Basic properties
Modulus: | \(4013\) | |
Conductor: | \(4013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(4012\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4013.l
\(\chi_{4013}(2,\cdot)\) \(\chi_{4013}(3,\cdot)\) \(\chi_{4013}(5,\cdot)\) \(\chi_{4013}(8,\cdot)\) \(\chi_{4013}(12,\cdot)\) \(\chi_{4013}(14,\cdot)\) \(\chi_{4013}(18,\cdot)\) \(\chi_{4013}(20,\cdot)\) \(\chi_{4013}(21,\cdot)\) \(\chi_{4013}(22,\cdot)\) \(\chi_{4013}(23,\cdot)\) \(\chi_{4013}(26,\cdot)\) \(\chi_{4013}(27,\cdot)\) \(\chi_{4013}(29,\cdot)\) \(\chi_{4013}(30,\cdot)\) \(\chi_{4013}(32,\cdot)\) \(\chi_{4013}(33,\cdot)\) \(\chi_{4013}(34,\cdot)\) \(\chi_{4013}(35,\cdot)\) \(\chi_{4013}(37,\cdot)\) \(\chi_{4013}(38,\cdot)\) \(\chi_{4013}(39,\cdot)\) \(\chi_{4013}(45,\cdot)\) \(\chi_{4013}(48,\cdot)\) \(\chi_{4013}(50,\cdot)\) \(\chi_{4013}(55,\cdot)\) \(\chi_{4013}(56,\cdot)\) \(\chi_{4013}(57,\cdot)\) \(\chi_{4013}(62,\cdot)\) \(\chi_{4013}(65,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{4012})$ |
Fixed field: | Number field defined by a degree 4012 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{2677}{4012}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4013 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2677}{4012}\right)\) | \(e\left(\frac{1397}{4012}\right)\) | \(e\left(\frac{671}{2006}\right)\) | \(e\left(\frac{1217}{4012}\right)\) | \(e\left(\frac{31}{2006}\right)\) | \(e\left(\frac{855}{1003}\right)\) | \(e\left(\frac{7}{4012}\right)\) | \(e\left(\frac{1397}{2006}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{264}{1003}\right)\) |