Basic properties
| Modulus: | \(8024\) | |
| Conductor: | \(4012\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(464\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4012}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8024.cx
\(\chi_{8024}(23,\cdot)\) \(\chi_{8024}(31,\cdot)\) \(\chi_{8024}(39,\cdot)\) \(\chi_{8024}(207,\cdot)\) \(\chi_{8024}(215,\cdot)\) \(\chi_{8024}(231,\cdot)\) \(\chi_{8024}(279,\cdot)\) \(\chi_{8024}(303,\cdot)\) \(\chi_{8024}(335,\cdot)\) \(\chi_{8024}(351,\cdot)\) \(\chi_{8024}(367,\cdot)\) \(\chi_{8024}(415,\cdot)\) \(\chi_{8024}(431,\cdot)\) \(\chi_{8024}(447,\cdot)\) \(\chi_{8024}(503,\cdot)\) \(\chi_{8024}(575,\cdot)\) \(\chi_{8024}(583,\cdot)\) \(\chi_{8024}(623,\cdot)\) \(\chi_{8024}(687,\cdot)\) \(\chi_{8024}(703,\cdot)\) \(\chi_{8024}(719,\cdot)\) \(\chi_{8024}(751,\cdot)\) \(\chi_{8024}(775,\cdot)\) \(\chi_{8024}(823,\cdot)\) \(\chi_{8024}(839,\cdot)\) \(\chi_{8024}(887,\cdot)\) \(\chi_{8024}(895,\cdot)\) \(\chi_{8024}(975,\cdot)\) \(\chi_{8024}(983,\cdot)\) \(\chi_{8024}(991,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{464})$ |
| Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((-1,1,e\left(\frac{15}{16}\right),e\left(\frac{15}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8024 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{171}{464}\right)\) | \(e\left(\frac{111}{464}\right)\) | \(e\left(\frac{217}{464}\right)\) | \(e\left(\frac{171}{232}\right)\) | \(e\left(\frac{245}{464}\right)\) | \(e\left(\frac{45}{116}\right)\) | \(e\left(\frac{141}{232}\right)\) | \(e\left(\frac{105}{232}\right)\) | \(e\left(\frac{97}{116}\right)\) | \(e\left(\frac{205}{464}\right)\) |