Basic properties
| Modulus: | \(4592\) | |
| Conductor: | \(4592\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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 4592.ib
\(\chi_{4592}(11,\cdot)\) \(\chi_{4592}(67,\cdot)\) \(\chi_{4592}(179,\cdot)\) \(\chi_{4592}(235,\cdot)\) \(\chi_{4592}(667,\cdot)\) \(\chi_{4592}(723,\cdot)\) \(\chi_{4592}(835,\cdot)\) \(\chi_{4592}(891,\cdot)\) \(\chi_{4592}(1243,\cdot)\) \(\chi_{4592}(1411,\cdot)\) \(\chi_{4592}(1523,\cdot)\) \(\chi_{4592}(1899,\cdot)\) \(\chi_{4592}(1915,\cdot)\) \(\chi_{4592}(2067,\cdot)\) \(\chi_{4592}(2139,\cdot)\) \(\chi_{4592}(2179,\cdot)\) \(\chi_{4592}(2195,\cdot)\) \(\chi_{4592}(2571,\cdot)\) \(\chi_{4592}(2643,\cdot)\) \(\chi_{4592}(2699,\cdot)\) \(\chi_{4592}(2795,\cdot)\) \(\chi_{4592}(2851,\cdot)\) \(\chi_{4592}(2923,\cdot)\) \(\chi_{4592}(3299,\cdot)\) \(\chi_{4592}(3315,\cdot)\) \(\chi_{4592}(3355,\cdot)\) \(\chi_{4592}(3427,\cdot)\) \(\chi_{4592}(3579,\cdot)\) \(\chi_{4592}(3595,\cdot)\) \(\chi_{4592}(3971,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((575,3445,3937,785)\) → \((-1,i,e\left(\frac{2}{3}\right),e\left(\frac{3}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 4592 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) |