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.br
\(\chi_{1859}(17,\cdot)\) \(\chi_{1859}(30,\cdot)\) \(\chi_{1859}(62,\cdot)\) \(\chi_{1859}(95,\cdot)\) \(\chi_{1859}(101,\cdot)\) \(\chi_{1859}(127,\cdot)\) \(\chi_{1859}(134,\cdot)\) \(\chi_{1859}(140,\cdot)\) \(\chi_{1859}(160,\cdot)\) \(\chi_{1859}(173,\cdot)\) \(\chi_{1859}(205,\cdot)\) \(\chi_{1859}(238,\cdot)\) \(\chi_{1859}(244,\cdot)\) \(\chi_{1859}(270,\cdot)\) \(\chi_{1859}(277,\cdot)\) \(\chi_{1859}(283,\cdot)\) \(\chi_{1859}(303,\cdot)\) \(\chi_{1859}(348,\cdot)\) \(\chi_{1859}(381,\cdot)\) \(\chi_{1859}(387,\cdot)\) \(\chi_{1859}(413,\cdot)\) \(\chi_{1859}(420,\cdot)\) \(\chi_{1859}(426,\cdot)\) \(\chi_{1859}(446,\cdot)\) \(\chi_{1859}(459,\cdot)\) \(\chi_{1859}(491,\cdot)\) \(\chi_{1859}(524,\cdot)\) \(\chi_{1859}(556,\cdot)\) \(\chi_{1859}(563,\cdot)\) \(\chi_{1859}(569,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((508,1354)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{67}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1859 }(30, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{195}\right)\) | \(e\left(\frac{178}{195}\right)\) | \(e\left(\frac{62}{195}\right)\) | \(e\left(\frac{121}{130}\right)\) | \(e\left(\frac{14}{195}\right)\) | \(e\left(\frac{2}{195}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{161}{195}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) |