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.gg
\(\chi_{8624}(211,\cdot)\) \(\chi_{8624}(435,\cdot)\) \(\chi_{8624}(547,\cdot)\) \(\chi_{8624}(827,\cdot)\) \(\chi_{8624}(1051,\cdot)\) \(\chi_{8624}(1107,\cdot)\) \(\chi_{8624}(1163,\cdot)\) \(\chi_{8624}(1443,\cdot)\) \(\chi_{8624}(1723,\cdot)\) \(\chi_{8624}(1779,\cdot)\) \(\chi_{8624}(2283,\cdot)\) \(\chi_{8624}(2339,\cdot)\) \(\chi_{8624}(2395,\cdot)\) \(\chi_{8624}(2675,\cdot)\) \(\chi_{8624}(2899,\cdot)\) \(\chi_{8624}(2955,\cdot)\) \(\chi_{8624}(3011,\cdot)\) \(\chi_{8624}(3291,\cdot)\) \(\chi_{8624}(3515,\cdot)\) \(\chi_{8624}(3571,\cdot)\) \(\chi_{8624}(3907,\cdot)\) \(\chi_{8624}(4131,\cdot)\) \(\chi_{8624}(4187,\cdot)\) \(\chi_{8624}(4243,\cdot)\) \(\chi_{8624}(4523,\cdot)\) \(\chi_{8624}(4747,\cdot)\) \(\chi_{8624}(4859,\cdot)\) \(\chi_{8624}(5139,\cdot)\) \(\chi_{8624}(5363,\cdot)\) \(\chi_{8624}(5419,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((5391,6469,7745,3137)\) → \((-1,-i,e\left(\frac{5}{7}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(211, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{140}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{129}{140}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{111}{140}\right)\) |