Basic properties
| Modulus: | \(4598\) | |
| Conductor: | \(209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{209}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4598.z
\(\chi_{4598}(9,\cdot)\) \(\chi_{4598}(81,\cdot)\) \(\chi_{4598}(245,\cdot)\) \(\chi_{4598}(251,\cdot)\) \(\chi_{4598}(511,\cdot)\) \(\chi_{4598}(807,\cdot)\) \(\chi_{4598}(1049,\cdot)\) \(\chi_{4598}(1213,\cdot)\) \(\chi_{4598}(1461,\cdot)\) \(\chi_{4598}(1479,\cdot)\) \(\chi_{4598}(1697,\cdot)\) \(\chi_{4598}(1963,\cdot)\) \(\chi_{4598}(2259,\cdot)\) \(\chi_{4598}(2429,\cdot)\) \(\chi_{4598}(2665,\cdot)\) \(\chi_{4598}(2913,\cdot)\) \(\chi_{4598}(2931,\cdot)\) \(\chi_{4598}(3227,\cdot)\) \(\chi_{4598}(3391,\cdot)\) \(\chi_{4598}(3633,\cdot)\) \(\chi_{4598}(3657,\cdot)\) \(\chi_{4598}(3711,\cdot)\) \(\chi_{4598}(3881,\cdot)\) \(\chi_{4598}(3899,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | 45.45.43679806300610465846484971330073185012597520004657724600953543350870941304329239684756561.1 |
Values on generators
\((3269,3631)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 4598 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{45}\right)\) |