Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(8624\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.gk
\(\chi_{8624}(69,\cdot)\) \(\chi_{8624}(125,\cdot)\) \(\chi_{8624}(181,\cdot)\) \(\chi_{8624}(405,\cdot)\) \(\chi_{8624}(741,\cdot)\) \(\chi_{8624}(797,\cdot)\) \(\chi_{8624}(1021,\cdot)\) \(\chi_{8624}(1301,\cdot)\) \(\chi_{8624}(1357,\cdot)\) \(\chi_{8624}(1413,\cdot)\) \(\chi_{8624}(1637,\cdot)\) \(\chi_{8624}(1917,\cdot)\) \(\chi_{8624}(1973,\cdot)\) \(\chi_{8624}(2029,\cdot)\) \(\chi_{8624}(2533,\cdot)\) \(\chi_{8624}(2589,\cdot)\) \(\chi_{8624}(2869,\cdot)\) \(\chi_{8624}(3149,\cdot)\) \(\chi_{8624}(3205,\cdot)\) \(\chi_{8624}(3261,\cdot)\) \(\chi_{8624}(3485,\cdot)\) \(\chi_{8624}(3765,\cdot)\) \(\chi_{8624}(3877,\cdot)\) \(\chi_{8624}(4101,\cdot)\) \(\chi_{8624}(4381,\cdot)\) \(\chi_{8624}(4437,\cdot)\) \(\chi_{8624}(4493,\cdot)\) \(\chi_{8624}(4717,\cdot)\) \(\chi_{8624}(5053,\cdot)\) \(\chi_{8624}(5109,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((5391,6469,7745,3137)\) → \((1,i,e\left(\frac{13}{14}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(69, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{140}\right)\) | \(e\left(\frac{53}{140}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{27}{140}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{33}{140}\right)\) |