Basic properties
| Modulus: | \(118\) | |
| Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(29\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{59}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 118.c
\(\chi_{118}(3,\cdot)\) \(\chi_{118}(5,\cdot)\) \(\chi_{118}(7,\cdot)\) \(\chi_{118}(9,\cdot)\) \(\chi_{118}(15,\cdot)\) \(\chi_{118}(17,\cdot)\) \(\chi_{118}(19,\cdot)\) \(\chi_{118}(21,\cdot)\) \(\chi_{118}(25,\cdot)\) \(\chi_{118}(27,\cdot)\) \(\chi_{118}(29,\cdot)\) \(\chi_{118}(35,\cdot)\) \(\chi_{118}(41,\cdot)\) \(\chi_{118}(45,\cdot)\) \(\chi_{118}(49,\cdot)\) \(\chi_{118}(51,\cdot)\) \(\chi_{118}(53,\cdot)\) \(\chi_{118}(57,\cdot)\) \(\chi_{118}(63,\cdot)\) \(\chi_{118}(71,\cdot)\) \(\chi_{118}(75,\cdot)\) \(\chi_{118}(79,\cdot)\) \(\chi_{118}(81,\cdot)\) \(\chi_{118}(85,\cdot)\) \(\chi_{118}(87,\cdot)\) \(\chi_{118}(95,\cdot)\) \(\chi_{118}(105,\cdot)\) \(\chi_{118}(107,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\(61\) → \(e\left(\frac{25}{29}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 118 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) |