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.gr
\(\chi_{4725}(59,\cdot)\) \(\chi_{4725}(614,\cdot)\) \(\chi_{4725}(689,\cdot)\) \(\chi_{4725}(929,\cdot)\) \(\chi_{4725}(1004,\cdot)\) \(\chi_{4725}(1244,\cdot)\) \(\chi_{4725}(1319,\cdot)\) \(\chi_{4725}(1559,\cdot)\) \(\chi_{4725}(1634,\cdot)\) \(\chi_{4725}(2189,\cdot)\) \(\chi_{4725}(2264,\cdot)\) \(\chi_{4725}(2504,\cdot)\) \(\chi_{4725}(2579,\cdot)\) \(\chi_{4725}(2819,\cdot)\) \(\chi_{4725}(2894,\cdot)\) \(\chi_{4725}(3134,\cdot)\) \(\chi_{4725}(3209,\cdot)\) \(\chi_{4725}(3764,\cdot)\) \(\chi_{4725}(3839,\cdot)\) \(\chi_{4725}(4079,\cdot)\) \(\chi_{4725}(4154,\cdot)\) \(\chi_{4725}(4394,\cdot)\) \(\chi_{4725}(4469,\cdot)\) \(\chi_{4725}(4709,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{7}{10}\right),e\left(\frac{1}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 4725 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{4}{45}\right)\) |