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.cm
\(\chi_{1425}(14,\cdot)\) \(\chi_{1425}(29,\cdot)\) \(\chi_{1425}(59,\cdot)\) \(\chi_{1425}(89,\cdot)\) \(\chi_{1425}(269,\cdot)\) \(\chi_{1425}(314,\cdot)\) \(\chi_{1425}(344,\cdot)\) \(\chi_{1425}(509,\cdot)\) \(\chi_{1425}(554,\cdot)\) \(\chi_{1425}(584,\cdot)\) \(\chi_{1425}(629,\cdot)\) \(\chi_{1425}(659,\cdot)\) \(\chi_{1425}(794,\cdot)\) \(\chi_{1425}(839,\cdot)\) \(\chi_{1425}(869,\cdot)\) \(\chi_{1425}(884,\cdot)\) \(\chi_{1425}(914,\cdot)\) \(\chi_{1425}(944,\cdot)\) \(\chi_{1425}(1079,\cdot)\) \(\chi_{1425}(1154,\cdot)\) \(\chi_{1425}(1169,\cdot)\) \(\chi_{1425}(1229,\cdot)\) \(\chi_{1425}(1364,\cdot)\) \(\chi_{1425}(1409,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((476,1027,1351)\) → \((-1,e\left(\frac{1}{10}\right),e\left(\frac{17}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
\( \chi_{ 1425 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) |