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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4025.dl
\(\chi_{4025}(19,\cdot)\) \(\chi_{4025}(89,\cdot)\) \(\chi_{4025}(129,\cdot)\) \(\chi_{4025}(159,\cdot)\) \(\chi_{4025}(194,\cdot)\) \(\chi_{4025}(264,\cdot)\) \(\chi_{4025}(304,\cdot)\) \(\chi_{4025}(339,\cdot)\) \(\chi_{4025}(444,\cdot)\) \(\chi_{4025}(479,\cdot)\) \(\chi_{4025}(544,\cdot)\) \(\chi_{4025}(619,\cdot)\) \(\chi_{4025}(654,\cdot)\) \(\chi_{4025}(684,\cdot)\) \(\chi_{4025}(789,\cdot)\) \(\chi_{4025}(894,\cdot)\) \(\chi_{4025}(934,\cdot)\) \(\chi_{4025}(964,\cdot)\) \(\chi_{4025}(1004,\cdot)\) \(\chi_{4025}(1069,\cdot)\) \(\chi_{4025}(1109,\cdot)\) \(\chi_{4025}(1144,\cdot)\) \(\chi_{4025}(1279,\cdot)\) \(\chi_{4025}(1284,\cdot)\) \(\chi_{4025}(1354,\cdot)\) \(\chi_{4025}(1454,\cdot)\) \(\chi_{4025}(1459,\cdot)\) \(\chi_{4025}(1489,\cdot)\) \(\chi_{4025}(1529,\cdot)\) \(\chi_{4025}(1594,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{1}{6}\right),e\left(\frac{1}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(304, a) \) | \(1\) | \(1\) | \(e\left(\frac{173}{330}\right)\) | \(e\left(\frac{98}{165}\right)\) | \(e\left(\frac{8}{165}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{31}{165}\right)\) | \(e\left(\frac{223}{330}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{16}{165}\right)\) |