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.gm
\(\chi_{4725}(41,\cdot)\) \(\chi_{4725}(146,\cdot)\) \(\chi_{4725}(356,\cdot)\) \(\chi_{4725}(461,\cdot)\) \(\chi_{4725}(671,\cdot)\) \(\chi_{4725}(986,\cdot)\) \(\chi_{4725}(1091,\cdot)\) \(\chi_{4725}(1406,\cdot)\) \(\chi_{4725}(1616,\cdot)\) \(\chi_{4725}(1721,\cdot)\) \(\chi_{4725}(1931,\cdot)\) \(\chi_{4725}(2036,\cdot)\) \(\chi_{4725}(2246,\cdot)\) \(\chi_{4725}(2561,\cdot)\) \(\chi_{4725}(2666,\cdot)\) \(\chi_{4725}(2981,\cdot)\) \(\chi_{4725}(3191,\cdot)\) \(\chi_{4725}(3296,\cdot)\) \(\chi_{4725}(3506,\cdot)\) \(\chi_{4725}(3611,\cdot)\) \(\chi_{4725}(3821,\cdot)\) \(\chi_{4725}(4136,\cdot)\) \(\chi_{4725}(4241,\cdot)\) \(\chi_{4725}(4556,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{1}{5}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 4725 }(1091, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{13}{90}\right)\) |