Basic properties
| Modulus: | \(8002\) | |
| Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4000\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4001}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8002.x
\(\chi_{8002}(3,\cdot)\) \(\chi_{8002}(15,\cdot)\) \(\chi_{8002}(17,\cdot)\) \(\chi_{8002}(21,\cdot)\) \(\chi_{8002}(23,\cdot)\) \(\chi_{8002}(27,\cdot)\) \(\chi_{8002}(37,\cdot)\) \(\chi_{8002}(41,\cdot)\) \(\chi_{8002}(43,\cdot)\) \(\chi_{8002}(67,\cdot)\) \(\chi_{8002}(75,\cdot)\) \(\chi_{8002}(77,\cdot)\) \(\chi_{8002}(85,\cdot)\) \(\chi_{8002}(87,\cdot)\) \(\chi_{8002}(93,\cdot)\) \(\chi_{8002}(99,\cdot)\) \(\chi_{8002}(101,\cdot)\) \(\chi_{8002}(103,\cdot)\) \(\chi_{8002}(105,\cdot)\) \(\chi_{8002}(109,\cdot)\) \(\chi_{8002}(113,\cdot)\) \(\chi_{8002}(115,\cdot)\) \(\chi_{8002}(119,\cdot)\) \(\chi_{8002}(131,\cdot)\) \(\chi_{8002}(135,\cdot)\) \(\chi_{8002}(141,\cdot)\) \(\chi_{8002}(143,\cdot)\) \(\chi_{8002}(147,\cdot)\) \(\chi_{8002}(153,\cdot)\) \(\chi_{8002}(161,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{4000})$ |
| Fixed field: | Number field defined by a degree 4000 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1}{4000}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8002 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{4000}\right)\) | \(e\left(\frac{59}{200}\right)\) | \(e\left(\frac{57}{1000}\right)\) | \(e\left(\frac{1}{2000}\right)\) | \(e\left(\frac{57}{160}\right)\) | \(e\left(\frac{541}{1000}\right)\) | \(e\left(\frac{1181}{4000}\right)\) | \(e\left(\frac{1431}{4000}\right)\) | \(e\left(\frac{981}{1000}\right)\) | \(e\left(\frac{229}{4000}\right)\) |