Basic properties
| Modulus: | \(759\) | |
| Conductor: | \(253\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{253}(58,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 759.y
\(\chi_{759}(4,\cdot)\) \(\chi_{759}(16,\cdot)\) \(\chi_{759}(25,\cdot)\) \(\chi_{759}(31,\cdot)\) \(\chi_{759}(49,\cdot)\) \(\chi_{759}(58,\cdot)\) \(\chi_{759}(64,\cdot)\) \(\chi_{759}(82,\cdot)\) \(\chi_{759}(124,\cdot)\) \(\chi_{759}(163,\cdot)\) \(\chi_{759}(169,\cdot)\) \(\chi_{759}(190,\cdot)\) \(\chi_{759}(196,\cdot)\) \(\chi_{759}(202,\cdot)\) \(\chi_{759}(223,\cdot)\) \(\chi_{759}(256,\cdot)\) \(\chi_{759}(262,\cdot)\) \(\chi_{759}(280,\cdot)\) \(\chi_{759}(289,\cdot)\) \(\chi_{759}(301,\cdot)\) \(\chi_{759}(328,\cdot)\) \(\chi_{759}(334,\cdot)\) \(\chi_{759}(361,\cdot)\) \(\chi_{759}(394,\cdot)\) \(\chi_{759}(400,\cdot)\) \(\chi_{759}(427,\cdot)\) \(\chi_{759}(445,\cdot)\) \(\chi_{759}(466,\cdot)\) \(\chi_{759}(478,\cdot)\) \(\chi_{759}(487,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((254,277,166)\) → \((1,e\left(\frac{4}{5}\right),e\left(\frac{10}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 759 }(58, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{31}{55}\right)\) |