Basic properties
Modulus: | \(1425\) | |
Conductor: | \(1425\) | 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 1425.cl
\(\chi_{1425}(41,\cdot)\) \(\chi_{1425}(71,\cdot)\) \(\chi_{1425}(86,\cdot)\) \(\chi_{1425}(116,\cdot)\) \(\chi_{1425}(146,\cdot)\) \(\chi_{1425}(281,\cdot)\) \(\chi_{1425}(356,\cdot)\) \(\chi_{1425}(371,\cdot)\) \(\chi_{1425}(431,\cdot)\) \(\chi_{1425}(566,\cdot)\) \(\chi_{1425}(611,\cdot)\) \(\chi_{1425}(641,\cdot)\) \(\chi_{1425}(656,\cdot)\) \(\chi_{1425}(686,\cdot)\) \(\chi_{1425}(716,\cdot)\) \(\chi_{1425}(896,\cdot)\) \(\chi_{1425}(941,\cdot)\) \(\chi_{1425}(971,\cdot)\) \(\chi_{1425}(1136,\cdot)\) \(\chi_{1425}(1181,\cdot)\) \(\chi_{1425}(1211,\cdot)\) \(\chi_{1425}(1256,\cdot)\) \(\chi_{1425}(1286,\cdot)\) \(\chi_{1425}(1421,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((476,1027,1351)\) → \((-1,e\left(\frac{1}{5}\right),e\left(\frac{13}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
\( \chi_{ 1425 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{71}{90}\right)\) |