Basic properties
| Modulus: | \(4425\) | |
| 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 \(\chi_{59}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4425.y
\(\chi_{4425}(76,\cdot)\) \(\chi_{4425}(226,\cdot)\) \(\chi_{4425}(376,\cdot)\) \(\chi_{4425}(676,\cdot)\) \(\chi_{4425}(901,\cdot)\) \(\chi_{4425}(1051,\cdot)\) \(\chi_{4425}(1126,\cdot)\) \(\chi_{4425}(1201,\cdot)\) \(\chi_{4425}(1351,\cdot)\) \(\chi_{4425}(1501,\cdot)\) \(\chi_{4425}(1726,\cdot)\) \(\chi_{4425}(1951,\cdot)\) \(\chi_{4425}(2026,\cdot)\) \(\chi_{4425}(2101,\cdot)\) \(\chi_{4425}(2251,\cdot)\) \(\chi_{4425}(2326,\cdot)\) \(\chi_{4425}(2401,\cdot)\) \(\chi_{4425}(2476,\cdot)\) \(\chi_{4425}(2701,\cdot)\) \(\chi_{4425}(2776,\cdot)\) \(\chi_{4425}(2851,\cdot)\) \(\chi_{4425}(2926,\cdot)\) \(\chi_{4425}(3001,\cdot)\) \(\chi_{4425}(3451,\cdot)\) \(\chi_{4425}(3526,\cdot)\) \(\chi_{4425}(3901,\cdot)\) \(\chi_{4425}(4201,\cdot)\) \(\chi_{4425}(4276,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\((2951,2302,3601)\) → \((1,1,e\left(\frac{6}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4425 }(2326, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) |