Basic properties
| Modulus: | \(162240\) | |
| Conductor: | \(81120\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(312\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{81120}(71819,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 162240.bng
\(\chi_{162240}(119,\cdot)\) \(\chi_{162240}(839,\cdot)\) \(\chi_{162240}(4439,\cdot)\) \(\chi_{162240}(6359,\cdot)\) \(\chi_{162240}(10679,\cdot)\) \(\chi_{162240}(11399,\cdot)\) \(\chi_{162240}(12599,\cdot)\) \(\chi_{162240}(13319,\cdot)\) \(\chi_{162240}(17639,\cdot)\) \(\chi_{162240}(19559,\cdot)\) \(\chi_{162240}(23159,\cdot)\) \(\chi_{162240}(23879,\cdot)\) \(\chi_{162240}(25079,\cdot)\) \(\chi_{162240}(25799,\cdot)\) \(\chi_{162240}(29399,\cdot)\) \(\chi_{162240}(30119,\cdot)\) \(\chi_{162240}(31319,\cdot)\) \(\chi_{162240}(32039,\cdot)\) \(\chi_{162240}(35639,\cdot)\) \(\chi_{162240}(36359,\cdot)\) \(\chi_{162240}(37559,\cdot)\) \(\chi_{162240}(38279,\cdot)\) \(\chi_{162240}(41879,\cdot)\) \(\chi_{162240}(42599,\cdot)\) \(\chi_{162240}(43799,\cdot)\) \(\chi_{162240}(44519,\cdot)\) \(\chi_{162240}(48119,\cdot)\) \(\chi_{162240}(48839,\cdot)\) \(\chi_{162240}(50039,\cdot)\) \(\chi_{162240}(50759,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{312})$ |
| Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((45631,70981,108161,64897,93121)\) → \((-1,e\left(\frac{5}{8}\right),-1,-1,e\left(\frac{47}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 162240 }(839, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{49}{312}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{133}{312}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{193}{312}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{275}{312}\right)\) |