Basic properties
| Modulus: | \(2183\) | |
| Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{59}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2183.u
\(\chi_{2183}(38,\cdot)\) \(\chi_{2183}(149,\cdot)\) \(\chi_{2183}(260,\cdot)\) \(\chi_{2183}(297,\cdot)\) \(\chi_{2183}(334,\cdot)\) \(\chi_{2183}(408,\cdot)\) \(\chi_{2183}(445,\cdot)\) \(\chi_{2183}(482,\cdot)\) \(\chi_{2183}(519,\cdot)\) \(\chi_{2183}(630,\cdot)\) \(\chi_{2183}(667,\cdot)\) \(\chi_{2183}(704,\cdot)\) \(\chi_{2183}(741,\cdot)\) \(\chi_{2183}(778,\cdot)\) \(\chi_{2183}(1000,\cdot)\) \(\chi_{2183}(1037,\cdot)\) \(\chi_{2183}(1222,\cdot)\) \(\chi_{2183}(1370,\cdot)\) \(\chi_{2183}(1407,\cdot)\) \(\chi_{2183}(1481,\cdot)\) \(\chi_{2183}(1518,\cdot)\) \(\chi_{2183}(1666,\cdot)\) \(\chi_{2183}(1814,\cdot)\) \(\chi_{2183}(1925,\cdot)\) \(\chi_{2183}(1999,\cdot)\) \(\chi_{2183}(2036,\cdot)\) \(\chi_{2183}(2073,\cdot)\) \(\chi_{2183}(2147,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((1889,297)\) → \((1,e\left(\frac{1}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2183 }(297, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{25}{58}\right)\) |