Basic properties
| Modulus: | \(8619\) | |
| Conductor: | \(8619\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.dh
\(\chi_{8619}(203,\cdot)\) \(\chi_{8619}(356,\cdot)\) \(\chi_{8619}(866,\cdot)\) \(\chi_{8619}(1019,\cdot)\) \(\chi_{8619}(1529,\cdot)\) \(\chi_{8619}(1682,\cdot)\) \(\chi_{8619}(2192,\cdot)\) \(\chi_{8619}(2345,\cdot)\) \(\chi_{8619}(2855,\cdot)\) \(\chi_{8619}(3008,\cdot)\) \(\chi_{8619}(3518,\cdot)\) \(\chi_{8619}(3671,\cdot)\) \(\chi_{8619}(4181,\cdot)\) \(\chi_{8619}(4334,\cdot)\) \(\chi_{8619}(4844,\cdot)\) \(\chi_{8619}(4997,\cdot)\) \(\chi_{8619}(5660,\cdot)\) \(\chi_{8619}(6170,\cdot)\) \(\chi_{8619}(6833,\cdot)\) \(\chi_{8619}(6986,\cdot)\) \(\chi_{8619}(7496,\cdot)\) \(\chi_{8619}(7649,\cdot)\) \(\chi_{8619}(8159,\cdot)\) \(\chi_{8619}(8312,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5747,5917,2536)\) → \((-1,e\left(\frac{49}{52}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(203, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(i\) |