Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(4312\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4312}(2339,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.fr
\(\chi_{8624}(183,\cdot)\) \(\chi_{8624}(519,\cdot)\) \(\chi_{8624}(743,\cdot)\) \(\chi_{8624}(855,\cdot)\) \(\chi_{8624}(1415,\cdot)\) \(\chi_{8624}(1751,\cdot)\) \(\chi_{8624}(1975,\cdot)\) \(\chi_{8624}(2087,\cdot)\) \(\chi_{8624}(2983,\cdot)\) \(\chi_{8624}(3207,\cdot)\) \(\chi_{8624}(3319,\cdot)\) \(\chi_{8624}(3879,\cdot)\) \(\chi_{8624}(4439,\cdot)\) \(\chi_{8624}(4551,\cdot)\) \(\chi_{8624}(5111,\cdot)\) \(\chi_{8624}(5447,\cdot)\) \(\chi_{8624}(5671,\cdot)\) \(\chi_{8624}(6343,\cdot)\) \(\chi_{8624}(6679,\cdot)\) \(\chi_{8624}(6903,\cdot)\) \(\chi_{8624}(7015,\cdot)\) \(\chi_{8624}(7575,\cdot)\) \(\chi_{8624}(7911,\cdot)\) \(\chi_{8624}(8247,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((5391,6469,7745,3137)\) → \((-1,-1,e\left(\frac{2}{7}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(183, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) |