Basic properties
| Modulus: | \(4031\) | |
| Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(322\) | 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.bm
\(\chi_{4031}(23,\cdot)\) \(\chi_{4031}(74,\cdot)\) \(\chi_{4031}(82,\cdot)\) \(\chi_{4031}(94,\cdot)\) \(\chi_{4031}(103,\cdot)\) \(\chi_{4031}(198,\cdot)\) \(\chi_{4031}(199,\cdot)\) \(\chi_{4031}(223,\cdot)\) \(\chi_{4031}(226,\cdot)\) \(\chi_{4031}(286,\cdot)\) \(\chi_{4031}(326,\cdot)\) \(\chi_{4031}(372,\cdot)\) \(\chi_{4031}(373,\cdot)\) \(\chi_{4031}(431,\cdot)\) \(\chi_{4031}(604,\cdot)\) \(\chi_{4031}(616,\cdot)\) \(\chi_{4031}(632,\cdot)\) \(\chi_{4031}(661,\cdot)\) \(\chi_{4031}(703,\cdot)\) \(\chi_{4031}(770,\cdot)\) \(\chi_{4031}(777,\cdot)\) \(\chi_{4031}(779,\cdot)\) \(\chi_{4031}(790,\cdot)\) \(\chi_{4031}(828,\cdot)\) \(\chi_{4031}(848,\cdot)\) \(\chi_{4031}(857,\cdot)\) \(\chi_{4031}(861,\cdot)\) \(\chi_{4031}(893,\cdot)\) \(\chi_{4031}(894,\cdot)\) \(\chi_{4031}(981,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{161})$ |
| Fixed field: | Number field defined by a degree 322 polynomial (not computed) |
Values on generators
\((3337,697)\) → \((e\left(\frac{5}{7}\right),e\left(\frac{9}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4031 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{293}{322}\right)\) | \(e\left(\frac{191}{322}\right)\) | \(e\left(\frac{132}{161}\right)\) | \(e\left(\frac{87}{161}\right)\) | \(e\left(\frac{81}{161}\right)\) | \(e\left(\frac{57}{161}\right)\) | \(e\left(\frac{235}{322}\right)\) | \(e\left(\frac{30}{161}\right)\) | \(e\left(\frac{145}{322}\right)\) | \(e\left(\frac{117}{161}\right)\) |