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
\((508,1354)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{10}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1859 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{373}{390}\right)\) | \(e\left(\frac{77}{195}\right)\) | \(e\left(\frac{178}{195}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{137}{390}\right)\) | \(e\left(\frac{131}{390}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{154}{195}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{4}{13}\right)\) |