Basic properties
| Modulus: | \(69696\) | |
| Conductor: | \(34848\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1320\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{34848}(13187,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 69696.lz
\(\chi_{69696}(119,\cdot)\) \(\chi_{69696}(311,\cdot)\) \(\chi_{69696}(455,\cdot)\) \(\chi_{69696}(599,\cdot)\) \(\chi_{69696}(839,\cdot)\) \(\chi_{69696}(983,\cdot)\) \(\chi_{69696}(1127,\cdot)\) \(\chi_{69696}(1175,\cdot)\) \(\chi_{69696}(1895,\cdot)\) \(\chi_{69696}(2039,\cdot)\) \(\chi_{69696}(2183,\cdot)\) \(\chi_{69696}(2567,\cdot)\) \(\chi_{69696}(2711,\cdot)\) \(\chi_{69696}(2759,\cdot)\) \(\chi_{69696}(3287,\cdot)\) \(\chi_{69696}(3479,\cdot)\) \(\chi_{69696}(3623,\cdot)\) \(\chi_{69696}(3767,\cdot)\) \(\chi_{69696}(4007,\cdot)\) \(\chi_{69696}(4151,\cdot)\) \(\chi_{69696}(4295,\cdot)\) \(\chi_{69696}(4343,\cdot)\) \(\chi_{69696}(4871,\cdot)\) \(\chi_{69696}(5063,\cdot)\) \(\chi_{69696}(5207,\cdot)\) \(\chi_{69696}(5591,\cdot)\) \(\chi_{69696}(5735,\cdot)\) \(\chi_{69696}(5879,\cdot)\) \(\chi_{69696}(5927,\cdot)\) \(\chi_{69696}(6455,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1320})$ |
| Fixed field: | Number field defined by a degree 1320 polynomial (not computed) |
Values on generators
\((67519,4357,54209,14401)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{1}{6}\right),e\left(\frac{28}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 69696 }(119, a) \) | \(1\) | \(1\) | \(e\left(\frac{1163}{1320}\right)\) | \(e\left(\frac{317}{660}\right)\) | \(e\left(\frac{497}{1320}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{167}{440}\right)\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{503}{660}\right)\) | \(e\left(\frac{1249}{1320}\right)\) | \(e\left(\frac{203}{330}\right)\) | \(e\left(\frac{159}{440}\right)\) |