Basic properties
| Modulus: | \(6013\) | |
| Conductor: | \(6013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(286\) | 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 6013.ck
\(\chi_{6013}(27,\cdot)\) \(\chi_{6013}(34,\cdot)\) \(\chi_{6013}(48,\cdot)\) \(\chi_{6013}(104,\cdot)\) \(\chi_{6013}(167,\cdot)\) \(\chi_{6013}(391,\cdot)\) \(\chi_{6013}(433,\cdot)\) \(\chi_{6013}(475,\cdot)\) \(\chi_{6013}(552,\cdot)\) \(\chi_{6013}(587,\cdot)\) \(\chi_{6013}(636,\cdot)\) \(\chi_{6013}(643,\cdot)\) \(\chi_{6013}(671,\cdot)\) \(\chi_{6013}(678,\cdot)\) \(\chi_{6013}(706,\cdot)\) \(\chi_{6013}(734,\cdot)\) \(\chi_{6013}(790,\cdot)\) \(\chi_{6013}(853,\cdot)\) \(\chi_{6013}(867,\cdot)\) \(\chi_{6013}(951,\cdot)\) \(\chi_{6013}(965,\cdot)\) \(\chi_{6013}(972,\cdot)\) \(\chi_{6013}(1021,\cdot)\) \(\chi_{6013}(1063,\cdot)\) \(\chi_{6013}(1133,\cdot)\) \(\chi_{6013}(1147,\cdot)\) \(\chi_{6013}(1196,\cdot)\) \(\chi_{6013}(1210,\cdot)\) \(\chi_{6013}(1224,\cdot)\) \(\chi_{6013}(1238,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{143})$ |
| Fixed field: | Number field defined by a degree 286 polynomial (not computed) |
Values on generators
\((5155,3438)\) → \((-1,e\left(\frac{119}{286}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 6013 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{119}{286}\right)\) | \(e\left(\frac{2}{143}\right)\) | \(e\left(\frac{119}{143}\right)\) | \(e\left(\frac{35}{286}\right)\) | \(e\left(\frac{123}{286}\right)\) | \(e\left(\frac{71}{286}\right)\) | \(e\left(\frac{4}{143}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{7}{286}\right)\) | \(e\left(\frac{11}{13}\right)\) |