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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 759.bd
\(\chi_{759}(2,\cdot)\) \(\chi_{759}(8,\cdot)\) \(\chi_{759}(29,\cdot)\) \(\chi_{759}(35,\cdot)\) \(\chi_{759}(41,\cdot)\) \(\chi_{759}(50,\cdot)\) \(\chi_{759}(62,\cdot)\) \(\chi_{759}(95,\cdot)\) \(\chi_{759}(101,\cdot)\) \(\chi_{759}(128,\cdot)\) \(\chi_{759}(140,\cdot)\) \(\chi_{759}(167,\cdot)\) \(\chi_{759}(173,\cdot)\) \(\chi_{759}(200,\cdot)\) \(\chi_{759}(215,\cdot)\) \(\chi_{759}(233,\cdot)\) \(\chi_{759}(239,\cdot)\) \(\chi_{759}(248,\cdot)\) \(\chi_{759}(266,\cdot)\) \(\chi_{759}(305,\cdot)\) \(\chi_{759}(326,\cdot)\) \(\chi_{759}(338,\cdot)\) \(\chi_{759}(347,\cdot)\) \(\chi_{759}(371,\cdot)\) \(\chi_{759}(380,\cdot)\) \(\chi_{759}(404,\cdot)\) \(\chi_{759}(446,\cdot)\) \(\chi_{759}(464,\cdot)\) \(\chi_{759}(491,\cdot)\) \(\chi_{759}(512,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((254,277,166)\) → \((-1,e\left(\frac{9}{10}\right),e\left(\frac{10}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 759 }(380, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{53}{55}\right)\) |