Basic properties
| Modulus: | \(1501\) | |
| Conductor: | \(1501\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1501.bq
\(\chi_{1501}(8,\cdot)\) \(\chi_{1501}(46,\cdot)\) \(\chi_{1501}(65,\cdot)\) \(\chi_{1501}(141,\cdot)\) \(\chi_{1501}(179,\cdot)\) \(\chi_{1501}(255,\cdot)\) \(\chi_{1501}(259,\cdot)\) \(\chi_{1501}(354,\cdot)\) \(\chi_{1501}(563,\cdot)\) \(\chi_{1501}(620,\cdot)\) \(\chi_{1501}(654,\cdot)\) \(\chi_{1501}(696,\cdot)\) \(\chi_{1501}(749,\cdot)\) \(\chi_{1501}(958,\cdot)\) \(\chi_{1501}(1000,\cdot)\) \(\chi_{1501}(1015,\cdot)\) \(\chi_{1501}(1091,\cdot)\) \(\chi_{1501}(1114,\cdot)\) \(\chi_{1501}(1152,\cdot)\) \(\chi_{1501}(1171,\cdot)\) \(\chi_{1501}(1247,\cdot)\) \(\chi_{1501}(1285,\cdot)\) \(\chi_{1501}(1361,\cdot)\) \(\chi_{1501}(1395,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1028,951)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{5}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1501 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{2}{13}\right)\) |