Basic properties
| Modulus: | \(8014\) | |
| Conductor: | \(4007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4006\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4007}(45,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8014.d
\(\chi_{8014}(5,\cdot)\) \(\chi_{8014}(11,\cdot)\) \(\chi_{8014}(15,\cdot)\) \(\chi_{8014}(17,\cdot)\) \(\chi_{8014}(19,\cdot)\) \(\chi_{8014}(31,\cdot)\) \(\chi_{8014}(33,\cdot)\) \(\chi_{8014}(35,\cdot)\) \(\chi_{8014}(41,\cdot)\) \(\chi_{8014}(45,\cdot)\) \(\chi_{8014}(47,\cdot)\) \(\chi_{8014}(51,\cdot)\) \(\chi_{8014}(53,\cdot)\) \(\chi_{8014}(57,\cdot)\) \(\chi_{8014}(65,\cdot)\) \(\chi_{8014}(67,\cdot)\) \(\chi_{8014}(77,\cdot)\) \(\chi_{8014}(83,\cdot)\) \(\chi_{8014}(93,\cdot)\) \(\chi_{8014}(97,\cdot)\) \(\chi_{8014}(99,\cdot)\) \(\chi_{8014}(103,\cdot)\) \(\chi_{8014}(105,\cdot)\) \(\chi_{8014}(107,\cdot)\) \(\chi_{8014}(115,\cdot)\) \(\chi_{8014}(119,\cdot)\) \(\chi_{8014}(123,\cdot)\) \(\chi_{8014}(125,\cdot)\) \(\chi_{8014}(127,\cdot)\) \(\chi_{8014}(131,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{2003})$ |
| Fixed field: | Number field defined by a degree 4006 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{3389}{4006}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8014 }(45, a) \) | \(-1\) | \(1\) | \(e\left(\frac{184}{2003}\right)\) | \(e\left(\frac{3389}{4006}\right)\) | \(e\left(\frac{140}{2003}\right)\) | \(e\left(\frac{368}{2003}\right)\) | \(e\left(\frac{1181}{4006}\right)\) | \(e\left(\frac{830}{2003}\right)\) | \(e\left(\frac{3757}{4006}\right)\) | \(e\left(\frac{2063}{4006}\right)\) | \(e\left(\frac{2407}{4006}\right)\) | \(e\left(\frac{324}{2003}\right)\) |