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.gt
\(\chi_{4725}(104,\cdot)\) \(\chi_{4725}(209,\cdot)\) \(\chi_{4725}(419,\cdot)\) \(\chi_{4725}(734,\cdot)\) \(\chi_{4725}(839,\cdot)\) \(\chi_{4725}(1154,\cdot)\) \(\chi_{4725}(1364,\cdot)\) \(\chi_{4725}(1469,\cdot)\) \(\chi_{4725}(1679,\cdot)\) \(\chi_{4725}(1784,\cdot)\) \(\chi_{4725}(1994,\cdot)\) \(\chi_{4725}(2309,\cdot)\) \(\chi_{4725}(2414,\cdot)\) \(\chi_{4725}(2729,\cdot)\) \(\chi_{4725}(2939,\cdot)\) \(\chi_{4725}(3044,\cdot)\) \(\chi_{4725}(3254,\cdot)\) \(\chi_{4725}(3359,\cdot)\) \(\chi_{4725}(3569,\cdot)\) \(\chi_{4725}(3884,\cdot)\) \(\chi_{4725}(3989,\cdot)\) \(\chi_{4725}(4304,\cdot)\) \(\chi_{4725}(4514,\cdot)\) \(\chi_{4725}(4619,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{1}{10}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 4725 }(104, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{37}{45}\right)\) |