Basic properties
Modulus: | \(4013\) | |
Conductor: | \(4013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2006\) | 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.k
\(\chi_{4013}(4,\cdot)\) \(\chi_{4013}(6,\cdot)\) \(\chi_{4013}(9,\cdot)\) \(\chi_{4013}(13,\cdot)\) \(\chi_{4013}(15,\cdot)\) \(\chi_{4013}(17,\cdot)\) \(\chi_{4013}(25,\cdot)\) \(\chi_{4013}(28,\cdot)\) \(\chi_{4013}(31,\cdot)\) \(\chi_{4013}(42,\cdot)\) \(\chi_{4013}(44,\cdot)\) \(\chi_{4013}(46,\cdot)\) \(\chi_{4013}(47,\cdot)\) \(\chi_{4013}(59,\cdot)\) \(\chi_{4013}(63,\cdot)\) \(\chi_{4013}(64,\cdot)\) \(\chi_{4013}(66,\cdot)\) \(\chi_{4013}(69,\cdot)\) \(\chi_{4013}(70,\cdot)\) \(\chi_{4013}(71,\cdot)\) \(\chi_{4013}(76,\cdot)\) \(\chi_{4013}(89,\cdot)\) \(\chi_{4013}(91,\cdot)\) \(\chi_{4013}(96,\cdot)\) \(\chi_{4013}(97,\cdot)\) \(\chi_{4013}(99,\cdot)\) \(\chi_{4013}(105,\cdot)\) \(\chi_{4013}(110,\cdot)\) \(\chi_{4013}(115,\cdot)\) \(\chi_{4013}(127,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1003})$ |
Fixed field: | Number field defined by a degree 2006 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1859}{2006}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4013 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{1859}{2006}\right)\) | \(e\left(\frac{253}{2006}\right)\) | \(e\left(\frac{856}{1003}\right)\) | \(e\left(\frac{1563}{2006}\right)\) | \(e\left(\frac{53}{1003}\right)\) | \(e\left(\frac{594}{1003}\right)\) | \(e\left(\frac{1565}{2006}\right)\) | \(e\left(\frac{253}{1003}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{838}{1003}\right)\) |