Basic properties
| Modulus: | \(2183\) | |
| Conductor: | \(2183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(116\) | 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 2183.y
\(\chi_{2183}(6,\cdot)\) \(\chi_{2183}(31,\cdot)\) \(\chi_{2183}(43,\cdot)\) \(\chi_{2183}(142,\cdot)\) \(\chi_{2183}(179,\cdot)\) \(\chi_{2183}(191,\cdot)\) \(\chi_{2183}(216,\cdot)\) \(\chi_{2183}(290,\cdot)\) \(\chi_{2183}(327,\cdot)\) \(\chi_{2183}(339,\cdot)\) \(\chi_{2183}(364,\cdot)\) \(\chi_{2183}(401,\cdot)\) \(\chi_{2183}(450,\cdot)\) \(\chi_{2183}(512,\cdot)\) \(\chi_{2183}(524,\cdot)\) \(\chi_{2183}(549,\cdot)\) \(\chi_{2183}(561,\cdot)\) \(\chi_{2183}(586,\cdot)\) \(\chi_{2183}(598,\cdot)\) \(\chi_{2183}(623,\cdot)\) \(\chi_{2183}(660,\cdot)\) \(\chi_{2183}(672,\cdot)\) \(\chi_{2183}(746,\cdot)\) \(\chi_{2183}(857,\cdot)\) \(\chi_{2183}(882,\cdot)\) \(\chi_{2183}(919,\cdot)\) \(\chi_{2183}(968,\cdot)\) \(\chi_{2183}(1005,\cdot)\) \(\chi_{2183}(1042,\cdot)\) \(\chi_{2183}(1104,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((1889,297)\) → \((i,e\left(\frac{49}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2183 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{116}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{95}{116}\right)\) | \(e\left(\frac{97}{116}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{33}{116}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{18}{29}\right)\) |