Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(8624\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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.fz
\(\chi_{8624}(285,\cdot)\) \(\chi_{8624}(549,\cdot)\) \(\chi_{8624}(1165,\cdot)\) \(\chi_{8624}(1517,\cdot)\) \(\chi_{8624}(1781,\cdot)\) \(\chi_{8624}(2133,\cdot)\) \(\chi_{8624}(2397,\cdot)\) \(\chi_{8624}(2749,\cdot)\) \(\chi_{8624}(3013,\cdot)\) \(\chi_{8624}(3365,\cdot)\) \(\chi_{8624}(3629,\cdot)\) \(\chi_{8624}(3981,\cdot)\) \(\chi_{8624}(4597,\cdot)\) \(\chi_{8624}(4861,\cdot)\) \(\chi_{8624}(5477,\cdot)\) \(\chi_{8624}(5829,\cdot)\) \(\chi_{8624}(6093,\cdot)\) \(\chi_{8624}(6445,\cdot)\) \(\chi_{8624}(6709,\cdot)\) \(\chi_{8624}(7061,\cdot)\) \(\chi_{8624}(7325,\cdot)\) \(\chi_{8624}(7677,\cdot)\) \(\chi_{8624}(7941,\cdot)\) \(\chi_{8624}(8293,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((5391,6469,7745,3137)\) → \((1,-i,e\left(\frac{23}{42}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(285, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{11}{28}\right)\) |