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.gn
\(\chi_{4725}(184,\cdot)\) \(\chi_{4725}(214,\cdot)\) \(\chi_{4725}(529,\cdot)\) \(\chi_{4725}(814,\cdot)\) \(\chi_{4725}(844,\cdot)\) \(\chi_{4725}(1129,\cdot)\) \(\chi_{4725}(1159,\cdot)\) \(\chi_{4725}(1444,\cdot)\) \(\chi_{4725}(1759,\cdot)\) \(\chi_{4725}(1789,\cdot)\) \(\chi_{4725}(2104,\cdot)\) \(\chi_{4725}(2389,\cdot)\) \(\chi_{4725}(2419,\cdot)\) \(\chi_{4725}(2704,\cdot)\) \(\chi_{4725}(2734,\cdot)\) \(\chi_{4725}(3019,\cdot)\) \(\chi_{4725}(3334,\cdot)\) \(\chi_{4725}(3364,\cdot)\) \(\chi_{4725}(3679,\cdot)\) \(\chi_{4725}(3964,\cdot)\) \(\chi_{4725}(3994,\cdot)\) \(\chi_{4725}(4279,\cdot)\) \(\chi_{4725}(4309,\cdot)\) \(\chi_{4725}(4594,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{7}{9}\right),e\left(\frac{7}{10}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 4725 }(184, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{83}{90}\right)\) |