Basic properties
| Modulus: | \(8013\) | |
| Conductor: | \(2671\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(445\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2671}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8013.v
\(\chi_{8013}(4,\cdot)\) \(\chi_{8013}(16,\cdot)\) \(\chi_{8013}(43,\cdot)\) \(\chi_{8013}(61,\cdot)\) \(\chi_{8013}(64,\cdot)\) \(\chi_{8013}(121,\cdot)\) \(\chi_{8013}(169,\cdot)\) \(\chi_{8013}(172,\cdot)\) \(\chi_{8013}(193,\cdot)\) \(\chi_{8013}(235,\cdot)\) \(\chi_{8013}(244,\cdot)\) \(\chi_{8013}(250,\cdot)\) \(\chi_{8013}(256,\cdot)\) \(\chi_{8013}(262,\cdot)\) \(\chi_{8013}(274,\cdot)\) \(\chi_{8013}(286,\cdot)\) \(\chi_{8013}(334,\cdot)\) \(\chi_{8013}(349,\cdot)\) \(\chi_{8013}(355,\cdot)\) \(\chi_{8013}(358,\cdot)\) \(\chi_{8013}(406,\cdot)\) \(\chi_{8013}(445,\cdot)\) \(\chi_{8013}(484,\cdot)\) \(\chi_{8013}(523,\cdot)\) \(\chi_{8013}(541,\cdot)\) \(\chi_{8013}(565,\cdot)\) \(\chi_{8013}(574,\cdot)\) \(\chi_{8013}(577,\cdot)\) \(\chi_{8013}(607,\cdot)\) \(\chi_{8013}(622,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{445})$ |
| Fixed field: | Number field defined by a degree 445 polynomial (not computed) |
Values on generators
\((2672,7)\) → \((1,e\left(\frac{72}{445}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8013 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{422}{445}\right)\) | \(e\left(\frac{399}{445}\right)\) | \(e\left(\frac{144}{445}\right)\) | \(e\left(\frac{72}{445}\right)\) | \(e\left(\frac{376}{445}\right)\) | \(e\left(\frac{121}{445}\right)\) | \(e\left(\frac{292}{445}\right)\) | \(e\left(\frac{294}{445}\right)\) | \(e\left(\frac{49}{445}\right)\) | \(e\left(\frac{353}{445}\right)\) |