Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(321,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.fk
\(\chi_{8624}(321,\cdot)\) \(\chi_{8624}(545,\cdot)\) \(\chi_{8624}(657,\cdot)\) \(\chi_{8624}(1217,\cdot)\) \(\chi_{8624}(1553,\cdot)\) \(\chi_{8624}(1777,\cdot)\) \(\chi_{8624}(1889,\cdot)\) \(\chi_{8624}(2785,\cdot)\) \(\chi_{8624}(3009,\cdot)\) \(\chi_{8624}(3121,\cdot)\) \(\chi_{8624}(3681,\cdot)\) \(\chi_{8624}(4241,\cdot)\) \(\chi_{8624}(4353,\cdot)\) \(\chi_{8624}(4913,\cdot)\) \(\chi_{8624}(5249,\cdot)\) \(\chi_{8624}(5473,\cdot)\) \(\chi_{8624}(6145,\cdot)\) \(\chi_{8624}(6481,\cdot)\) \(\chi_{8624}(6705,\cdot)\) \(\chi_{8624}(6817,\cdot)\) \(\chi_{8624}(7377,\cdot)\) \(\chi_{8624}(7713,\cdot)\) \(\chi_{8624}(8049,\cdot)\) \(\chi_{8624}(8609,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((5391,6469,7745,3137)\) → \((1,1,e\left(\frac{1}{14}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(321, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{43}{70}\right)\) |