Basic properties
| Modulus: | \(1521\) | |
| Conductor: | \(1521\) | 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 1521.bs
\(\chi_{1521}(43,\cdot)\) \(\chi_{1521}(49,\cdot)\) \(\chi_{1521}(160,\cdot)\) \(\chi_{1521}(166,\cdot)\) \(\chi_{1521}(277,\cdot)\) \(\chi_{1521}(283,\cdot)\) \(\chi_{1521}(394,\cdot)\) \(\chi_{1521}(400,\cdot)\) \(\chi_{1521}(511,\cdot)\) \(\chi_{1521}(517,\cdot)\) \(\chi_{1521}(628,\cdot)\) \(\chi_{1521}(634,\cdot)\) \(\chi_{1521}(745,\cdot)\) \(\chi_{1521}(751,\cdot)\) \(\chi_{1521}(862,\cdot)\) \(\chi_{1521}(979,\cdot)\) \(\chi_{1521}(985,\cdot)\) \(\chi_{1521}(1096,\cdot)\) \(\chi_{1521}(1102,\cdot)\) \(\chi_{1521}(1213,\cdot)\) \(\chi_{1521}(1219,\cdot)\) \(\chi_{1521}(1336,\cdot)\) \(\chi_{1521}(1447,\cdot)\) \(\chi_{1521}(1453,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,847)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{29}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 1521 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) |