Basic properties
| Modulus: | \(4050\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{675}(511,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4050.bd
\(\chi_{4050}(91,\cdot)\) \(\chi_{4050}(181,\cdot)\) \(\chi_{4050}(361,\cdot)\) \(\chi_{4050}(631,\cdot)\) \(\chi_{4050}(721,\cdot)\) \(\chi_{4050}(991,\cdot)\) \(\chi_{4050}(1171,\cdot)\) \(\chi_{4050}(1261,\cdot)\) \(\chi_{4050}(1441,\cdot)\) \(\chi_{4050}(1531,\cdot)\) \(\chi_{4050}(1711,\cdot)\) \(\chi_{4050}(1981,\cdot)\) \(\chi_{4050}(2071,\cdot)\) \(\chi_{4050}(2341,\cdot)\) \(\chi_{4050}(2521,\cdot)\) \(\chi_{4050}(2611,\cdot)\) \(\chi_{4050}(2791,\cdot)\) \(\chi_{4050}(2881,\cdot)\) \(\chi_{4050}(3061,\cdot)\) \(\chi_{4050}(3331,\cdot)\) \(\chi_{4050}(3421,\cdot)\) \(\chi_{4050}(3691,\cdot)\) \(\chi_{4050}(3871,\cdot)\) \(\chi_{4050}(3961,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((2351,3727)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 4050 }(3961, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{45}\right)\) |