Basic properties
Modulus: | \(1323\) | |
Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(63\) | 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)
|
Galois orbit 1323.cc
\(\chi_{1323}(4,\cdot)\) \(\chi_{1323}(16,\cdot)\) \(\chi_{1323}(130,\cdot)\) \(\chi_{1323}(142,\cdot)\) \(\chi_{1323}(193,\cdot)\) \(\chi_{1323}(205,\cdot)\) \(\chi_{1323}(256,\cdot)\) \(\chi_{1323}(268,\cdot)\) \(\chi_{1323}(319,\cdot)\) \(\chi_{1323}(331,\cdot)\) \(\chi_{1323}(382,\cdot)\) \(\chi_{1323}(394,\cdot)\) \(\chi_{1323}(445,\cdot)\) \(\chi_{1323}(457,\cdot)\) \(\chi_{1323}(571,\cdot)\) \(\chi_{1323}(583,\cdot)\) \(\chi_{1323}(634,\cdot)\) \(\chi_{1323}(646,\cdot)\) \(\chi_{1323}(697,\cdot)\) \(\chi_{1323}(709,\cdot)\) \(\chi_{1323}(760,\cdot)\) \(\chi_{1323}(772,\cdot)\) \(\chi_{1323}(823,\cdot)\) \(\chi_{1323}(835,\cdot)\) \(\chi_{1323}(886,\cdot)\) \(\chi_{1323}(898,\cdot)\) \(\chi_{1323}(1012,\cdot)\) \(\chi_{1323}(1024,\cdot)\) \(\chi_{1323}(1075,\cdot)\) \(\chi_{1323}(1087,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((785,1081)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{10}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1323 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) |