Basic properties
Modulus: | \(4732\) | |
Conductor: | \(4732\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | 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 4732.ds
\(\chi_{4732}(103,\cdot)\) \(\chi_{4732}(311,\cdot)\) \(\chi_{4732}(467,\cdot)\) \(\chi_{4732}(831,\cdot)\) \(\chi_{4732}(1039,\cdot)\) \(\chi_{4732}(1195,\cdot)\) \(\chi_{4732}(1403,\cdot)\) \(\chi_{4732}(1559,\cdot)\) \(\chi_{4732}(1767,\cdot)\) \(\chi_{4732}(1923,\cdot)\) \(\chi_{4732}(2131,\cdot)\) \(\chi_{4732}(2287,\cdot)\) \(\chi_{4732}(2495,\cdot)\) \(\chi_{4732}(2651,\cdot)\) \(\chi_{4732}(2859,\cdot)\) \(\chi_{4732}(3015,\cdot)\) \(\chi_{4732}(3223,\cdot)\) \(\chi_{4732}(3587,\cdot)\) \(\chi_{4732}(3743,\cdot)\) \(\chi_{4732}(3951,\cdot)\) \(\chi_{4732}(4107,\cdot)\) \(\chi_{4732}(4315,\cdot)\) \(\chi_{4732}(4471,\cdot)\) \(\chi_{4732}(4679,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,2705,4565)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{9}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 4732 }(1767, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) |