Basic properties
| Modulus: | \(59\) | |
| Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | 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 59.d
\(\chi_{59}(2,\cdot)\) \(\chi_{59}(6,\cdot)\) \(\chi_{59}(8,\cdot)\) \(\chi_{59}(10,\cdot)\) \(\chi_{59}(11,\cdot)\) \(\chi_{59}(13,\cdot)\) \(\chi_{59}(14,\cdot)\) \(\chi_{59}(18,\cdot)\) \(\chi_{59}(23,\cdot)\) \(\chi_{59}(24,\cdot)\) \(\chi_{59}(30,\cdot)\) \(\chi_{59}(31,\cdot)\) \(\chi_{59}(32,\cdot)\) \(\chi_{59}(33,\cdot)\) \(\chi_{59}(34,\cdot)\) \(\chi_{59}(37,\cdot)\) \(\chi_{59}(38,\cdot)\) \(\chi_{59}(39,\cdot)\) \(\chi_{59}(40,\cdot)\) \(\chi_{59}(42,\cdot)\) \(\chi_{59}(43,\cdot)\) \(\chi_{59}(44,\cdot)\) \(\chi_{59}(47,\cdot)\) \(\chi_{59}(50,\cdot)\) \(\chi_{59}(52,\cdot)\) \(\chi_{59}(54,\cdot)\) \(\chi_{59}(55,\cdot)\) \(\chi_{59}(56,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\(2\) → \(e\left(\frac{39}{58}\right)\)
Values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 59 }(38, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{41}{58}\right)\) | \(e\left(\frac{47}{58}\right)\) |