Basic properties
Modulus: | \(4275\) | |
Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{475}(321,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4275.fl
\(\chi_{4275}(271,\cdot)\) \(\chi_{4275}(541,\cdot)\) \(\chi_{4275}(586,\cdot)\) \(\chi_{4275}(631,\cdot)\) \(\chi_{4275}(766,\cdot)\) \(\chi_{4275}(1081,\cdot)\) \(\chi_{4275}(1396,\cdot)\) \(\chi_{4275}(1441,\cdot)\) \(\chi_{4275}(1486,\cdot)\) \(\chi_{4275}(1621,\cdot)\) \(\chi_{4275}(1936,\cdot)\) \(\chi_{4275}(1981,\cdot)\) \(\chi_{4275}(2296,\cdot)\) \(\chi_{4275}(2341,\cdot)\) \(\chi_{4275}(2791,\cdot)\) \(\chi_{4275}(2836,\cdot)\) \(\chi_{4275}(3106,\cdot)\) \(\chi_{4275}(3196,\cdot)\) \(\chi_{4275}(3331,\cdot)\) \(\chi_{4275}(3646,\cdot)\) \(\chi_{4275}(3691,\cdot)\) \(\chi_{4275}(3961,\cdot)\) \(\chi_{4275}(4006,\cdot)\) \(\chi_{4275}(4186,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((1901,1027,1351)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{5}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
\( \chi_{ 4275 }(3646, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) |