from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2450, base_ring=CyclotomicField(70))
M = H._module
chi = DirichletCharacter(H, M([42,40]))
chi.galois_orbit()
[g,chi] = znchar(Mod(71,2450))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(2450\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 1225.bd | 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: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Characters in Galois orbit
Character | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{2450}(71,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{2450}(141,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{2450}(211,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{2450}(281,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{2450}(421,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{2450}(561,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{2450}(631,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{2450}(771,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{2450}(841,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{2450}(911,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{2450}(1121,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{2450}(1191,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{2450}(1261,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{2450}(1331,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{2450}(1541,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{2450}(1611,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{2450}(1681,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{2450}(1821,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{2450}(1891,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{2450}(2031,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{2450}(2171,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{2450}(2241,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{2450}(2311,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{2450}(2381,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) |