Basic properties
Modulus: | \(4725\) | |
Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | 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 4725.go
\(\chi_{4725}(11,\cdot)\) \(\chi_{4725}(86,\cdot)\) \(\chi_{4725}(641,\cdot)\) \(\chi_{4725}(716,\cdot)\) \(\chi_{4725}(956,\cdot)\) \(\chi_{4725}(1031,\cdot)\) \(\chi_{4725}(1271,\cdot)\) \(\chi_{4725}(1346,\cdot)\) \(\chi_{4725}(1586,\cdot)\) \(\chi_{4725}(1661,\cdot)\) \(\chi_{4725}(2216,\cdot)\) \(\chi_{4725}(2291,\cdot)\) \(\chi_{4725}(2531,\cdot)\) \(\chi_{4725}(2606,\cdot)\) \(\chi_{4725}(2846,\cdot)\) \(\chi_{4725}(2921,\cdot)\) \(\chi_{4725}(3161,\cdot)\) \(\chi_{4725}(3236,\cdot)\) \(\chi_{4725}(3791,\cdot)\) \(\chi_{4725}(3866,\cdot)\) \(\chi_{4725}(4106,\cdot)\) \(\chi_{4725}(4181,\cdot)\) \(\chi_{4725}(4421,\cdot)\) \(\chi_{4725}(4496,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{2}{5}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 4725 }(4181, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{71}{90}\right)\) |