Basic properties
| Modulus: | \(2873\) | |
| Conductor: | \(2873\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(104\) | 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 2873.bz
\(\chi_{2873}(53,\cdot)\) \(\chi_{2873}(66,\cdot)\) \(\chi_{2873}(144,\cdot)\) \(\chi_{2873}(196,\cdot)\) \(\chi_{2873}(274,\cdot)\) \(\chi_{2873}(287,\cdot)\) \(\chi_{2873}(365,\cdot)\) \(\chi_{2873}(417,\cdot)\) \(\chi_{2873}(495,\cdot)\) \(\chi_{2873}(586,\cdot)\) \(\chi_{2873}(638,\cdot)\) \(\chi_{2873}(716,\cdot)\) \(\chi_{2873}(729,\cdot)\) \(\chi_{2873}(807,\cdot)\) \(\chi_{2873}(859,\cdot)\) \(\chi_{2873}(937,\cdot)\) \(\chi_{2873}(950,\cdot)\) \(\chi_{2873}(1028,\cdot)\) \(\chi_{2873}(1080,\cdot)\) \(\chi_{2873}(1158,\cdot)\) \(\chi_{2873}(1171,\cdot)\) \(\chi_{2873}(1249,\cdot)\) \(\chi_{2873}(1301,\cdot)\) \(\chi_{2873}(1379,\cdot)\) \(\chi_{2873}(1392,\cdot)\) \(\chi_{2873}(1470,\cdot)\) \(\chi_{2873}(1600,\cdot)\) \(\chi_{2873}(1613,\cdot)\) \(\chi_{2873}(1743,\cdot)\) \(\chi_{2873}(1821,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{104})$ |
| Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
Values on generators
\((171,2536)\) → \((e\left(\frac{10}{13}\right),e\left(\frac{7}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2873 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{27}{104}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{31}{104}\right)\) | \(e\left(\frac{29}{104}\right)\) | \(e\left(\frac{97}{104}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{33}{104}\right)\) | \(e\left(\frac{37}{104}\right)\) |