Basic properties
| Modulus: | \(7524\) | |
| Conductor: | \(836\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{836}(271,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7524.je
\(\chi_{7524}(271,\cdot)\) \(\chi_{7524}(415,\cdot)\) \(\chi_{7524}(739,\cdot)\) \(\chi_{7524}(1315,\cdot)\) \(\chi_{7524}(1999,\cdot)\) \(\chi_{7524}(2107,\cdot)\) \(\chi_{7524}(2251,\cdot)\) \(\chi_{7524}(2323,\cdot)\) \(\chi_{7524}(2647,\cdot)\) \(\chi_{7524}(2791,\cdot)\) \(\chi_{7524}(3691,\cdot)\) \(\chi_{7524}(3835,\cdot)\) \(\chi_{7524}(4303,\cdot)\) \(\chi_{7524}(4375,\cdot)\) \(\chi_{7524}(4699,\cdot)\) \(\chi_{7524}(5419,\cdot)\) \(\chi_{7524}(5671,\cdot)\) \(\chi_{7524}(5887,\cdot)\) \(\chi_{7524}(6067,\cdot)\) \(\chi_{7524}(6211,\cdot)\) \(\chi_{7524}(6355,\cdot)\) \(\chi_{7524}(6751,\cdot)\) \(\chi_{7524}(7255,\cdot)\) \(\chi_{7524}(7471,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((-1,1,e\left(\frac{7}{10}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(271, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{2}{5}\right)\) |