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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4725.gk
\(\chi_{4725}(236,\cdot)\) \(\chi_{4725}(311,\cdot)\) \(\chi_{4725}(866,\cdot)\) \(\chi_{4725}(941,\cdot)\) \(\chi_{4725}(1181,\cdot)\) \(\chi_{4725}(1256,\cdot)\) \(\chi_{4725}(1496,\cdot)\) \(\chi_{4725}(1571,\cdot)\) \(\chi_{4725}(1811,\cdot)\) \(\chi_{4725}(1886,\cdot)\) \(\chi_{4725}(2441,\cdot)\) \(\chi_{4725}(2516,\cdot)\) \(\chi_{4725}(2756,\cdot)\) \(\chi_{4725}(2831,\cdot)\) \(\chi_{4725}(3071,\cdot)\) \(\chi_{4725}(3146,\cdot)\) \(\chi_{4725}(3386,\cdot)\) \(\chi_{4725}(3461,\cdot)\) \(\chi_{4725}(4016,\cdot)\) \(\chi_{4725}(4091,\cdot)\) \(\chi_{4725}(4331,\cdot)\) \(\chi_{4725}(4406,\cdot)\) \(\chi_{4725}(4646,\cdot)\) \(\chi_{4725}(4721,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{4}{5}\right),e\left(\frac{1}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 4725 }(311, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{47}{90}\right)\) |