Basic properties
| Modulus: | \(1859\) | |
| Conductor: | \(1859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(195\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1859.bo
\(\chi_{1859}(3,\cdot)\) \(\chi_{1859}(9,\cdot)\) \(\chi_{1859}(16,\cdot)\) \(\chi_{1859}(42,\cdot)\) \(\chi_{1859}(48,\cdot)\) \(\chi_{1859}(81,\cdot)\) \(\chi_{1859}(113,\cdot)\) \(\chi_{1859}(126,\cdot)\) \(\chi_{1859}(152,\cdot)\) \(\chi_{1859}(159,\cdot)\) \(\chi_{1859}(185,\cdot)\) \(\chi_{1859}(224,\cdot)\) \(\chi_{1859}(256,\cdot)\) \(\chi_{1859}(269,\cdot)\) \(\chi_{1859}(289,\cdot)\) \(\chi_{1859}(295,\cdot)\) \(\chi_{1859}(302,\cdot)\) \(\chi_{1859}(328,\cdot)\) \(\chi_{1859}(334,\cdot)\) \(\chi_{1859}(367,\cdot)\) \(\chi_{1859}(399,\cdot)\) \(\chi_{1859}(412,\cdot)\) \(\chi_{1859}(432,\cdot)\) \(\chi_{1859}(438,\cdot)\) \(\chi_{1859}(445,\cdot)\) \(\chi_{1859}(471,\cdot)\) \(\chi_{1859}(477,\cdot)\) \(\chi_{1859}(510,\cdot)\) \(\chi_{1859}(542,\cdot)\) \(\chi_{1859}(555,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 195 polynomial (not computed) |
Values on generators
\((508,1354)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{23}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 1859 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{195}\right)\) | \(e\left(\frac{181}{195}\right)\) | \(e\left(\frac{74}{195}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{23}{195}\right)\) | \(e\left(\frac{59}{195}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{167}{195}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) |