from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4608, base_ring=CyclotomicField(64))
M = H._module
chi = DirichletCharacter(H, M([32,43,0]))
chi.galois_orbit()
[g,chi] = znchar(Mod(55,4608))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
Modulus: | \(4608\) | |
Conductor: | \(256\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from 256.n | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
First 31 of 32 characters in Galois orbit
Character | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{4608}(55,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{4608}(199,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{4608}(343,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{47}{64}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{25}{64}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{21}{64}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{4608}(487,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{47}{64}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{4608}(631,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{4608}(775,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{4608}(919,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{35}{64}\right)\) | \(e\left(\frac{25}{64}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{4608}(1063,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{47}{64}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{4608}(1207,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{21}{64}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{25}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{4608}(1351,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{35}{64}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{63}{64}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{4608}(1495,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{63}{64}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{4608}(1639,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{31}{64}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{4608}(1783,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{31}{64}\right)\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{4608}(1927,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{21}{64}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{25}{64}\right)\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{4608}(2071,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{4608}(2215,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{25}{64}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{31}{64}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{4608}(2359,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{4608}(2503,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{47}{64}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{4608}(2647,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{4608}(2791,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{21}{64}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{4608}(2935,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{47}{64}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{21}{64}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{4608}(3079,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{4608}(3223,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{4608}(3367,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{4608}(3511,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{4608}(3655,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{31}{64}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{4608}(3799,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{64}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{4608}(3943,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{63}{64}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{4608}(4087,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{35}{64}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{63}{64}\right)\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{4608}(4231,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{35}{64}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{4608}(4375,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{41}{64}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{3}{8}\right)\) |