Basic properties
| Modulus: | \(162240\) | |
| Conductor: | \(27040\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(104\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{27040}(3453,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 162240.bdc
\(\chi_{162240}(73,\cdot)\) \(\chi_{162240}(2137,\cdot)\) \(\chi_{162240}(6313,\cdot)\) \(\chi_{162240}(8377,\cdot)\) \(\chi_{162240}(12553,\cdot)\) \(\chi_{162240}(14617,\cdot)\) \(\chi_{162240}(18793,\cdot)\) \(\chi_{162240}(25033,\cdot)\) \(\chi_{162240}(27097,\cdot)\) \(\chi_{162240}(31273,\cdot)\) \(\chi_{162240}(33337,\cdot)\) \(\chi_{162240}(37513,\cdot)\) \(\chi_{162240}(39577,\cdot)\) \(\chi_{162240}(43753,\cdot)\) \(\chi_{162240}(45817,\cdot)\) \(\chi_{162240}(49993,\cdot)\) \(\chi_{162240}(52057,\cdot)\) \(\chi_{162240}(56233,\cdot)\) \(\chi_{162240}(58297,\cdot)\) \(\chi_{162240}(62473,\cdot)\) \(\chi_{162240}(64537,\cdot)\) \(\chi_{162240}(70777,\cdot)\) \(\chi_{162240}(74953,\cdot)\) \(\chi_{162240}(77017,\cdot)\) \(\chi_{162240}(81193,\cdot)\) \(\chi_{162240}(83257,\cdot)\) \(\chi_{162240}(87433,\cdot)\) \(\chi_{162240}(89497,\cdot)\) \(\chi_{162240}(93673,\cdot)\) \(\chi_{162240}(95737,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{104})$ |
| Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
Values on generators
\((45631,70981,108161,64897,93121)\) → \((1,e\left(\frac{3}{8}\right),1,-i,e\left(\frac{17}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 162240 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{57}{104}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(e\left(\frac{73}{104}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{51}{104}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{1}{104}\right)\) |