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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8619.fi
\(\chi_{8619}(29,\cdot)\) \(\chi_{8619}(74,\cdot)\) \(\chi_{8619}(107,\cdot)\) \(\chi_{8619}(113,\cdot)\) \(\chi_{8619}(224,\cdot)\) \(\chi_{8619}(269,\cdot)\) \(\chi_{8619}(347,\cdot)\) \(\chi_{8619}(380,\cdot)\) \(\chi_{8619}(386,\cdot)\) \(\chi_{8619}(419,\cdot)\) \(\chi_{8619}(464,\cdot)\) \(\chi_{8619}(503,\cdot)\) \(\chi_{8619}(575,\cdot)\) \(\chi_{8619}(581,\cdot)\) \(\chi_{8619}(692,\cdot)\) \(\chi_{8619}(737,\cdot)\) \(\chi_{8619}(770,\cdot)\) \(\chi_{8619}(776,\cdot)\) \(\chi_{8619}(809,\cdot)\) \(\chi_{8619}(887,\cdot)\) \(\chi_{8619}(932,\cdot)\) \(\chi_{8619}(1010,\cdot)\) \(\chi_{8619}(1043,\cdot)\) \(\chi_{8619}(1049,\cdot)\) \(\chi_{8619}(1082,\cdot)\) \(\chi_{8619}(1127,\cdot)\) \(\chi_{8619}(1166,\cdot)\) \(\chi_{8619}(1238,\cdot)\) \(\chi_{8619}(1244,\cdot)\) \(\chi_{8619}(1316,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((5747,5917,2536)\) → \((-1,e\left(\frac{10}{39}\right),e\left(\frac{13}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 8619 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{312}\right)\) | \(e\left(\frac{41}{156}\right)\) | \(e\left(\frac{181}{208}\right)\) | \(e\left(\frac{233}{624}\right)\) | \(e\left(\frac{41}{104}\right)\) | \(e\left(\frac{1}{624}\right)\) | \(e\left(\frac{373}{624}\right)\) | \(e\left(\frac{105}{208}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{1}{24}\right)\) |