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.dn
\(\chi_{4732}(251,\cdot)\) \(\chi_{4732}(335,\cdot)\) \(\chi_{4732}(615,\cdot)\) \(\chi_{4732}(979,\cdot)\) \(\chi_{4732}(1063,\cdot)\) \(\chi_{4732}(1343,\cdot)\) \(\chi_{4732}(1427,\cdot)\) \(\chi_{4732}(1707,\cdot)\) \(\chi_{4732}(1791,\cdot)\) \(\chi_{4732}(2071,\cdot)\) \(\chi_{4732}(2155,\cdot)\) \(\chi_{4732}(2435,\cdot)\) \(\chi_{4732}(2519,\cdot)\) \(\chi_{4732}(2799,\cdot)\) \(\chi_{4732}(2883,\cdot)\) \(\chi_{4732}(3163,\cdot)\) \(\chi_{4732}(3247,\cdot)\) \(\chi_{4732}(3611,\cdot)\) \(\chi_{4732}(3891,\cdot)\) \(\chi_{4732}(3975,\cdot)\) \(\chi_{4732}(4255,\cdot)\) \(\chi_{4732}(4339,\cdot)\) \(\chi_{4732}(4619,\cdot)\) \(\chi_{4732}(4703,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((2367,2705,4565)\) → \((-1,-1,e\left(\frac{43}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 4732 }(251, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) |