Basic properties
| Modulus: | \(8013\) | |
| Conductor: | \(8013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(890\) | 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.z
\(\chi_{8013}(11,\cdot)\) \(\chi_{8013}(26,\cdot)\) \(\chi_{8013}(44,\cdot)\) \(\chi_{8013}(146,\cdot)\) \(\chi_{8013}(149,\cdot)\) \(\chi_{8013}(158,\cdot)\) \(\chi_{8013}(173,\cdot)\) \(\chi_{8013}(194,\cdot)\) \(\chi_{8013}(233,\cdot)\) \(\chi_{8013}(269,\cdot)\) \(\chi_{8013}(329,\cdot)\) \(\chi_{8013}(350,\cdot)\) \(\chi_{8013}(383,\cdot)\) \(\chi_{8013}(401,\cdot)\) \(\chi_{8013}(410,\cdot)\) \(\chi_{8013}(416,\cdot)\) \(\chi_{8013}(422,\cdot)\) \(\chi_{8013}(443,\cdot)\) \(\chi_{8013}(530,\cdot)\) \(\chi_{8013}(575,\cdot)\) \(\chi_{8013}(584,\cdot)\) \(\chi_{8013}(590,\cdot)\) \(\chi_{8013}(596,\cdot)\) \(\chi_{8013}(617,\cdot)\) \(\chi_{8013}(623,\cdot)\) \(\chi_{8013}(626,\cdot)\) \(\chi_{8013}(632,\cdot)\) \(\chi_{8013}(686,\cdot)\) \(\chi_{8013}(692,\cdot)\) \(\chi_{8013}(704,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{445})$ |
| Fixed field: | Number field defined by a degree 890 polynomial (not computed) |
Values on generators
\((2672,7)\) → \((-1,e\left(\frac{537}{890}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8013 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{737}{890}\right)\) | \(e\left(\frac{292}{445}\right)\) | \(e\left(\frac{629}{890}\right)\) | \(e\left(\frac{537}{890}\right)\) | \(e\left(\frac{431}{890}\right)\) | \(e\left(\frac{238}{445}\right)\) | \(e\left(\frac{236}{445}\right)\) | \(e\left(\frac{79}{890}\right)\) | \(e\left(\frac{192}{445}\right)\) | \(e\left(\frac{139}{445}\right)\) |