Basic properties
Modulus: | \(199\) | |
Conductor: | \(199\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(99\) | 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 199.k
\(\chi_{199}(2,\cdot)\) \(\chi_{199}(4,\cdot)\) \(\chi_{199}(7,\cdot)\) \(\chi_{199}(9,\cdot)\) \(\chi_{199}(10,\cdot)\) \(\chi_{199}(13,\cdot)\) \(\chi_{199}(14,\cdot)\) \(\chi_{199}(16,\cdot)\) \(\chi_{199}(20,\cdot)\) \(\chi_{199}(23,\cdot)\) \(\chi_{199}(26,\cdot)\) \(\chi_{199}(29,\cdot)\) \(\chi_{199}(31,\cdot)\) \(\chi_{199}(32,\cdot)\) \(\chi_{199}(33,\cdot)\) \(\chi_{199}(35,\cdot)\) \(\chi_{199}(36,\cdot)\) \(\chi_{199}(45,\cdot)\) \(\chi_{199}(46,\cdot)\) \(\chi_{199}(47,\cdot)\) \(\chi_{199}(49,\cdot)\) \(\chi_{199}(50,\cdot)\) \(\chi_{199}(51,\cdot)\) \(\chi_{199}(53,\cdot)\) \(\chi_{199}(56,\cdot)\) \(\chi_{199}(57,\cdot)\) \(\chi_{199}(65,\cdot)\) \(\chi_{199}(66,\cdot)\) \(\chi_{199}(70,\cdot)\) \(\chi_{199}(72,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{99})$ |
Fixed field: | Number field defined by a degree 99 polynomial |
Values on generators
\(3\) → \(e\left(\frac{67}{99}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 199 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{99}\right)\) | \(e\left(\frac{67}{99}\right)\) | \(e\left(\frac{47}{99}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{41}{99}\right)\) | \(e\left(\frac{10}{99}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{35}{99}\right)\) | \(e\left(\frac{13}{99}\right)\) | \(e\left(\frac{10}{11}\right)\) |