Basic properties
Modulus: | \(4025\) | |
Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{575}(237,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4025.df
\(\chi_{4025}(113,\cdot)\) \(\chi_{4025}(148,\cdot)\) \(\chi_{4025}(267,\cdot)\) \(\chi_{4025}(337,\cdot)\) \(\chi_{4025}(428,\cdot)\) \(\chi_{4025}(442,\cdot)\) \(\chi_{4025}(477,\cdot)\) \(\chi_{4025}(498,\cdot)\) \(\chi_{4025}(603,\cdot)\) \(\chi_{4025}(617,\cdot)\) \(\chi_{4025}(638,\cdot)\) \(\chi_{4025}(687,\cdot)\) \(\chi_{4025}(778,\cdot)\) \(\chi_{4025}(792,\cdot)\) \(\chi_{4025}(848,\cdot)\) \(\chi_{4025}(862,\cdot)\) \(\chi_{4025}(953,\cdot)\) \(\chi_{4025}(1023,\cdot)\) \(\chi_{4025}(1072,\cdot)\) \(\chi_{4025}(1142,\cdot)\) \(\chi_{4025}(1233,\cdot)\) \(\chi_{4025}(1247,\cdot)\) \(\chi_{4025}(1303,\cdot)\) \(\chi_{4025}(1387,\cdot)\) \(\chi_{4025}(1408,\cdot)\) \(\chi_{4025}(1422,\cdot)\) \(\chi_{4025}(1492,\cdot)\) \(\chi_{4025}(1548,\cdot)\) \(\chi_{4025}(1562,\cdot)\) \(\chi_{4025}(1583,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{9}{20}\right),1,e\left(\frac{19}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(1387, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{220}\right)\) | \(e\left(\frac{213}{220}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{117}{220}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{71}{220}\right)\) | \(e\left(\frac{141}{220}\right)\) | \(e\left(\frac{39}{55}\right)\) |