Basic properties
Modulus: | \(8027\) | |
Conductor: | \(8027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(348\) | 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 8027.bk
\(\chi_{8027}(114,\cdot)\) \(\chi_{8027}(137,\cdot)\) \(\chi_{8027}(183,\cdot)\) \(\chi_{8027}(229,\cdot)\) \(\chi_{8027}(252,\cdot)\) \(\chi_{8027}(275,\cdot)\) \(\chi_{8027}(367,\cdot)\) \(\chi_{8027}(505,\cdot)\) \(\chi_{8027}(643,\cdot)\) \(\chi_{8027}(666,\cdot)\) \(\chi_{8027}(827,\cdot)\) \(\chi_{8027}(850,\cdot)\) \(\chi_{8027}(873,\cdot)\) \(\chi_{8027}(919,\cdot)\) \(\chi_{8027}(942,\cdot)\) \(\chi_{8027}(965,\cdot)\) \(\chi_{8027}(988,\cdot)\) \(\chi_{8027}(1034,\cdot)\) \(\chi_{8027}(1080,\cdot)\) \(\chi_{8027}(1264,\cdot)\) \(\chi_{8027}(1333,\cdot)\) \(\chi_{8027}(1356,\cdot)\) \(\chi_{8027}(1586,\cdot)\) \(\chi_{8027}(1632,\cdot)\) \(\chi_{8027}(1655,\cdot)\) \(\chi_{8027}(1701,\cdot)\) \(\chi_{8027}(1747,\cdot)\) \(\chi_{8027}(1816,\cdot)\) \(\chi_{8027}(1862,\cdot)\) \(\chi_{8027}(1885,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{348})$ |
Fixed field: | Number field defined by a degree 348 polynomial (not computed) |
Values on generators
\((350,5935)\) → \((-1,e\left(\frac{163}{348}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8027 }(827, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{348}\right)\) | \(e\left(\frac{31}{174}\right)\) | \(e\left(\frac{163}{174}\right)\) | \(e\left(\frac{50}{87}\right)\) | \(e\left(\frac{75}{116}\right)\) | \(e\left(\frac{307}{348}\right)\) | \(e\left(\frac{47}{116}\right)\) | \(e\left(\frac{31}{87}\right)\) | \(e\left(\frac{5}{116}\right)\) | \(e\left(\frac{39}{116}\right)\) |