Basic properties
| Modulus: | \(12675\) | |
| Conductor: | \(12675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(780\) | 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 12675.fv
\(\chi_{12675}(17,\cdot)\) \(\chi_{12675}(62,\cdot)\) \(\chi_{12675}(173,\cdot)\) \(\chi_{12675}(212,\cdot)\) \(\chi_{12675}(413,\cdot)\) \(\chi_{12675}(452,\cdot)\) \(\chi_{12675}(563,\cdot)\) \(\chi_{12675}(602,\cdot)\) \(\chi_{12675}(608,\cdot)\) \(\chi_{12675}(647,\cdot)\) \(\chi_{12675}(758,\cdot)\) \(\chi_{12675}(797,\cdot)\) \(\chi_{12675}(803,\cdot)\) \(\chi_{12675}(842,\cdot)\) \(\chi_{12675}(953,\cdot)\) \(\chi_{12675}(998,\cdot)\) \(\chi_{12675}(1148,\cdot)\) \(\chi_{12675}(1187,\cdot)\) \(\chi_{12675}(1388,\cdot)\) \(\chi_{12675}(1427,\cdot)\) \(\chi_{12675}(1538,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{780})$ |
| Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((4226,9127,12001)\) → \((-1,e\left(\frac{9}{20}\right),e\left(\frac{11}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 12675 }(62, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{780}\right)\) | \(e\left(\frac{71}{390}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{71}{260}\right)\) | \(e\left(\frac{44}{195}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{71}{195}\right)\) | \(e\left(\frac{733}{780}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) |