Basic properties
| Modulus: | \(8325\) | |
| Conductor: | \(8325\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8325.ie
\(\chi_{8325}(16,\cdot)\) \(\chi_{8325}(256,\cdot)\) \(\chi_{8325}(1291,\cdot)\) \(\chi_{8325}(1561,\cdot)\) \(\chi_{8325}(1681,\cdot)\) \(\chi_{8325}(1921,\cdot)\) \(\chi_{8325}(2266,\cdot)\) \(\chi_{8325}(2491,\cdot)\) \(\chi_{8325}(2956,\cdot)\) \(\chi_{8325}(3346,\cdot)\) \(\chi_{8325}(3586,\cdot)\) \(\chi_{8325}(3931,\cdot)\) \(\chi_{8325}(4156,\cdot)\) \(\chi_{8325}(4621,\cdot)\) \(\chi_{8325}(4891,\cdot)\) \(\chi_{8325}(5011,\cdot)\) \(\chi_{8325}(5596,\cdot)\) \(\chi_{8325}(5821,\cdot)\) \(\chi_{8325}(6286,\cdot)\) \(\chi_{8325}(6556,\cdot)\) \(\chi_{8325}(6916,\cdot)\) \(\chi_{8325}(7261,\cdot)\) \(\chi_{8325}(7486,\cdot)\) \(\chi_{8325}(8221,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((3701,7327,5626)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{4}{5}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8325 }(5011, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{13}{45}\right)\) |