Basic properties
| Modulus: | \(533\) | |
| Conductor: | \(533\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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 533.cd
\(\chi_{533}(6,\cdot)\) \(\chi_{533}(7,\cdot)\) \(\chi_{533}(11,\cdot)\) \(\chi_{533}(15,\cdot)\) \(\chi_{533}(19,\cdot)\) \(\chi_{533}(58,\cdot)\) \(\chi_{533}(67,\cdot)\) \(\chi_{533}(89,\cdot)\) \(\chi_{533}(97,\cdot)\) \(\chi_{533}(106,\cdot)\) \(\chi_{533}(111,\cdot)\) \(\chi_{533}(145,\cdot)\) \(\chi_{533}(149,\cdot)\) \(\chi_{533}(158,\cdot)\) \(\chi_{533}(176,\cdot)\) \(\chi_{533}(188,\cdot)\) \(\chi_{533}(193,\cdot)\) \(\chi_{533}(227,\cdot)\) \(\chi_{533}(240,\cdot)\) \(\chi_{533}(258,\cdot)\) \(\chi_{533}(280,\cdot)\) \(\chi_{533}(358,\cdot)\) \(\chi_{533}(362,\cdot)\) \(\chi_{533}(397,\cdot)\) \(\chi_{533}(423,\cdot)\) \(\chi_{533}(440,\cdot)\) \(\chi_{533}(457,\cdot)\) \(\chi_{533}(462,\cdot)\) \(\chi_{533}(470,\cdot)\) \(\chi_{533}(479,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((288,170)\) → \((e\left(\frac{5}{12}\right),e\left(\frac{13}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 533 }(188, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{107}{120}\right)\) |