Basic properties
Modulus: | \(4725\) | |
Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | 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.gz
\(\chi_{4725}(52,\cdot)\) \(\chi_{4725}(103,\cdot)\) \(\chi_{4725}(178,\cdot)\) \(\chi_{4725}(292,\cdot)\) \(\chi_{4725}(367,\cdot)\) \(\chi_{4725}(733,\cdot)\) \(\chi_{4725}(808,\cdot)\) \(\chi_{4725}(922,\cdot)\) \(\chi_{4725}(997,\cdot)\) \(\chi_{4725}(1048,\cdot)\) \(\chi_{4725}(1123,\cdot)\) \(\chi_{4725}(1237,\cdot)\) \(\chi_{4725}(1312,\cdot)\) \(\chi_{4725}(1363,\cdot)\) \(\chi_{4725}(1438,\cdot)\) \(\chi_{4725}(1552,\cdot)\) \(\chi_{4725}(1627,\cdot)\) \(\chi_{4725}(1678,\cdot)\) \(\chi_{4725}(1753,\cdot)\) \(\chi_{4725}(1867,\cdot)\) \(\chi_{4725}(1942,\cdot)\) \(\chi_{4725}(2308,\cdot)\) \(\chi_{4725}(2383,\cdot)\) \(\chi_{4725}(2497,\cdot)\) \(\chi_{4725}(2572,\cdot)\) \(\chi_{4725}(2623,\cdot)\) \(\chi_{4725}(2698,\cdot)\) \(\chi_{4725}(2812,\cdot)\) \(\chi_{4725}(2887,\cdot)\) \(\chi_{4725}(2938,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((4376,1702,2026)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{1}{20}\right),e\left(\frac{1}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
\( \chi_{ 4725 }(52, a) \) | \(1\) | \(1\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{161}{180}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{113}{180}\right)\) | \(e\left(\frac{179}{180}\right)\) |