Basic properties
| Modulus: | \(711\) | |
| Conductor: | \(711\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | 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 711.y
\(\chi_{711}(13,\cdot)\) \(\chi_{711}(49,\cdot)\) \(\chi_{711}(76,\cdot)\) \(\chi_{711}(88,\cdot)\) \(\chi_{711}(121,\cdot)\) \(\chi_{711}(130,\cdot)\) \(\chi_{711}(151,\cdot)\) \(\chi_{711}(169,\cdot)\) \(\chi_{711}(202,\cdot)\) \(\chi_{711}(241,\cdot)\) \(\chi_{711}(268,\cdot)\) \(\chi_{711}(277,\cdot)\) \(\chi_{711}(421,\cdot)\) \(\chi_{711}(490,\cdot)\) \(\chi_{711}(493,\cdot)\) \(\chi_{711}(499,\cdot)\) \(\chi_{711}(547,\cdot)\) \(\chi_{711}(589,\cdot)\) \(\chi_{711}(598,\cdot)\) \(\chi_{711}(634,\cdot)\) \(\chi_{711}(637,\cdot)\) \(\chi_{711}(652,\cdot)\) \(\chi_{711}(664,\cdot)\) \(\chi_{711}(682,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((317,82)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{19}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 711 }(421, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) |