Basic properties
| Modulus: | \(199\) | |
| Conductor: | \(199\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(198\) | 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 199.l
\(\chi_{199}(3,\cdot)\) \(\chi_{199}(6,\cdot)\) \(\chi_{199}(15,\cdot)\) \(\chi_{199}(22,\cdot)\) \(\chi_{199}(30,\cdot)\) \(\chi_{199}(34,\cdot)\) \(\chi_{199}(38,\cdot)\) \(\chi_{199}(39,\cdot)\) \(\chi_{199}(41,\cdot)\) \(\chi_{199}(44,\cdot)\) \(\chi_{199}(48,\cdot)\) \(\chi_{199}(54,\cdot)\) \(\chi_{199}(68,\cdot)\) \(\chi_{199}(69,\cdot)\) \(\chi_{199}(71,\cdot)\) \(\chi_{199}(73,\cdot)\) \(\chi_{199}(75,\cdot)\) \(\chi_{199}(77,\cdot)\) \(\chi_{199}(84,\cdot)\) \(\chi_{199}(87,\cdot)\) \(\chi_{199}(95,\cdot)\) \(\chi_{199}(97,\cdot)\) \(\chi_{199}(99,\cdot)\) \(\chi_{199}(105,\cdot)\) \(\chi_{199}(108,\cdot)\) \(\chi_{199}(110,\cdot)\) \(\chi_{199}(113,\cdot)\) \(\chi_{199}(118,\cdot)\) \(\chi_{199}(119,\cdot)\) \(\chi_{199}(120,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{99})$ |
| Fixed field: | Number field defined by a degree 198 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1}{198}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 199 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{99}\right)\) | \(e\left(\frac{1}{198}\right)\) | \(e\left(\frac{7}{99}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{107}{198}\right)\) | \(e\left(\frac{71}{99}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{1}{99}\right)\) | \(e\left(\frac{23}{99}\right)\) | \(e\left(\frac{21}{22}\right)\) |