Basic properties
Modulus: | \(4025\) | |
Conductor: | \(4025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | 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 4025.dn
\(\chi_{4025}(44,\cdot)\) \(\chi_{4025}(79,\cdot)\) \(\chi_{4025}(109,\cdot)\) \(\chi_{4025}(214,\cdot)\) \(\chi_{4025}(319,\cdot)\) \(\chi_{4025}(359,\cdot)\) \(\chi_{4025}(389,\cdot)\) \(\chi_{4025}(429,\cdot)\) \(\chi_{4025}(494,\cdot)\) \(\chi_{4025}(534,\cdot)\) \(\chi_{4025}(569,\cdot)\) \(\chi_{4025}(704,\cdot)\) \(\chi_{4025}(709,\cdot)\) \(\chi_{4025}(779,\cdot)\) \(\chi_{4025}(879,\cdot)\) \(\chi_{4025}(884,\cdot)\) \(\chi_{4025}(914,\cdot)\) \(\chi_{4025}(954,\cdot)\) \(\chi_{4025}(1019,\cdot)\) \(\chi_{4025}(1054,\cdot)\) \(\chi_{4025}(1164,\cdot)\) \(\chi_{4025}(1194,\cdot)\) \(\chi_{4025}(1229,\cdot)\) \(\chi_{4025}(1234,\cdot)\) \(\chi_{4025}(1339,\cdot)\) \(\chi_{4025}(1479,\cdot)\) \(\chi_{4025}(1509,\cdot)\) \(\chi_{4025}(1514,\cdot)\) \(\chi_{4025}(1579,\cdot)\) \(\chi_{4025}(1584,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{1}{3}\right),e\left(\frac{21}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(359, a) \) | \(-1\) | \(1\) | \(e\left(\frac{91}{330}\right)\) | \(e\left(\frac{167}{330}\right)\) | \(e\left(\frac{91}{165}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{2}{165}\right)\) | \(e\left(\frac{41}{330}\right)\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{17}{165}\right)\) |