Basic properties
Modulus: | \(8015\) | |
Conductor: | \(8015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 8015.fa
\(\chi_{8015}(44,\cdot)\) \(\chi_{8015}(214,\cdot)\) \(\chi_{8015}(289,\cdot)\) \(\chi_{8015}(394,\cdot)\) \(\chi_{8015}(704,\cdot)\) \(\chi_{8015}(744,\cdot)\) \(\chi_{8015}(1619,\cdot)\) \(\chi_{8015}(1724,\cdot)\) \(\chi_{8015}(1859,\cdot)\) \(\chi_{8015}(2104,\cdot)\) \(\chi_{8015}(2279,\cdot)\) \(\chi_{8015}(2809,\cdot)\) \(\chi_{8015}(2909,\cdot)\) \(\chi_{8015}(3019,\cdot)\) \(\chi_{8015}(3259,\cdot)\) \(\chi_{8015}(3539,\cdot)\) \(\chi_{8015}(3649,\cdot)\) \(\chi_{8015}(3889,\cdot)\) \(\chi_{8015}(4139,\cdot)\) \(\chi_{8015}(4554,\cdot)\) \(\chi_{8015}(4624,\cdot)\) \(\chi_{8015}(4869,\cdot)\) \(\chi_{8015}(4974,\cdot)\) \(\chi_{8015}(5294,\cdot)\) \(\chi_{8015}(5324,\cdot)\) \(\chi_{8015}(5539,\cdot)\) \(\chi_{8015}(5714,\cdot)\) \(\chi_{8015}(6199,\cdot)\) \(\chi_{8015}(6304,\cdot)\) \(\chi_{8015}(6344,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{17}{19}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 8015 }(44, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{114}\right)\) | \(e\left(\frac{107}{114}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{97}{114}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{47}{57}\right)\) |