Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(2156\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2156}(15,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.fo
\(\chi_{8624}(15,\cdot)\) \(\chi_{8624}(575,\cdot)\) \(\chi_{8624}(911,\cdot)\) \(\chi_{8624}(1247,\cdot)\) \(\chi_{8624}(1807,\cdot)\) \(\chi_{8624}(1919,\cdot)\) \(\chi_{8624}(2143,\cdot)\) \(\chi_{8624}(2479,\cdot)\) \(\chi_{8624}(3151,\cdot)\) \(\chi_{8624}(3375,\cdot)\) \(\chi_{8624}(3711,\cdot)\) \(\chi_{8624}(4271,\cdot)\) \(\chi_{8624}(4383,\cdot)\) \(\chi_{8624}(4943,\cdot)\) \(\chi_{8624}(5503,\cdot)\) \(\chi_{8624}(5615,\cdot)\) \(\chi_{8624}(5839,\cdot)\) \(\chi_{8624}(6735,\cdot)\) \(\chi_{8624}(6847,\cdot)\) \(\chi_{8624}(7071,\cdot)\) \(\chi_{8624}(7407,\cdot)\) \(\chi_{8624}(7967,\cdot)\) \(\chi_{8624}(8079,\cdot)\) \(\chi_{8624}(8303,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((5391,6469,7745,3137)\) → \((-1,1,e\left(\frac{5}{7}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) |