Basic properties
Modulus: | \(4725\) | |
Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{675}(106,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4725.fm
\(\chi_{4725}(106,\cdot)\) \(\chi_{4725}(211,\cdot)\) \(\chi_{4725}(421,\cdot)\) \(\chi_{4725}(736,\cdot)\) \(\chi_{4725}(841,\cdot)\) \(\chi_{4725}(1156,\cdot)\) \(\chi_{4725}(1366,\cdot)\) \(\chi_{4725}(1471,\cdot)\) \(\chi_{4725}(1681,\cdot)\) \(\chi_{4725}(1786,\cdot)\) \(\chi_{4725}(1996,\cdot)\) \(\chi_{4725}(2311,\cdot)\) \(\chi_{4725}(2416,\cdot)\) \(\chi_{4725}(2731,\cdot)\) \(\chi_{4725}(2941,\cdot)\) \(\chi_{4725}(3046,\cdot)\) \(\chi_{4725}(3256,\cdot)\) \(\chi_{4725}(3361,\cdot)\) \(\chi_{4725}(3571,\cdot)\) \(\chi_{4725}(3886,\cdot)\) \(\chi_{4725}(3991,\cdot)\) \(\chi_{4725}(4306,\cdot)\) \(\chi_{4725}(4516,\cdot)\) \(\chi_{4725}(4621,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{2}{5}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 4725 }(106, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) |