Basic properties
| Modulus: | \(162240\) | |
| Conductor: | \(13520\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{13520}(3459,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 162240.bag
\(\chi_{162240}(79,\cdot)\) \(\chi_{162240}(6319,\cdot)\) \(\chi_{162240}(12559,\cdot)\) \(\chi_{162240}(18799,\cdot)\) \(\chi_{162240}(25039,\cdot)\) \(\chi_{162240}(31279,\cdot)\) \(\chi_{162240}(43759,\cdot)\) \(\chi_{162240}(49999,\cdot)\) \(\chi_{162240}(56239,\cdot)\) \(\chi_{162240}(62479,\cdot)\) \(\chi_{162240}(68719,\cdot)\) \(\chi_{162240}(74959,\cdot)\) \(\chi_{162240}(81199,\cdot)\) \(\chi_{162240}(87439,\cdot)\) \(\chi_{162240}(93679,\cdot)\) \(\chi_{162240}(99919,\cdot)\) \(\chi_{162240}(106159,\cdot)\) \(\chi_{162240}(112399,\cdot)\) \(\chi_{162240}(124879,\cdot)\) \(\chi_{162240}(131119,\cdot)\) \(\chi_{162240}(137359,\cdot)\) \(\chi_{162240}(143599,\cdot)\) \(\chi_{162240}(149839,\cdot)\) \(\chi_{162240}(156079,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((45631,70981,108161,64897,93121)\) → \((-1,-i,1,-1,e\left(\frac{2}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 162240 }(81199, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{27}{52}\right)\) |