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.gm
\(\chi_{8624}(13,\cdot)\) \(\chi_{8624}(237,\cdot)\) \(\chi_{8624}(349,\cdot)\) \(\chi_{8624}(629,\cdot)\) \(\chi_{8624}(853,\cdot)\) \(\chi_{8624}(909,\cdot)\) \(\chi_{8624}(965,\cdot)\) \(\chi_{8624}(1245,\cdot)\) \(\chi_{8624}(1525,\cdot)\) \(\chi_{8624}(1581,\cdot)\) \(\chi_{8624}(2085,\cdot)\) \(\chi_{8624}(2141,\cdot)\) \(\chi_{8624}(2197,\cdot)\) \(\chi_{8624}(2477,\cdot)\) \(\chi_{8624}(2701,\cdot)\) \(\chi_{8624}(2757,\cdot)\) \(\chi_{8624}(2813,\cdot)\) \(\chi_{8624}(3093,\cdot)\) \(\chi_{8624}(3317,\cdot)\) \(\chi_{8624}(3373,\cdot)\) \(\chi_{8624}(3709,\cdot)\) \(\chi_{8624}(3933,\cdot)\) \(\chi_{8624}(3989,\cdot)\) \(\chi_{8624}(4045,\cdot)\) \(\chi_{8624}(4325,\cdot)\) \(\chi_{8624}(4549,\cdot)\) \(\chi_{8624}(4661,\cdot)\) \(\chi_{8624}(4941,\cdot)\) \(\chi_{8624}(5165,\cdot)\) \(\chi_{8624}(5221,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((5391,6469,7745,3137)\) → \((1,-i,e\left(\frac{11}{14}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{71}{140}\right)\) |