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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.gl
\(\chi_{8624}(141,\cdot)\) \(\chi_{8624}(421,\cdot)\) \(\chi_{8624}(477,\cdot)\) \(\chi_{8624}(533,\cdot)\) \(\chi_{8624}(757,\cdot)\) \(\chi_{8624}(1037,\cdot)\) \(\chi_{8624}(1093,\cdot)\) \(\chi_{8624}(1149,\cdot)\) \(\chi_{8624}(1653,\cdot)\) \(\chi_{8624}(1709,\cdot)\) \(\chi_{8624}(1989,\cdot)\) \(\chi_{8624}(2269,\cdot)\) \(\chi_{8624}(2325,\cdot)\) \(\chi_{8624}(2381,\cdot)\) \(\chi_{8624}(2605,\cdot)\) \(\chi_{8624}(2885,\cdot)\) \(\chi_{8624}(2997,\cdot)\) \(\chi_{8624}(3221,\cdot)\) \(\chi_{8624}(3501,\cdot)\) \(\chi_{8624}(3557,\cdot)\) \(\chi_{8624}(3613,\cdot)\) \(\chi_{8624}(3837,\cdot)\) \(\chi_{8624}(4173,\cdot)\) \(\chi_{8624}(4229,\cdot)\) \(\chi_{8624}(4453,\cdot)\) \(\chi_{8624}(4733,\cdot)\) \(\chi_{8624}(4789,\cdot)\) \(\chi_{8624}(4845,\cdot)\) \(\chi_{8624}(5069,\cdot)\) \(\chi_{8624}(5349,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((5391,6469,7745,3137)\) → \((1,-i,e\left(\frac{1}{7}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(141, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{140}\right)\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{79}{140}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{81}{140}\right)\) |