Basic properties
Modulus: | \(869\) | |
Conductor: | \(869\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 869.ba
\(\chi_{869}(8,\cdot)\) \(\chi_{869}(18,\cdot)\) \(\chi_{869}(46,\cdot)\) \(\chi_{869}(52,\cdot)\) \(\chi_{869}(62,\cdot)\) \(\chi_{869}(101,\cdot)\) \(\chi_{869}(117,\cdot)\) \(\chi_{869}(204,\cdot)\) \(\chi_{869}(222,\cdot)\) \(\chi_{869}(255,\cdot)\) \(\chi_{869}(259,\cdot)\) \(\chi_{869}(283,\cdot)\) \(\chi_{869}(299,\cdot)\) \(\chi_{869}(304,\cdot)\) \(\chi_{869}(326,\cdot)\) \(\chi_{869}(337,\cdot)\) \(\chi_{869}(338,\cdot)\) \(\chi_{869}(354,\cdot)\) \(\chi_{869}(380,\cdot)\) \(\chi_{869}(381,\cdot)\) \(\chi_{869}(403,\cdot)\) \(\chi_{869}(413,\cdot)\) \(\chi_{869}(447,\cdot)\) \(\chi_{869}(457,\cdot)\) \(\chi_{869}(459,\cdot)\) \(\chi_{869}(492,\cdot)\) \(\chi_{869}(512,\cdot)\) \(\chi_{869}(536,\cdot)\) \(\chi_{869}(541,\cdot)\) \(\chi_{869}(563,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((475,793)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{6}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 869 }(354, a) \) | \(-1\) | \(1\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{21}{130}\right)\) | \(e\left(\frac{109}{130}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) |