Basic properties
Modulus: | \(59\) | |
Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(29\) | 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 59.c
\(\chi_{59}(3,\cdot)\) \(\chi_{59}(4,\cdot)\) \(\chi_{59}(5,\cdot)\) \(\chi_{59}(7,\cdot)\) \(\chi_{59}(9,\cdot)\) \(\chi_{59}(12,\cdot)\) \(\chi_{59}(15,\cdot)\) \(\chi_{59}(16,\cdot)\) \(\chi_{59}(17,\cdot)\) \(\chi_{59}(19,\cdot)\) \(\chi_{59}(20,\cdot)\) \(\chi_{59}(21,\cdot)\) \(\chi_{59}(22,\cdot)\) \(\chi_{59}(25,\cdot)\) \(\chi_{59}(26,\cdot)\) \(\chi_{59}(27,\cdot)\) \(\chi_{59}(28,\cdot)\) \(\chi_{59}(29,\cdot)\) \(\chi_{59}(35,\cdot)\) \(\chi_{59}(36,\cdot)\) \(\chi_{59}(41,\cdot)\) \(\chi_{59}(45,\cdot)\) \(\chi_{59}(46,\cdot)\) \(\chi_{59}(48,\cdot)\) \(\chi_{59}(49,\cdot)\) \(\chi_{59}(51,\cdot)\) \(\chi_{59}(53,\cdot)\) \(\chi_{59}(57,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\(2\) → \(e\left(\frac{1}{29}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 59 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) |