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 \(\chi_{253}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 759.z
\(\chi_{759}(7,\cdot)\) \(\chi_{759}(19,\cdot)\) \(\chi_{759}(28,\cdot)\) \(\chi_{759}(40,\cdot)\) \(\chi_{759}(61,\cdot)\) \(\chi_{759}(79,\cdot)\) \(\chi_{759}(106,\cdot)\) \(\chi_{759}(112,\cdot)\) \(\chi_{759}(145,\cdot)\) \(\chi_{759}(172,\cdot)\) \(\chi_{759}(178,\cdot)\) \(\chi_{759}(205,\cdot)\) \(\chi_{759}(217,\cdot)\) \(\chi_{759}(226,\cdot)\) \(\chi_{759}(244,\cdot)\) \(\chi_{759}(250,\cdot)\) \(\chi_{759}(283,\cdot)\) \(\chi_{759}(304,\cdot)\) \(\chi_{759}(310,\cdot)\) \(\chi_{759}(316,\cdot)\) \(\chi_{759}(337,\cdot)\) \(\chi_{759}(343,\cdot)\) \(\chi_{759}(382,\cdot)\) \(\chi_{759}(424,\cdot)\) \(\chi_{759}(442,\cdot)\) \(\chi_{759}(448,\cdot)\) \(\chi_{759}(457,\cdot)\) \(\chi_{759}(475,\cdot)\) \(\chi_{759}(481,\cdot)\) \(\chi_{759}(490,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((254,277,166)\) → \((1,e\left(\frac{3}{10}\right),e\left(\frac{15}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 759 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) |