Basic properties
| Modulus: | \(1521\) | |
| Conductor: | \(1521\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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.cg
\(\chi_{1521}(2,\cdot)\) \(\chi_{1521}(11,\cdot)\) \(\chi_{1521}(32,\cdot)\) \(\chi_{1521}(59,\cdot)\) \(\chi_{1521}(119,\cdot)\) \(\chi_{1521}(128,\cdot)\) \(\chi_{1521}(149,\cdot)\) \(\chi_{1521}(176,\cdot)\) \(\chi_{1521}(236,\cdot)\) \(\chi_{1521}(245,\cdot)\) \(\chi_{1521}(266,\cdot)\) \(\chi_{1521}(293,\cdot)\) \(\chi_{1521}(353,\cdot)\) \(\chi_{1521}(362,\cdot)\) \(\chi_{1521}(383,\cdot)\) \(\chi_{1521}(410,\cdot)\) \(\chi_{1521}(470,\cdot)\) \(\chi_{1521}(479,\cdot)\) \(\chi_{1521}(500,\cdot)\) \(\chi_{1521}(527,\cdot)\) \(\chi_{1521}(617,\cdot)\) \(\chi_{1521}(644,\cdot)\) \(\chi_{1521}(704,\cdot)\) \(\chi_{1521}(713,\cdot)\) \(\chi_{1521}(734,\cdot)\) \(\chi_{1521}(761,\cdot)\) \(\chi_{1521}(821,\cdot)\) \(\chi_{1521}(830,\cdot)\) \(\chi_{1521}(851,\cdot)\) \(\chi_{1521}(878,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((677,847)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{103}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 1521 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{35}{39}\right)\) |