Basic properties
Modulus: | \(583\) | |
Conductor: | \(583\) | 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 583.v
\(\chi_{583}(6,\cdot)\) \(\chi_{583}(7,\cdot)\) \(\chi_{583}(17,\cdot)\) \(\chi_{583}(29,\cdot)\) \(\chi_{583}(40,\cdot)\) \(\chi_{583}(57,\cdot)\) \(\chi_{583}(62,\cdot)\) \(\chi_{583}(90,\cdot)\) \(\chi_{583}(96,\cdot)\) \(\chi_{583}(112,\cdot)\) \(\chi_{583}(117,\cdot)\) \(\chi_{583}(123,\cdot)\) \(\chi_{583}(149,\cdot)\) \(\chi_{583}(184,\cdot)\) \(\chi_{583}(216,\cdot)\) \(\chi_{583}(237,\cdot)\) \(\chi_{583}(249,\cdot)\) \(\chi_{583}(250,\cdot)\) \(\chi_{583}(255,\cdot)\) \(\chi_{583}(271,\cdot)\) \(\chi_{583}(272,\cdot)\) \(\chi_{583}(282,\cdot)\) \(\chi_{583}(294,\cdot)\) \(\chi_{583}(303,\cdot)\) \(\chi_{583}(305,\cdot)\) \(\chi_{583}(325,\cdot)\) \(\chi_{583}(327,\cdot)\) \(\chi_{583}(343,\cdot)\) \(\chi_{583}(347,\cdot)\) \(\chi_{583}(358,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{65})$ |
Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((266,320)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{9}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 583 }(6, a) \) | \(-1\) | \(1\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{43}{130}\right)\) | \(e\left(\frac{19}{130}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{15}{26}\right)\) |