Basic properties
| Modulus: | \(7524\) | |
| Conductor: | \(2508\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2508}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7524.jd
\(\chi_{7524}(35,\cdot)\) \(\chi_{7524}(215,\cdot)\) \(\chi_{7524}(359,\cdot)\) \(\chi_{7524}(503,\cdot)\) \(\chi_{7524}(899,\cdot)\) \(\chi_{7524}(1403,\cdot)\) \(\chi_{7524}(1619,\cdot)\) \(\chi_{7524}(1943,\cdot)\) \(\chi_{7524}(2087,\cdot)\) \(\chi_{7524}(2411,\cdot)\) \(\chi_{7524}(2987,\cdot)\) \(\chi_{7524}(3671,\cdot)\) \(\chi_{7524}(3779,\cdot)\) \(\chi_{7524}(3923,\cdot)\) \(\chi_{7524}(3995,\cdot)\) \(\chi_{7524}(4319,\cdot)\) \(\chi_{7524}(4463,\cdot)\) \(\chi_{7524}(5363,\cdot)\) \(\chi_{7524}(5507,\cdot)\) \(\chi_{7524}(5975,\cdot)\) \(\chi_{7524}(6047,\cdot)\) \(\chi_{7524}(6371,\cdot)\) \(\chi_{7524}(7091,\cdot)\) \(\chi_{7524}(7343,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((-1,-1,e\left(\frac{1}{10}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{1}{5}\right)\) |