Basic properties
Modulus: | \(6369\) | |
Conductor: | \(6369\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(320\) | 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 6369.dz
\(\chi_{6369}(20,\cdot)\) \(\chi_{6369}(71,\cdot)\) \(\chi_{6369}(104,\cdot)\) \(\chi_{6369}(119,\cdot)\) \(\chi_{6369}(125,\cdot)\) \(\chi_{6369}(158,\cdot)\) \(\chi_{6369}(269,\cdot)\) \(\chi_{6369}(566,\cdot)\) \(\chi_{6369}(599,\cdot)\) \(\chi_{6369}(608,\cdot)\) \(\chi_{6369}(614,\cdot)\) \(\chi_{6369}(647,\cdot)\) \(\chi_{6369}(653,\cdot)\) \(\chi_{6369}(698,\cdot)\) \(\chi_{6369}(752,\cdot)\) \(\chi_{6369}(785,\cdot)\) \(\chi_{6369}(878,\cdot)\) \(\chi_{6369}(905,\cdot)\) \(\chi_{6369}(1004,\cdot)\) \(\chi_{6369}(1070,\cdot)\) \(\chi_{6369}(1082,\cdot)\) \(\chi_{6369}(1169,\cdot)\) \(\chi_{6369}(1193,\cdot)\) \(\chi_{6369}(1226,\cdot)\) \(\chi_{6369}(1247,\cdot)\) \(\chi_{6369}(1280,\cdot)\) \(\chi_{6369}(1340,\cdot)\) \(\chi_{6369}(1439,\cdot)\) \(\chi_{6369}(1445,\cdot)\) \(\chi_{6369}(1457,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{320})$ |
Fixed field: | Number field defined by a degree 320 polynomial (not computed) |
Values on generators
\((4247,4633,2707)\) → \((-1,e\left(\frac{4}{5}\right),e\left(\frac{63}{64}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 6369 }(1070, a) \) | \(1\) | \(1\) | \(e\left(\frac{123}{160}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{219}{320}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{49}{160}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{191}{320}\right)\) | \(e\left(\frac{119}{160}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{69}{320}\right)\) |