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 \(\chi_{2508}(431,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7524.jj
\(\chi_{7524}(431,\cdot)\) \(\chi_{7524}(611,\cdot)\) \(\chi_{7524}(755,\cdot)\) \(\chi_{7524}(827,\cdot)\) \(\chi_{7524}(1295,\cdot)\) \(\chi_{7524}(1799,\cdot)\) \(\chi_{7524}(2195,\cdot)\) \(\chi_{7524}(2339,\cdot)\) \(\chi_{7524}(2483,\cdot)\) \(\chi_{7524}(2807,\cdot)\) \(\chi_{7524}(2879,\cdot)\) \(\chi_{7524}(3131,\cdot)\) \(\chi_{7524}(4175,\cdot)\) \(\chi_{7524}(4391,\cdot)\) \(\chi_{7524}(4715,\cdot)\) \(\chi_{7524}(4859,\cdot)\) \(\chi_{7524}(5183,\cdot)\) \(\chi_{7524}(5759,\cdot)\) \(\chi_{7524}(5903,\cdot)\) \(\chi_{7524}(6299,\cdot)\) \(\chi_{7524}(6443,\cdot)\) \(\chi_{7524}(6551,\cdot)\) \(\chi_{7524}(6767,\cdot)\) \(\chi_{7524}(7235,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3763,6689,4105,2377)\) → \((-1,-1,e\left(\frac{1}{10}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 7524 }(431, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{7}{10}\right)\) |