Basic properties
| Modulus: | \(4425\) | |
| Conductor: | \(295\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{295}(74,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4425.bf
\(\chi_{4425}(49,\cdot)\) \(\chi_{4425}(199,\cdot)\) \(\chi_{4425}(499,\cdot)\) \(\chi_{4425}(724,\cdot)\) \(\chi_{4425}(874,\cdot)\) \(\chi_{4425}(949,\cdot)\) \(\chi_{4425}(1024,\cdot)\) \(\chi_{4425}(1174,\cdot)\) \(\chi_{4425}(1324,\cdot)\) \(\chi_{4425}(1549,\cdot)\) \(\chi_{4425}(1774,\cdot)\) \(\chi_{4425}(1849,\cdot)\) \(\chi_{4425}(1924,\cdot)\) \(\chi_{4425}(2074,\cdot)\) \(\chi_{4425}(2149,\cdot)\) \(\chi_{4425}(2224,\cdot)\) \(\chi_{4425}(2299,\cdot)\) \(\chi_{4425}(2524,\cdot)\) \(\chi_{4425}(2599,\cdot)\) \(\chi_{4425}(2674,\cdot)\) \(\chi_{4425}(2749,\cdot)\) \(\chi_{4425}(2824,\cdot)\) \(\chi_{4425}(3274,\cdot)\) \(\chi_{4425}(3349,\cdot)\) \(\chi_{4425}(3724,\cdot)\) \(\chi_{4425}(4024,\cdot)\) \(\chi_{4425}(4099,\cdot)\) \(\chi_{4425}(4324,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((2951,2302,3601)\) → \((1,-1,e\left(\frac{28}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4425 }(1549, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{20}{29}\right)\) |