Basic properties
| Modulus: | \(4013\) | |
| Conductor: | \(4013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1003\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4013.j
\(\chi_{4013}(7,\cdot)\) \(\chi_{4013}(11,\cdot)\) \(\chi_{4013}(16,\cdot)\) \(\chi_{4013}(19,\cdot)\) \(\chi_{4013}(24,\cdot)\) \(\chi_{4013}(36,\cdot)\) \(\chi_{4013}(41,\cdot)\) \(\chi_{4013}(43,\cdot)\) \(\chi_{4013}(49,\cdot)\) \(\chi_{4013}(52,\cdot)\) \(\chi_{4013}(58,\cdot)\) \(\chi_{4013}(60,\cdot)\) \(\chi_{4013}(61,\cdot)\) \(\chi_{4013}(67,\cdot)\) \(\chi_{4013}(68,\cdot)\) \(\chi_{4013}(73,\cdot)\) \(\chi_{4013}(74,\cdot)\) \(\chi_{4013}(77,\cdot)\) \(\chi_{4013}(78,\cdot)\) \(\chi_{4013}(81,\cdot)\) \(\chi_{4013}(83,\cdot)\) \(\chi_{4013}(87,\cdot)\) \(\chi_{4013}(90,\cdot)\) \(\chi_{4013}(102,\cdot)\) \(\chi_{4013}(109,\cdot)\) \(\chi_{4013}(111,\cdot)\) \(\chi_{4013}(112,\cdot)\) \(\chi_{4013}(117,\cdot)\) \(\chi_{4013}(121,\cdot)\) \(\chi_{4013}(124,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1003})$ |
| Fixed field: | Number field defined by a degree 1003 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{653}{1003}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4013 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{653}{1003}\right)\) | \(e\left(\frac{77}{1003}\right)\) | \(e\left(\frac{303}{1003}\right)\) | \(e\left(\frac{999}{1003}\right)\) | \(e\left(\frac{730}{1003}\right)\) | \(e\left(\frac{536}{1003}\right)\) | \(e\left(\frac{956}{1003}\right)\) | \(e\left(\frac{154}{1003}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{74}{1003}\right)\) |