Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(8619\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(624\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.fg
\(\chi_{8619}(11,\cdot)\) \(\chi_{8619}(71,\cdot)\) \(\chi_{8619}(158,\cdot)\) \(\chi_{8619}(176,\cdot)\) \(\chi_{8619}(215,\cdot)\) \(\chi_{8619}(245,\cdot)\) \(\chi_{8619}(275,\cdot)\) \(\chi_{8619}(401,\cdot)\) \(\chi_{8619}(422,\cdot)\) \(\chi_{8619}(449,\cdot)\) \(\chi_{8619}(539,\cdot)\) \(\chi_{8619}(605,\cdot)\) \(\chi_{8619}(617,\cdot)\) \(\chi_{8619}(626,\cdot)\) \(\chi_{8619}(635,\cdot)\) \(\chi_{8619}(674,\cdot)\) \(\chi_{8619}(734,\cdot)\) \(\chi_{8619}(743,\cdot)\) \(\chi_{8619}(821,\cdot)\) \(\chi_{8619}(839,\cdot)\) \(\chi_{8619}(878,\cdot)\) \(\chi_{8619}(908,\cdot)\) \(\chi_{8619}(938,\cdot)\) \(\chi_{8619}(1064,\cdot)\) \(\chi_{8619}(1085,\cdot)\) \(\chi_{8619}(1112,\cdot)\) \(\chi_{8619}(1268,\cdot)\) \(\chi_{8619}(1280,\cdot)\) \(\chi_{8619}(1289,\cdot)\) \(\chi_{8619}(1298,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((5747,5917,2536)\) → \((-1,e\left(\frac{5}{156}\right),e\left(\frac{13}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(539, a) \) | \(-1\) | \(1\) | \(e\left(\frac{283}{312}\right)\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{177}{208}\right)\) | \(e\left(\frac{229}{624}\right)\) | \(e\left(\frac{75}{104}\right)\) | \(e\left(\frac{473}{624}\right)\) | \(e\left(\frac{305}{624}\right)\) | \(e\left(\frac{57}{208}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{11}{24}\right)\) |