Basic properties
Modulus: | \(8014\) | |
Conductor: | \(4007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2003\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4007}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8014.c
\(\chi_{8014}(3,\cdot)\) \(\chi_{8014}(7,\cdot)\) \(\chi_{8014}(9,\cdot)\) \(\chi_{8014}(13,\cdot)\) \(\chi_{8014}(21,\cdot)\) \(\chi_{8014}(23,\cdot)\) \(\chi_{8014}(25,\cdot)\) \(\chi_{8014}(27,\cdot)\) \(\chi_{8014}(29,\cdot)\) \(\chi_{8014}(37,\cdot)\) \(\chi_{8014}(39,\cdot)\) \(\chi_{8014}(43,\cdot)\) \(\chi_{8014}(49,\cdot)\) \(\chi_{8014}(55,\cdot)\) \(\chi_{8014}(59,\cdot)\) \(\chi_{8014}(61,\cdot)\) \(\chi_{8014}(63,\cdot)\) \(\chi_{8014}(69,\cdot)\) \(\chi_{8014}(71,\cdot)\) \(\chi_{8014}(73,\cdot)\) \(\chi_{8014}(75,\cdot)\) \(\chi_{8014}(79,\cdot)\) \(\chi_{8014}(81,\cdot)\) \(\chi_{8014}(85,\cdot)\) \(\chi_{8014}(87,\cdot)\) \(\chi_{8014}(89,\cdot)\) \(\chi_{8014}(91,\cdot)\) \(\chi_{8014}(95,\cdot)\) \(\chi_{8014}(101,\cdot)\) \(\chi_{8014}(109,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{2003})$ |
Fixed field: | Number field defined by a degree 2003 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{359}{2003}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8014 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{1237}{2003}\right)\) | \(e\left(\frac{359}{2003}\right)\) | \(e\left(\frac{1246}{2003}\right)\) | \(e\left(\frac{471}{2003}\right)\) | \(e\left(\frac{949}{2003}\right)\) | \(e\left(\frac{1378}{2003}\right)\) | \(e\left(\frac{1596}{2003}\right)\) | \(e\left(\frac{267}{2003}\right)\) | \(e\left(\frac{596}{2003}\right)\) | \(e\left(\frac{480}{2003}\right)\) |