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 \(\chi_{253}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 759.bb
\(\chi_{759}(13,\cdot)\) \(\chi_{759}(52,\cdot)\) \(\chi_{759}(73,\cdot)\) \(\chi_{759}(85,\cdot)\) \(\chi_{759}(94,\cdot)\) \(\chi_{759}(118,\cdot)\) \(\chi_{759}(127,\cdot)\) \(\chi_{759}(151,\cdot)\) \(\chi_{759}(193,\cdot)\) \(\chi_{759}(211,\cdot)\) \(\chi_{759}(238,\cdot)\) \(\chi_{759}(259,\cdot)\) \(\chi_{759}(271,\cdot)\) \(\chi_{759}(292,\cdot)\) \(\chi_{759}(325,\cdot)\) \(\chi_{759}(349,\cdot)\) \(\chi_{759}(358,\cdot)\) \(\chi_{759}(370,\cdot)\) \(\chi_{759}(376,\cdot)\) \(\chi_{759}(403,\cdot)\) \(\chi_{759}(409,\cdot)\) \(\chi_{759}(469,\cdot)\) \(\chi_{759}(508,\cdot)\) \(\chi_{759}(514,\cdot)\) \(\chi_{759}(535,\cdot)\) \(\chi_{759}(541,\cdot)\) \(\chi_{759}(547,\cdot)\) \(\chi_{759}(556,\cdot)\) \(\chi_{759}(568,\cdot)\) \(\chi_{759}(601,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((254,277,166)\) → \((1,e\left(\frac{1}{10}\right),e\left(\frac{7}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 759 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{39}{110}\right)\) |