Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(2873\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(312\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2873}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.fc
\(\chi_{8619}(43,\cdot)\) \(\chi_{8619}(49,\cdot)\) \(\chi_{8619}(121,\cdot)\) \(\chi_{8619}(127,\cdot)\) \(\chi_{8619}(355,\cdot)\) \(\chi_{8619}(400,\cdot)\) \(\chi_{8619}(433,\cdot)\) \(\chi_{8619}(478,\cdot)\) \(\chi_{8619}(706,\cdot)\) \(\chi_{8619}(712,\cdot)\) \(\chi_{8619}(784,\cdot)\) \(\chi_{8619}(790,\cdot)\) \(\chi_{8619}(1018,\cdot)\) \(\chi_{8619}(1063,\cdot)\) \(\chi_{8619}(1096,\cdot)\) \(\chi_{8619}(1141,\cdot)\) \(\chi_{8619}(1369,\cdot)\) \(\chi_{8619}(1447,\cdot)\) \(\chi_{8619}(1453,\cdot)\) \(\chi_{8619}(1681,\cdot)\) \(\chi_{8619}(1726,\cdot)\) \(\chi_{8619}(1759,\cdot)\) \(\chi_{8619}(1804,\cdot)\) \(\chi_{8619}(2032,\cdot)\) \(\chi_{8619}(2038,\cdot)\) \(\chi_{8619}(2110,\cdot)\) \(\chi_{8619}(2116,\cdot)\) \(\chi_{8619}(2422,\cdot)\) \(\chi_{8619}(2467,\cdot)\) \(\chi_{8619}(2695,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{312})$ |
| Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((5747,5917,2536)\) → \((1,e\left(\frac{61}{78}\right),e\left(\frac{1}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{69}{104}\right)\) | \(e\left(\frac{17}{312}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{61}{312}\right)\) | \(e\left(\frac{133}{312}\right)\) | \(e\left(\frac{61}{104}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) |