Basic properties
| Modulus: | \(4025\) | |
| Conductor: | \(4025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | 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.de
\(\chi_{4025}(13,\cdot)\) \(\chi_{4025}(27,\cdot)\) \(\chi_{4025}(48,\cdot)\) \(\chi_{4025}(62,\cdot)\) \(\chi_{4025}(167,\cdot)\) \(\chi_{4025}(188,\cdot)\) \(\chi_{4025}(202,\cdot)\) \(\chi_{4025}(223,\cdot)\) \(\chi_{4025}(328,\cdot)\) \(\chi_{4025}(363,\cdot)\) \(\chi_{4025}(377,\cdot)\) \(\chi_{4025}(538,\cdot)\) \(\chi_{4025}(587,\cdot)\) \(\chi_{4025}(692,\cdot)\) \(\chi_{4025}(748,\cdot)\) \(\chi_{4025}(762,\cdot)\) \(\chi_{4025}(853,\cdot)\) \(\chi_{4025}(867,\cdot)\) \(\chi_{4025}(923,\cdot)\) \(\chi_{4025}(972,\cdot)\) \(\chi_{4025}(1028,\cdot)\) \(\chi_{4025}(1112,\cdot)\) \(\chi_{4025}(1133,\cdot)\) \(\chi_{4025}(1273,\cdot)\) \(\chi_{4025}(1392,\cdot)\) \(\chi_{4025}(1462,\cdot)\) \(\chi_{4025}(1497,\cdot)\) \(\chi_{4025}(1553,\cdot)\) \(\chi_{4025}(1567,\cdot)\) \(\chi_{4025}(1623,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{7}{20}\right),-1,e\left(\frac{9}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 4025 }(328, a) \) | \(1\) | \(1\) | \(e\left(\frac{217}{220}\right)\) | \(e\left(\frac{9}{220}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{3}{220}\right)\) | \(e\left(\frac{133}{220}\right)\) | \(e\left(\frac{52}{55}\right)\) |