Basic properties
| Modulus: | \(8013\) | |
| Conductor: | \(8013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2670\) | 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 8013.be
\(\chi_{8013}(14,\cdot)\) \(\chi_{8013}(23,\cdot)\) \(\chi_{8013}(29,\cdot)\) \(\chi_{8013}(35,\cdot)\) \(\chi_{8013}(38,\cdot)\) \(\chi_{8013}(41,\cdot)\) \(\chi_{8013}(53,\cdot)\) \(\chi_{8013}(56,\cdot)\) \(\chi_{8013}(59,\cdot)\) \(\chi_{8013}(65,\cdot)\) \(\chi_{8013}(95,\cdot)\) \(\chi_{8013}(110,\cdot)\) \(\chi_{8013}(116,\cdot)\) \(\chi_{8013}(119,\cdot)\) \(\chi_{8013}(152,\cdot)\) \(\chi_{8013}(155,\cdot)\) \(\chi_{8013}(164,\cdot)\) \(\chi_{8013}(197,\cdot)\) \(\chi_{8013}(218,\cdot)\) \(\chi_{8013}(221,\cdot)\) \(\chi_{8013}(224,\cdot)\) \(\chi_{8013}(230,\cdot)\) \(\chi_{8013}(248,\cdot)\) \(\chi_{8013}(251,\cdot)\) \(\chi_{8013}(260,\cdot)\) \(\chi_{8013}(281,\cdot)\) \(\chi_{8013}(293,\cdot)\) \(\chi_{8013}(314,\cdot)\) \(\chi_{8013}(323,\cdot)\) \(\chi_{8013}(359,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1335})$ |
| Fixed field: | Number field defined by a degree 2670 polynomial (not computed) |
Values on generators
\((2672,7)\) → \((-1,e\left(\frac{217}{2670}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8013 }(14, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{890}\right)\) | \(e\left(\frac{49}{445}\right)\) | \(e\left(\frac{2659}{2670}\right)\) | \(e\left(\frac{217}{2670}\right)\) | \(e\left(\frac{147}{890}\right)\) | \(e\left(\frac{68}{1335}\right)\) | \(e\left(\frac{192}{445}\right)\) | \(e\left(\frac{283}{890}\right)\) | \(e\left(\frac{182}{1335}\right)\) | \(e\left(\frac{98}{445}\right)\) |