Basic properties
| Modulus: | \(7168\) | |
| Conductor: | \(7168\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(768\) | 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 7168.cr
\(\chi_{7168}(3,\cdot)\) \(\chi_{7168}(19,\cdot)\) \(\chi_{7168}(59,\cdot)\) \(\chi_{7168}(75,\cdot)\) \(\chi_{7168}(115,\cdot)\) \(\chi_{7168}(131,\cdot)\) \(\chi_{7168}(171,\cdot)\) \(\chi_{7168}(187,\cdot)\) \(\chi_{7168}(227,\cdot)\) \(\chi_{7168}(243,\cdot)\) \(\chi_{7168}(283,\cdot)\) \(\chi_{7168}(299,\cdot)\) \(\chi_{7168}(339,\cdot)\) \(\chi_{7168}(355,\cdot)\) \(\chi_{7168}(395,\cdot)\) \(\chi_{7168}(411,\cdot)\) \(\chi_{7168}(451,\cdot)\) \(\chi_{7168}(467,\cdot)\) \(\chi_{7168}(507,\cdot)\) \(\chi_{7168}(523,\cdot)\) \(\chi_{7168}(563,\cdot)\) \(\chi_{7168}(579,\cdot)\) \(\chi_{7168}(619,\cdot)\) \(\chi_{7168}(635,\cdot)\) \(\chi_{7168}(675,\cdot)\) \(\chi_{7168}(691,\cdot)\) \(\chi_{7168}(731,\cdot)\) \(\chi_{7168}(747,\cdot)\) \(\chi_{7168}(787,\cdot)\) \(\chi_{7168}(803,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{768})$ |
| Fixed field: | Number field defined by a degree 768 polynomial (not computed) |
Values on generators
\((1023,5125,1025)\) → \((-1,e\left(\frac{163}{256}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 7168 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{347}{768}\right)\) | \(e\left(\frac{361}{768}\right)\) | \(e\left(\frac{347}{384}\right)\) | \(e\left(\frac{605}{768}\right)\) | \(e\left(\frac{173}{256}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{95}{192}\right)\) | \(e\left(\frac{367}{768}\right)\) | \(e\left(\frac{95}{384}\right)\) | \(e\left(\frac{361}{384}\right)\) |