Basic properties
Modulus: | \(203\) | |
Conductor: | \(203\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | 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 203.w
\(\chi_{203}(2,\cdot)\) \(\chi_{203}(11,\cdot)\) \(\chi_{203}(18,\cdot)\) \(\chi_{203}(32,\cdot)\) \(\chi_{203}(37,\cdot)\) \(\chi_{203}(39,\cdot)\) \(\chi_{203}(44,\cdot)\) \(\chi_{203}(60,\cdot)\) \(\chi_{203}(72,\cdot)\) \(\chi_{203}(79,\cdot)\) \(\chi_{203}(95,\cdot)\) \(\chi_{203}(102,\cdot)\) \(\chi_{203}(114,\cdot)\) \(\chi_{203}(130,\cdot)\) \(\chi_{203}(135,\cdot)\) \(\chi_{203}(137,\cdot)\) \(\chi_{203}(142,\cdot)\) \(\chi_{203}(156,\cdot)\) \(\chi_{203}(163,\cdot)\) \(\chi_{203}(172,\cdot)\) \(\chi_{203}(177,\cdot)\) \(\chi_{203}(184,\cdot)\) \(\chi_{203}(193,\cdot)\) \(\chi_{203}(200,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((59,176)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{27}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 203 }(102, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{71}{84}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{1}{12}\right)\) |