Basic properties
| Modulus: | \(477\) | |
| Conductor: | \(477\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | 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 477.q
\(\chi_{477}(13,\cdot)\) \(\chi_{477}(16,\cdot)\) \(\chi_{477}(49,\cdot)\) \(\chi_{477}(97,\cdot)\) \(\chi_{477}(121,\cdot)\) \(\chi_{477}(130,\cdot)\) \(\chi_{477}(142,\cdot)\) \(\chi_{477}(148,\cdot)\) \(\chi_{477}(169,\cdot)\) \(\chi_{477}(175,\cdot)\) \(\chi_{477}(187,\cdot)\) \(\chi_{477}(205,\cdot)\) \(\chi_{477}(256,\cdot)\) \(\chi_{477}(259,\cdot)\) \(\chi_{477}(301,\cdot)\) \(\chi_{477}(328,\cdot)\) \(\chi_{477}(331,\cdot)\) \(\chi_{477}(346,\cdot)\) \(\chi_{477}(364,\cdot)\) \(\chi_{477}(367,\cdot)\) \(\chi_{477}(418,\cdot)\) \(\chi_{477}(439,\cdot)\) \(\chi_{477}(448,\cdot)\) \(\chi_{477}(466,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((425,55)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{2}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 477 }(97, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) |