Basic properties
| Modulus: | \(6013\) | |
| Conductor: | \(6013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(429\) | 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.cn
\(\chi_{6013}(74,\cdot)\) \(\chi_{6013}(79,\cdot)\) \(\chi_{6013}(121,\cdot)\) \(\chi_{6013}(149,\cdot)\) \(\chi_{6013}(163,\cdot)\) \(\chi_{6013}(219,\cdot)\) \(\chi_{6013}(228,\cdot)\) \(\chi_{6013}(235,\cdot)\) \(\chi_{6013}(249,\cdot)\) \(\chi_{6013}(270,\cdot)\) \(\chi_{6013}(291,\cdot)\) \(\chi_{6013}(303,\cdot)\) \(\chi_{6013}(340,\cdot)\) \(\chi_{6013}(347,\cdot)\) \(\chi_{6013}(354,\cdot)\) \(\chi_{6013}(366,\cdot)\) \(\chi_{6013}(387,\cdot)\) \(\chi_{6013}(401,\cdot)\) \(\chi_{6013}(417,\cdot)\) \(\chi_{6013}(466,\cdot)\) \(\chi_{6013}(471,\cdot)\) \(\chi_{6013}(480,\cdot)\) \(\chi_{6013}(494,\cdot)\) \(\chi_{6013}(499,\cdot)\) \(\chi_{6013}(508,\cdot)\) \(\chi_{6013}(522,\cdot)\) \(\chi_{6013}(527,\cdot)\) \(\chi_{6013}(571,\cdot)\) \(\chi_{6013}(585,\cdot)\) \(\chi_{6013}(604,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{429})$ |
| Fixed field: | Number field defined by a degree 429 polynomial (not computed) |
Values on generators
\((5155,3438)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{63}{143}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 6013 }(401, a) \) | \(1\) | \(1\) | \(e\left(\frac{46}{429}\right)\) | \(e\left(\frac{326}{429}\right)\) | \(e\left(\frac{92}{429}\right)\) | \(e\left(\frac{64}{429}\right)\) | \(e\left(\frac{124}{143}\right)\) | \(e\left(\frac{46}{143}\right)\) | \(e\left(\frac{223}{429}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{356}{429}\right)\) | \(e\left(\frac{38}{39}\right)\) |