Basic properties
Modulus: | \(4031\) | |
Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(644\) | 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 4031.bq
\(\chi_{4031}(8,\cdot)\) \(\chi_{4031}(10,\cdot)\) \(\chi_{4031}(14,\cdot)\) \(\chi_{4031}(27,\cdot)\) \(\chi_{4031}(39,\cdot)\) \(\chi_{4031}(48,\cdot)\) \(\chi_{4031}(60,\cdot)\) \(\chi_{4031}(76,\cdot)\) \(\chi_{4031}(84,\cdot)\) \(\chi_{4031}(95,\cdot)\) \(\chi_{4031}(105,\cdot)\) \(\chi_{4031}(147,\cdot)\) \(\chi_{4031}(153,\cdot)\) \(\chi_{4031}(166,\cdot)\) \(\chi_{4031}(172,\cdot)\) \(\chi_{4031}(201,\cdot)\) \(\chi_{4031}(213,\cdot)\) \(\chi_{4031}(214,\cdot)\) \(\chi_{4031}(221,\cdot)\) \(\chi_{4031}(234,\cdot)\) \(\chi_{4031}(242,\cdot)\) \(\chi_{4031}(272,\cdot)\) \(\chi_{4031}(288,\cdot)\) \(\chi_{4031}(292,\cdot)\) \(\chi_{4031}(301,\cdot)\) \(\chi_{4031}(305,\cdot)\) \(\chi_{4031}(311,\cdot)\) \(\chi_{4031}(317,\cdot)\) \(\chi_{4031}(337,\cdot)\) \(\chi_{4031}(338,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{644})$ |
Fixed field: | Number field defined by a degree 644 polynomial (not computed) |
Values on generators
\((3337,697)\) → \((e\left(\frac{3}{28}\right),e\left(\frac{1}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4031 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{644}\right)\) | \(e\left(\frac{275}{644}\right)\) | \(e\left(\frac{83}{322}\right)\) | \(e\left(\frac{73}{322}\right)\) | \(e\left(\frac{179}{322}\right)\) | \(e\left(\frac{60}{161}\right)\) | \(e\left(\frac{249}{644}\right)\) | \(e\left(\frac{275}{322}\right)\) | \(e\left(\frac{229}{644}\right)\) | \(e\left(\frac{213}{644}\right)\) |