Basic properties
| Modulus: | \(8325\) | |
| Conductor: | \(8325\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | 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.ku
\(\chi_{8325}(139,\cdot)\) \(\chi_{8325}(484,\cdot)\) \(\chi_{8325}(844,\cdot)\) \(\chi_{8325}(1114,\cdot)\) \(\chi_{8325}(1579,\cdot)\) \(\chi_{8325}(1804,\cdot)\) \(\chi_{8325}(2389,\cdot)\) \(\chi_{8325}(2509,\cdot)\) \(\chi_{8325}(2779,\cdot)\) \(\chi_{8325}(3244,\cdot)\) \(\chi_{8325}(3469,\cdot)\) \(\chi_{8325}(3814,\cdot)\) \(\chi_{8325}(4054,\cdot)\) \(\chi_{8325}(4444,\cdot)\) \(\chi_{8325}(4909,\cdot)\) \(\chi_{8325}(5134,\cdot)\) \(\chi_{8325}(5479,\cdot)\) \(\chi_{8325}(5719,\cdot)\) \(\chi_{8325}(5839,\cdot)\) \(\chi_{8325}(6109,\cdot)\) \(\chi_{8325}(7144,\cdot)\) \(\chi_{8325}(7384,\cdot)\) \(\chi_{8325}(7504,\cdot)\) \(\chi_{8325}(8239,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3701,7327,5626)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{10}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8325 }(5479, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{7}{90}\right)\) |