Basic properties
| Modulus: | \(8002\) | |
| Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(800\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4001}(39,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8002.u
\(\chi_{8002}(39,\cdot)\) \(\chi_{8002}(53,\cdot)\) \(\chi_{8002}(55,\cdot)\) \(\chi_{8002}(73,\cdot)\) \(\chi_{8002}(139,\cdot)\) \(\chi_{8002}(151,\cdot)\) \(\chi_{8002}(195,\cdot)\) \(\chi_{8002}(199,\cdot)\) \(\chi_{8002}(221,\cdot)\) \(\chi_{8002}(243,\cdot)\) \(\chi_{8002}(275,\cdot)\) \(\chi_{8002}(283,\cdot)\) \(\chi_{8002}(285,\cdot)\) \(\chi_{8002}(291,\cdot)\) \(\chi_{8002}(323,\cdot)\) \(\chi_{8002}(333,\cdot)\) \(\chi_{8002}(365,\cdot)\) \(\chi_{8002}(369,\cdot)\) \(\chi_{8002}(411,\cdot)\) \(\chi_{8002}(447,\cdot)\) \(\chi_{8002}(547,\cdot)\) \(\chi_{8002}(649,\cdot)\) \(\chi_{8002}(661,\cdot)\) \(\chi_{8002}(691,\cdot)\) \(\chi_{8002}(693,\cdot)\) \(\chi_{8002}(695,\cdot)\) \(\chi_{8002}(727,\cdot)\) \(\chi_{8002}(739,\cdot)\) \(\chi_{8002}(755,\cdot)\) \(\chi_{8002}(759,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{800})$ |
| Fixed field: | Number field defined by a degree 800 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{433}{800}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8002 }(39, a) \) | \(-1\) | \(1\) | \(e\left(\frac{433}{800}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{81}{200}\right)\) | \(e\left(\frac{33}{400}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{53}{200}\right)\) | \(e\left(\frac{173}{800}\right)\) | \(e\left(\frac{423}{800}\right)\) | \(e\left(\frac{173}{200}\right)\) | \(e\left(\frac{757}{800}\right)\) |