\(\chi_{683}(443,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{5}{31}\right)\) | \(1\) | \(e\left(\frac{8}{31}\right)\) | \(e\left(\frac{5}{31}\right)\) | \(e\left(\frac{12}{31}\right)\) | \(1\) | \(e\left(\frac{10}{31}\right)\) | \(e\left(\frac{8}{31}\right)\) | \(e\left(\frac{17}{31}\right)\) |
\(\chi_{683}(490,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{29}{31}\right)\) | \(1\) | \(e\left(\frac{3}{31}\right)\) | \(e\left(\frac{29}{31}\right)\) | \(e\left(\frac{20}{31}\right)\) | \(1\) | \(e\left(\frac{27}{31}\right)\) | \(e\left(\frac{3}{31}\right)\) | \(e\left(\frac{18}{31}\right)\) |
\(\chi_{683}(559,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{3}{31}\right)\) | \(1\) | \(e\left(\frac{11}{31}\right)\) | \(e\left(\frac{3}{31}\right)\) | \(e\left(\frac{1}{31}\right)\) | \(1\) | \(e\left(\frac{6}{31}\right)\) | \(e\left(\frac{11}{31}\right)\) | \(e\left(\frac{4}{31}\right)\) |
\(\chi_{683}(571,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{7}{31}\right)\) | \(1\) | \(e\left(\frac{5}{31}\right)\) | \(e\left(\frac{7}{31}\right)\) | \(e\left(\frac{23}{31}\right)\) | \(1\) | \(e\left(\frac{14}{31}\right)\) | \(e\left(\frac{5}{31}\right)\) | \(e\left(\frac{30}{31}\right)\) |
\(\chi_{683}(572,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{16}{31}\right)\) | \(1\) | \(e\left(\frac{7}{31}\right)\) | \(e\left(\frac{16}{31}\right)\) | \(e\left(\frac{26}{31}\right)\) | \(1\) | \(e\left(\frac{1}{31}\right)\) | \(e\left(\frac{7}{31}\right)\) | \(e\left(\frac{11}{31}\right)\) |
\(\chi_{683}(603,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{15}{31}\right)\) | \(1\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{15}{31}\right)\) | \(e\left(\frac{5}{31}\right)\) | \(1\) | \(e\left(\frac{30}{31}\right)\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{20}{31}\right)\) |
\(\chi_{683}(646,\cdot)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{26}{31}\right)\) | \(1\) | \(e\left(\frac{23}{31}\right)\) | \(e\left(\frac{26}{31}\right)\) | \(e\left(\frac{19}{31}\right)\) | \(1\) | \(e\left(\frac{21}{31}\right)\) | \(e\left(\frac{23}{31}\right)\) | \(e\left(\frac{14}{31}\right)\) |