Basic properties
Modulus: | \(7803\) | |
Conductor: | \(7803\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2448\) | 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 7803.cg
\(\chi_{7803}(5,\cdot)\) \(\chi_{7803}(11,\cdot)\) \(\chi_{7803}(14,\cdot)\) \(\chi_{7803}(20,\cdot)\) \(\chi_{7803}(23,\cdot)\) \(\chi_{7803}(29,\cdot)\) \(\chi_{7803}(41,\cdot)\) \(\chi_{7803}(56,\cdot)\) \(\chi_{7803}(74,\cdot)\) \(\chi_{7803}(92,\cdot)\) \(\chi_{7803}(95,\cdot)\) \(\chi_{7803}(113,\cdot)\) \(\chi_{7803}(122,\cdot)\) \(\chi_{7803}(146,\cdot)\) \(\chi_{7803}(164,\cdot)\) \(\chi_{7803}(167,\cdot)\) \(\chi_{7803}(173,\cdot)\) \(\chi_{7803}(176,\cdot)\) \(\chi_{7803}(182,\cdot)\) \(\chi_{7803}(194,\cdot)\) \(\chi_{7803}(209,\cdot)\) \(\chi_{7803}(218,\cdot)\) \(\chi_{7803}(227,\cdot)\) \(\chi_{7803}(245,\cdot)\) \(\chi_{7803}(248,\cdot)\) \(\chi_{7803}(266,\cdot)\) \(\chi_{7803}(275,\cdot)\) \(\chi_{7803}(284,\cdot)\) \(\chi_{7803}(299,\cdot)\) \(\chi_{7803}(311,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{2448})$ |
Fixed field: | Number field defined by a degree 2448 polynomial (not computed) |
Values on generators
\((2891,2026)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{229}{272}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 7803 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{295}{1224}\right)\) | \(e\left(\frac{295}{612}\right)\) | \(e\left(\frac{457}{2448}\right)\) | \(e\left(\frac{2303}{2448}\right)\) | \(e\left(\frac{295}{408}\right)\) | \(e\left(\frac{349}{816}\right)\) | \(e\left(\frac{2387}{2448}\right)\) | \(e\left(\frac{145}{612}\right)\) | \(e\left(\frac{445}{2448}\right)\) | \(e\left(\frac{295}{306}\right)\) |