Basic properties
| Modulus: | \(4275\) | |
| Conductor: | \(4275\) | 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 4275.fk
\(\chi_{4275}(61,\cdot)\) \(\chi_{4275}(196,\cdot)\) \(\chi_{4275}(796,\cdot)\) \(\chi_{4275}(841,\cdot)\) \(\chi_{4275}(916,\cdot)\) \(\chi_{4275}(1156,\cdot)\) \(\chi_{4275}(1681,\cdot)\) \(\chi_{4275}(1696,\cdot)\) \(\chi_{4275}(1771,\cdot)\) \(\chi_{4275}(1906,\cdot)\) \(\chi_{4275}(2011,\cdot)\) \(\chi_{4275}(2506,\cdot)\) \(\chi_{4275}(2536,\cdot)\) \(\chi_{4275}(2761,\cdot)\) \(\chi_{4275}(2866,\cdot)\) \(\chi_{4275}(3361,\cdot)\) \(\chi_{4275}(3391,\cdot)\) \(\chi_{4275}(3406,\cdot)\) \(\chi_{4275}(3481,\cdot)\) \(\chi_{4275}(3616,\cdot)\) \(\chi_{4275}(3721,\cdot)\) \(\chi_{4275}(4216,\cdot)\) \(\chi_{4275}(4246,\cdot)\) \(\chi_{4275}(4261,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((1901,1027,1351)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{4}{5}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 4275 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{17}{45}\right)\) |