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.in
\(\chi_{4592}(275,\cdot)\) \(\chi_{4592}(347,\cdot)\) \(\chi_{4592}(403,\cdot)\) \(\chi_{4592}(499,\cdot)\) \(\chi_{4592}(555,\cdot)\) \(\chi_{4592}(627,\cdot)\) \(\chi_{4592}(1003,\cdot)\) \(\chi_{4592}(1019,\cdot)\) \(\chi_{4592}(1059,\cdot)\) \(\chi_{4592}(1131,\cdot)\) \(\chi_{4592}(1283,\cdot)\) \(\chi_{4592}(1299,\cdot)\) \(\chi_{4592}(1675,\cdot)\) \(\chi_{4592}(1787,\cdot)\) \(\chi_{4592}(1955,\cdot)\) \(\chi_{4592}(2307,\cdot)\) \(\chi_{4592}(2363,\cdot)\) \(\chi_{4592}(2475,\cdot)\) \(\chi_{4592}(2531,\cdot)\) \(\chi_{4592}(2963,\cdot)\) \(\chi_{4592}(3019,\cdot)\) \(\chi_{4592}(3131,\cdot)\) \(\chi_{4592}(3187,\cdot)\) \(\chi_{4592}(3539,\cdot)\) \(\chi_{4592}(3707,\cdot)\) \(\chi_{4592}(3819,\cdot)\) \(\chi_{4592}(4195,\cdot)\) \(\chi_{4592}(4211,\cdot)\) \(\chi_{4592}(4363,\cdot)\) \(\chi_{4592}(4435,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((575,3445,3937,785)\) → \((-1,-i,e\left(\frac{1}{3}\right),e\left(\frac{7}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 4592 }(275, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) |