Basic properties
| Modulus: | \(4725\) | |
| Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | 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 4725.fk
\(\chi_{4725}(121,\cdot)\) \(\chi_{4725}(436,\cdot)\) \(\chi_{4725}(466,\cdot)\) \(\chi_{4725}(781,\cdot)\) \(\chi_{4725}(1066,\cdot)\) \(\chi_{4725}(1096,\cdot)\) \(\chi_{4725}(1381,\cdot)\) \(\chi_{4725}(1411,\cdot)\) \(\chi_{4725}(1696,\cdot)\) \(\chi_{4725}(2011,\cdot)\) \(\chi_{4725}(2041,\cdot)\) \(\chi_{4725}(2356,\cdot)\) \(\chi_{4725}(2641,\cdot)\) \(\chi_{4725}(2671,\cdot)\) \(\chi_{4725}(2956,\cdot)\) \(\chi_{4725}(2986,\cdot)\) \(\chi_{4725}(3271,\cdot)\) \(\chi_{4725}(3586,\cdot)\) \(\chi_{4725}(3616,\cdot)\) \(\chi_{4725}(3931,\cdot)\) \(\chi_{4725}(4216,\cdot)\) \(\chi_{4725}(4246,\cdot)\) \(\chi_{4725}(4531,\cdot)\) \(\chi_{4725}(4561,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{3}{5}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
| \( \chi_{ 4725 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) |