Basic properties
| Modulus: | \(4031\) | |
| Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(966\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4031.br
\(\chi_{4031}(22,\cdot)\) \(\chi_{4031}(92,\cdot)\) \(\chi_{4031}(93,\cdot)\) \(\chi_{4031}(109,\cdot)\) \(\chi_{4031}(151,\cdot)\) \(\chi_{4031}(154,\cdot)\) \(\chi_{4031}(158,\cdot)\) \(\chi_{4031}(179,\cdot)\) \(\chi_{4031}(207,\cdot)\) \(\chi_{4031}(209,\cdot)\) \(\chi_{4031}(212,\cdot)\) \(\chi_{4031}(237,\cdot)\) \(\chi_{4031}(241,\cdot)\) \(\chi_{4031}(254,\cdot)\) \(\chi_{4031}(265,\cdot)\) \(\chi_{4031}(267,\cdot)\) \(\chi_{4031}(274,\cdot)\) \(\chi_{4031}(295,\cdot)\) \(\chi_{4031}(296,\cdot)\) \(\chi_{4031}(299,\cdot)\) \(\chi_{4031}(328,\cdot)\) \(\chi_{4031}(370,\cdot)\) \(\chi_{4031}(382,\cdot)\) \(\chi_{4031}(386,\cdot)\) \(\chi_{4031}(410,\cdot)\) \(\chi_{4031}(412,\cdot)\) \(\chi_{4031}(419,\cdot)\) \(\chi_{4031}(439,\cdot)\) \(\chi_{4031}(457,\cdot)\) \(\chi_{4031}(470,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{483})$ |
| Fixed field: | Number field defined by a degree 966 polynomial (not computed) |
Values on generators
\((3337,697)\) → \((e\left(\frac{13}{14}\right),e\left(\frac{77}{138}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4031 }(22, a) \) | \(-1\) | \(1\) | \(e\left(\frac{235}{483}\right)\) | \(e\left(\frac{251}{483}\right)\) | \(e\left(\frac{470}{483}\right)\) | \(e\left(\frac{200}{483}\right)\) | \(e\left(\frac{1}{161}\right)\) | \(e\left(\frac{20}{483}\right)\) | \(e\left(\frac{74}{161}\right)\) | \(e\left(\frac{19}{483}\right)\) | \(e\left(\frac{145}{161}\right)\) | \(e\left(\frac{599}{966}\right)\) |