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.bc
\(\chi_{759}(5,\cdot)\) \(\chi_{759}(14,\cdot)\) \(\chi_{759}(20,\cdot)\) \(\chi_{759}(38,\cdot)\) \(\chi_{759}(53,\cdot)\) \(\chi_{759}(80,\cdot)\) \(\chi_{759}(86,\cdot)\) \(\chi_{759}(113,\cdot)\) \(\chi_{759}(125,\cdot)\) \(\chi_{759}(152,\cdot)\) \(\chi_{759}(158,\cdot)\) \(\chi_{759}(191,\cdot)\) \(\chi_{759}(203,\cdot)\) \(\chi_{759}(212,\cdot)\) \(\chi_{759}(218,\cdot)\) \(\chi_{759}(224,\cdot)\) \(\chi_{759}(245,\cdot)\) \(\chi_{759}(251,\cdot)\) \(\chi_{759}(290,\cdot)\) \(\chi_{759}(350,\cdot)\) \(\chi_{759}(356,\cdot)\) \(\chi_{759}(383,\cdot)\) \(\chi_{759}(389,\cdot)\) \(\chi_{759}(401,\cdot)\) \(\chi_{759}(410,\cdot)\) \(\chi_{759}(434,\cdot)\) \(\chi_{759}(467,\cdot)\) \(\chi_{759}(488,\cdot)\) \(\chi_{759}(500,\cdot)\) \(\chi_{759}(521,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((254,277,166)\) → \((-1,e\left(\frac{3}{5}\right),e\left(\frac{5}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 759 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) |