Basic properties
| Modulus: | \(6013\) | |
| Conductor: | \(859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(429\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{859}(22,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6013.cm
\(\chi_{6013}(22,\cdot)\) \(\chi_{6013}(57,\cdot)\) \(\chi_{6013}(85,\cdot)\) \(\chi_{6013}(127,\cdot)\) \(\chi_{6013}(134,\cdot)\) \(\chi_{6013}(190,\cdot)\) \(\chi_{6013}(211,\cdot)\) \(\chi_{6013}(218,\cdot)\) \(\chi_{6013}(232,\cdot)\) \(\chi_{6013}(246,\cdot)\) \(\chi_{6013}(253,\cdot)\) \(\chi_{6013}(281,\cdot)\) \(\chi_{6013}(295,\cdot)\) \(\chi_{6013}(386,\cdot)\) \(\chi_{6013}(407,\cdot)\) \(\chi_{6013}(421,\cdot)\) \(\chi_{6013}(435,\cdot)\) \(\chi_{6013}(449,\cdot)\) \(\chi_{6013}(484,\cdot)\) \(\chi_{6013}(491,\cdot)\) \(\chi_{6013}(533,\cdot)\) \(\chi_{6013}(561,\cdot)\) \(\chi_{6013}(596,\cdot)\) \(\chi_{6013}(617,\cdot)\) \(\chi_{6013}(652,\cdot)\) \(\chi_{6013}(659,\cdot)\) \(\chi_{6013}(701,\cdot)\) \(\chi_{6013}(764,\cdot)\) \(\chi_{6013}(792,\cdot)\) \(\chi_{6013}(820,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{429})$ |
| Fixed field: | Number field defined by a degree 429 polynomial (not computed) |
Values on generators
\((5155,3438)\) → \((1,e\left(\frac{194}{429}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 6013 }(22, a) \) | \(1\) | \(1\) | \(e\left(\frac{194}{429}\right)\) | \(e\left(\frac{349}{429}\right)\) | \(e\left(\frac{388}{429}\right)\) | \(e\left(\frac{301}{429}\right)\) | \(e\left(\frac{38}{143}\right)\) | \(e\left(\frac{51}{143}\right)\) | \(e\left(\frac{269}{429}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{1}{143}\right)\) | \(e\left(\frac{28}{39}\right)\) |