Basic properties
| Modulus: | \(539\) | |
| Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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 539.bf
\(\chi_{539}(17,\cdot)\) \(\chi_{539}(24,\cdot)\) \(\chi_{539}(40,\cdot)\) \(\chi_{539}(52,\cdot)\) \(\chi_{539}(61,\cdot)\) \(\chi_{539}(73,\cdot)\) \(\chi_{539}(94,\cdot)\) \(\chi_{539}(96,\cdot)\) \(\chi_{539}(101,\cdot)\) \(\chi_{539}(138,\cdot)\) \(\chi_{539}(145,\cdot)\) \(\chi_{539}(150,\cdot)\) \(\chi_{539}(171,\cdot)\) \(\chi_{539}(173,\cdot)\) \(\chi_{539}(194,\cdot)\) \(\chi_{539}(206,\cdot)\) \(\chi_{539}(222,\cdot)\) \(\chi_{539}(248,\cdot)\) \(\chi_{539}(250,\cdot)\) \(\chi_{539}(255,\cdot)\) \(\chi_{539}(271,\cdot)\) \(\chi_{539}(283,\cdot)\) \(\chi_{539}(292,\cdot)\) \(\chi_{539}(299,\cdot)\) \(\chi_{539}(304,\cdot)\) \(\chi_{539}(327,\cdot)\) \(\chi_{539}(332,\cdot)\) \(\chi_{539}(348,\cdot)\) \(\chi_{539}(360,\cdot)\) \(\chi_{539}(369,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((199,442)\) → \((e\left(\frac{1}{42}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 539 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{151}{210}\right)\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{19}{210}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{31}{35}\right)\) |