Basic properties
| Modulus: | \(2793\) | |
| Conductor: | \(2793\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 2793.eo
\(\chi_{2793}(137,\cdot)\) \(\chi_{2793}(149,\cdot)\) \(\chi_{2793}(158,\cdot)\) \(\chi_{2793}(233,\cdot)\) \(\chi_{2793}(359,\cdot)\) \(\chi_{2793}(389,\cdot)\) \(\chi_{2793}(536,\cdot)\) \(\chi_{2793}(548,\cdot)\) \(\chi_{2793}(632,\cdot)\) \(\chi_{2793}(758,\cdot)\) \(\chi_{2793}(788,\cdot)\) \(\chi_{2793}(935,\cdot)\) \(\chi_{2793}(947,\cdot)\) \(\chi_{2793}(956,\cdot)\) \(\chi_{2793}(1031,\cdot)\) \(\chi_{2793}(1187,\cdot)\) \(\chi_{2793}(1334,\cdot)\) \(\chi_{2793}(1346,\cdot)\) \(\chi_{2793}(1355,\cdot)\) \(\chi_{2793}(1430,\cdot)\) \(\chi_{2793}(1556,\cdot)\) \(\chi_{2793}(1754,\cdot)\) \(\chi_{2793}(1829,\cdot)\) \(\chi_{2793}(1955,\cdot)\) \(\chi_{2793}(1985,\cdot)\) \(\chi_{2793}(2132,\cdot)\) \(\chi_{2793}(2144,\cdot)\) \(\chi_{2793}(2153,\cdot)\) \(\chi_{2793}(2228,\cdot)\) \(\chi_{2793}(2354,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((932,2110,2206)\) → \((-1,e\left(\frac{16}{21}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 2793 }(233, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{55}{126}\right)\) | \(e\left(\frac{3}{14}\right)\) |