Basic properties
| Modulus: | \(1012\) | |
| 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 \(\chi_{253}(238,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1012.bf
\(\chi_{1012}(13,\cdot)\) \(\chi_{1012}(29,\cdot)\) \(\chi_{1012}(41,\cdot)\) \(\chi_{1012}(73,\cdot)\) \(\chi_{1012}(85,\cdot)\) \(\chi_{1012}(101,\cdot)\) \(\chi_{1012}(105,\cdot)\) \(\chi_{1012}(117,\cdot)\) \(\chi_{1012}(173,\cdot)\) \(\chi_{1012}(193,\cdot)\) \(\chi_{1012}(233,\cdot)\) \(\chi_{1012}(261,\cdot)\) \(\chi_{1012}(305,\cdot)\) \(\chi_{1012}(325,\cdot)\) \(\chi_{1012}(349,\cdot)\) \(\chi_{1012}(381,\cdot)\) \(\chi_{1012}(393,\cdot)\) \(\chi_{1012}(409,\cdot)\) \(\chi_{1012}(453,\cdot)\) \(\chi_{1012}(469,\cdot)\) \(\chi_{1012}(501,\cdot)\) \(\chi_{1012}(541,\cdot)\) \(\chi_{1012}(545,\cdot)\) \(\chi_{1012}(601,\cdot)\) \(\chi_{1012}(629,\cdot)\) \(\chi_{1012}(633,\cdot)\) \(\chi_{1012}(657,\cdot)\) \(\chi_{1012}(673,\cdot)\) \(\chi_{1012}(717,\cdot)\) \(\chi_{1012}(721,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((507,277,925)\) → \((1,e\left(\frac{7}{10}\right),e\left(\frac{3}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(25\) |
| \( \chi_{ 1012 }(997, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{8}{55}\right)\) |