Basic properties
Modulus: | \(2014\) | |
Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(468\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1007}(51,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2014.bi
\(\chi_{2014}(3,\cdot)\) \(\chi_{2014}(21,\cdot)\) \(\chi_{2014}(33,\cdot)\) \(\chi_{2014}(41,\cdot)\) \(\chi_{2014}(51,\cdot)\) \(\chi_{2014}(67,\cdot)\) \(\chi_{2014}(71,\cdot)\) \(\chi_{2014}(79,\cdot)\) \(\chi_{2014}(109,\cdot)\) \(\chi_{2014}(127,\cdot)\) \(\chi_{2014}(147,\cdot)\) \(\chi_{2014}(167,\cdot)\) \(\chi_{2014}(173,\cdot)\) \(\chi_{2014}(181,\cdot)\) \(\chi_{2014}(185,\cdot)\) \(\chi_{2014}(193,\cdot)\) \(\chi_{2014}(231,\cdot)\) \(\chi_{2014}(243,\cdot)\) \(\chi_{2014}(257,\cdot)\) \(\chi_{2014}(279,\cdot)\) \(\chi_{2014}(287,\cdot)\) \(\chi_{2014}(299,\cdot)\) \(\chi_{2014}(337,\cdot)\) \(\chi_{2014}(345,\cdot)\) \(\chi_{2014}(357,\cdot)\) \(\chi_{2014}(363,\cdot)\) \(\chi_{2014}(383,\cdot)\) \(\chi_{2014}(393,\cdot)\) \(\chi_{2014}(421,\cdot)\) \(\chi_{2014}(451,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{468})$ |
Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
Values on generators
\((743,267)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{27}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 2014 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{205}{468}\right)\) | \(e\left(\frac{397}{468}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{205}{234}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{199}{234}\right)\) | \(e\left(\frac{67}{234}\right)\) | \(e\left(\frac{227}{234}\right)\) | \(e\left(\frac{175}{468}\right)\) | \(e\left(\frac{29}{36}\right)\) |