Basic properties
| Modulus: | \(759\) | |
| Conductor: | \(759\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 759.bf
\(\chi_{759}(17,\cdot)\) \(\chi_{759}(74,\cdot)\) \(\chi_{759}(83,\cdot)\) \(\chi_{759}(107,\cdot)\) \(\chi_{759}(134,\cdot)\) \(\chi_{759}(149,\cdot)\) \(\chi_{759}(182,\cdot)\) \(\chi_{759}(194,\cdot)\) \(\chi_{759}(227,\cdot)\) \(\chi_{759}(260,\cdot)\) \(\chi_{759}(272,\cdot)\) \(\chi_{759}(281,\cdot)\) \(\chi_{759}(293,\cdot)\) \(\chi_{759}(314,\cdot)\) \(\chi_{759}(332,\cdot)\) \(\chi_{759}(359,\cdot)\) \(\chi_{759}(365,\cdot)\) \(\chi_{759}(398,\cdot)\) \(\chi_{759}(425,\cdot)\) \(\chi_{759}(431,\cdot)\) \(\chi_{759}(458,\cdot)\) \(\chi_{759}(470,\cdot)\) \(\chi_{759}(479,\cdot)\) \(\chi_{759}(497,\cdot)\) \(\chi_{759}(503,\cdot)\) \(\chi_{759}(536,\cdot)\) \(\chi_{759}(557,\cdot)\) \(\chi_{759}(563,\cdot)\) \(\chi_{759}(569,\cdot)\) \(\chi_{759}(590,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((254,277,166)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{13}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 759 }(458, a) \) | \(-1\) | \(1\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{103}{110}\right)\) |