Basic properties
| Modulus: | \(14365\) | |
| Conductor: | \(14365\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(624\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 14365.jw
\(\chi_{14365}(7,\cdot)\) \(\chi_{14365}(158,\cdot)\) \(\chi_{14365}(232,\cdot)\) \(\chi_{14365}(318,\cdot)\) \(\chi_{14365}(397,\cdot)\) \(\chi_{14365}(513,\cdot)\) \(\chi_{14365}(622,\cdot)\) \(\chi_{14365}(643,\cdot)\) \(\chi_{14365}(687,\cdot)\) \(\chi_{14365}(743,\cdot)\) \(\chi_{14365}(838,\cdot)\) \(\chi_{14365}(938,\cdot)\) \(\chi_{14365}(1047,\cdot)\) \(\chi_{14365}(1068,\cdot)\) \(\chi_{14365}(1077,\cdot)\) \(\chi_{14365}(1112,\cdot)\) \(\chi_{14365}(1337,\cdot)\) \(\chi_{14365}(1423,\cdot)\) \(\chi_{14365}(1618,\cdot)\) \(\chi_{14365}(1727,\cdot)\) \(\chi_{14365}(1748,\cdot)\) \(\chi_{14365}(1762,\cdot)\) \(\chi_{14365}(1792,\cdot)\) \(\chi_{14365}(1848,\cdot)\) \(\chi_{14365}(1943,\cdot)\) \(\chi_{14365}(2043,\cdot)\) \(\chi_{14365}(2152,\cdot)\) \(\chi_{14365}(2173,\cdot)\) \(\chi_{14365}(2182,\cdot)\) \(\chi_{14365}(2217,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((5747,171,2536)\) → \((i,e\left(\frac{131}{156}\right),e\left(\frac{11}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 14365 }(6637, a) \) | \(-1\) | \(1\) | \(e\left(\frac{223}{312}\right)\) | \(e\left(\frac{353}{624}\right)\) | \(e\left(\frac{67}{156}\right)\) | \(e\left(\frac{175}{624}\right)\) | \(e\left(\frac{415}{624}\right)\) | \(e\left(\frac{15}{104}\right)\) | \(e\left(\frac{41}{312}\right)\) | \(e\left(\frac{191}{624}\right)\) | \(e\left(\frac{207}{208}\right)\) | \(e\left(\frac{79}{208}\right)\) |