Basic properties
| Modulus: | \(2665\) | |
| Conductor: | \(533\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{533}(6,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2665.hw
\(\chi_{2665}(6,\cdot)\) \(\chi_{2665}(11,\cdot)\) \(\chi_{2665}(106,\cdot)\) \(\chi_{2665}(111,\cdot)\) \(\chi_{2665}(176,\cdot)\) \(\chi_{2665}(591,\cdot)\) \(\chi_{2665}(691,\cdot)\) \(\chi_{2665}(721,\cdot)\) \(\chi_{2665}(726,\cdot)\) \(\chi_{2665}(791,\cdot)\) \(\chi_{2665}(891,\cdot)\) \(\chi_{2665}(956,\cdot)\) \(\chi_{2665}(1081,\cdot)\) \(\chi_{2665}(1211,\cdot)\) \(\chi_{2665}(1306,\cdot)\) \(\chi_{2665}(1346,\cdot)\) \(\chi_{2665}(1506,\cdot)\) \(\chi_{2665}(1536,\cdot)\) \(\chi_{2665}(1571,\cdot)\) \(\chi_{2665}(1606,\cdot)\) \(\chi_{2665}(1666,\cdot)\) \(\chi_{2665}(1696,\cdot)\) \(\chi_{2665}(1826,\cdot)\) \(\chi_{2665}(1961,\cdot)\) \(\chi_{2665}(1996,\cdot)\) \(\chi_{2665}(2056,\cdot)\) \(\chi_{2665}(2061,\cdot)\) \(\chi_{2665}(2151,\cdot)\) \(\chi_{2665}(2221,\cdot)\) \(\chi_{2665}(2281,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((1067,821,1236)\) → \((1,e\left(\frac{5}{12}\right),e\left(\frac{1}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 2665 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{5}{8}\right)\) |