Basic properties
| Modulus: | \(7524\) | |
| Conductor: | \(1881\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1881}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7524.ja
\(\chi_{7524}(5,\cdot)\) \(\chi_{7524}(137,\cdot)\) \(\chi_{7524}(389,\cdot)\) \(\chi_{7524}(785,\cdot)\) \(\chi_{7524}(1373,\cdot)\) \(\chi_{7524}(1505,\cdot)\) \(\chi_{7524}(1841,\cdot)\) \(\chi_{7524}(2885,\cdot)\) \(\chi_{7524}(3425,\cdot)\) \(\chi_{7524}(3557,\cdot)\) \(\chi_{7524}(3569,\cdot)\) \(\chi_{7524}(3809,\cdot)\) \(\chi_{7524}(4205,\cdot)\) \(\chi_{7524}(4493,\cdot)\) \(\chi_{7524}(4889,\cdot)\) \(\chi_{7524}(4937,\cdot)\) \(\chi_{7524}(5261,\cdot)\) \(\chi_{7524}(5861,\cdot)\) \(\chi_{7524}(5945,\cdot)\) \(\chi_{7524}(6257,\cdot)\) \(\chi_{7524}(6845,\cdot)\) \(\chi_{7524}(6977,\cdot)\) \(\chi_{7524}(6989,\cdot)\) \(\chi_{7524}(7313,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{2}{5}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{4}{5}\right)\) |