Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{539}(113,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.ej
\(\chi_{8624}(113,\cdot)\) \(\chi_{8624}(225,\cdot)\) \(\chi_{8624}(449,\cdot)\) \(\chi_{8624}(1345,\cdot)\) \(\chi_{8624}(1457,\cdot)\) \(\chi_{8624}(1681,\cdot)\) \(\chi_{8624}(2017,\cdot)\) \(\chi_{8624}(2577,\cdot)\) \(\chi_{8624}(2689,\cdot)\) \(\chi_{8624}(2913,\cdot)\) \(\chi_{8624}(3249,\cdot)\) \(\chi_{8624}(3809,\cdot)\) \(\chi_{8624}(4145,\cdot)\) \(\chi_{8624}(4481,\cdot)\) \(\chi_{8624}(5041,\cdot)\) \(\chi_{8624}(5153,\cdot)\) \(\chi_{8624}(5377,\cdot)\) \(\chi_{8624}(5713,\cdot)\) \(\chi_{8624}(6385,\cdot)\) \(\chi_{8624}(6609,\cdot)\) \(\chi_{8624}(6945,\cdot)\) \(\chi_{8624}(7505,\cdot)\) \(\chi_{8624}(7617,\cdot)\) \(\chi_{8624}(8177,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((5391,6469,7745,3137)\) → \((1,1,e\left(\frac{5}{7}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(113, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) |