Basic properties
| Modulus: | \(759\) | |
| Conductor: | \(253\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{253}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 759.be
\(\chi_{759}(37,\cdot)\) \(\chi_{759}(97,\cdot)\) \(\chi_{759}(103,\cdot)\) \(\chi_{759}(130,\cdot)\) \(\chi_{759}(136,\cdot)\) \(\chi_{759}(148,\cdot)\) \(\chi_{759}(157,\cdot)\) \(\chi_{759}(181,\cdot)\) \(\chi_{759}(214,\cdot)\) \(\chi_{759}(235,\cdot)\) \(\chi_{759}(247,\cdot)\) \(\chi_{759}(268,\cdot)\) \(\chi_{759}(295,\cdot)\) \(\chi_{759}(313,\cdot)\) \(\chi_{759}(355,\cdot)\) \(\chi_{759}(379,\cdot)\) \(\chi_{759}(388,\cdot)\) \(\chi_{759}(412,\cdot)\) \(\chi_{759}(421,\cdot)\) \(\chi_{759}(433,\cdot)\) \(\chi_{759}(454,\cdot)\) \(\chi_{759}(493,\cdot)\) \(\chi_{759}(511,\cdot)\) \(\chi_{759}(520,\cdot)\) \(\chi_{759}(526,\cdot)\) \(\chi_{759}(544,\cdot)\) \(\chi_{759}(559,\cdot)\) \(\chi_{759}(586,\cdot)\) \(\chi_{759}(592,\cdot)\) \(\chi_{759}(619,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((254,277,166)\) → \((1,e\left(\frac{1}{5}\right),e\left(\frac{21}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 759 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{53}{110}\right)\) |