Basic properties
Modulus: | \(1859\) | |
Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(390\) | 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 1859.bt
\(\chi_{1859}(29,\cdot)\) \(\chi_{1859}(35,\cdot)\) \(\chi_{1859}(61,\cdot)\) \(\chi_{1859}(68,\cdot)\) \(\chi_{1859}(74,\cdot)\) \(\chi_{1859}(94,\cdot)\) \(\chi_{1859}(107,\cdot)\) \(\chi_{1859}(139,\cdot)\) \(\chi_{1859}(172,\cdot)\) \(\chi_{1859}(178,\cdot)\) \(\chi_{1859}(204,\cdot)\) \(\chi_{1859}(211,\cdot)\) \(\chi_{1859}(217,\cdot)\) \(\chi_{1859}(237,\cdot)\) \(\chi_{1859}(250,\cdot)\) \(\chi_{1859}(282,\cdot)\) \(\chi_{1859}(321,\cdot)\) \(\chi_{1859}(347,\cdot)\) \(\chi_{1859}(354,\cdot)\) \(\chi_{1859}(380,\cdot)\) \(\chi_{1859}(393,\cdot)\) \(\chi_{1859}(425,\cdot)\) \(\chi_{1859}(458,\cdot)\) \(\chi_{1859}(464,\cdot)\) \(\chi_{1859}(490,\cdot)\) \(\chi_{1859}(497,\cdot)\) \(\chi_{1859}(503,\cdot)\) \(\chi_{1859}(523,\cdot)\) \(\chi_{1859}(536,\cdot)\) \(\chi_{1859}(568,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{195})$ |
Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((508,1354)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{1}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 1859 }(354, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{390}\right)\) | \(e\left(\frac{191}{195}\right)\) | \(e\left(\frac{49}{195}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{41}{390}\right)\) | \(e\left(\frac{173}{390}\right)\) | \(e\left(\frac{49}{130}\right)\) | \(e\left(\frac{187}{195}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) |