Basic properties
| Modulus: | \(9405\) | |
| Conductor: | \(1881\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1881}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9405.ku
\(\chi_{9405}(16,\cdot)\) \(\chi_{9405}(256,\cdot)\) \(\chi_{9405}(346,\cdot)\) \(\chi_{9405}(511,\cdot)\) \(\chi_{9405}(1336,\cdot)\) \(\chi_{9405}(1411,\cdot)\) \(\chi_{9405}(2821,\cdot)\) \(\chi_{9405}(3436,\cdot)\) \(\chi_{9405}(3766,\cdot)\) \(\chi_{9405}(3931,\cdot)\) \(\chi_{9405}(3976,\cdot)\) \(\chi_{9405}(4756,\cdot)\) \(\chi_{9405}(5146,\cdot)\) \(\chi_{9405}(5476,\cdot)\) \(\chi_{9405}(5641,\cdot)\) \(\chi_{9405}(6241,\cdot)\) \(\chi_{9405}(6466,\cdot)\) \(\chi_{9405}(6856,\cdot)\) \(\chi_{9405}(7186,\cdot)\) \(\chi_{9405}(7351,\cdot)\) \(\chi_{9405}(7396,\cdot)\) \(\chi_{9405}(7951,\cdot)\) \(\chi_{9405}(8176,\cdot)\) \(\chi_{9405}(9106,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((1046,1882,5986,496)\) → \((e\left(\frac{2}{3}\right),1,e\left(\frac{2}{5}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(23\) | \(26\) |
| \( \chi_{ 9405 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{2}{15}\right)\) |