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 \(\chi_{253}(218,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1012.bd
\(\chi_{1012}(5,\cdot)\) \(\chi_{1012}(37,\cdot)\) \(\chi_{1012}(53,\cdot)\) \(\chi_{1012}(97,\cdot)\) \(\chi_{1012}(113,\cdot)\) \(\chi_{1012}(125,\cdot)\) \(\chi_{1012}(157,\cdot)\) \(\chi_{1012}(181,\cdot)\) \(\chi_{1012}(201,\cdot)\) \(\chi_{1012}(245,\cdot)\) \(\chi_{1012}(273,\cdot)\) \(\chi_{1012}(313,\cdot)\) \(\chi_{1012}(333,\cdot)\) \(\chi_{1012}(389,\cdot)\) \(\chi_{1012}(401,\cdot)\) \(\chi_{1012}(405,\cdot)\) \(\chi_{1012}(421,\cdot)\) \(\chi_{1012}(433,\cdot)\) \(\chi_{1012}(465,\cdot)\) \(\chi_{1012}(477,\cdot)\) \(\chi_{1012}(493,\cdot)\) \(\chi_{1012}(521,\cdot)\) \(\chi_{1012}(609,\cdot)\) \(\chi_{1012}(641,\cdot)\) \(\chi_{1012}(665,\cdot)\) \(\chi_{1012}(697,\cdot)\) \(\chi_{1012}(709,\cdot)\) \(\chi_{1012}(741,\cdot)\) \(\chi_{1012}(753,\cdot)\) \(\chi_{1012}(757,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((507,277,925)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{9}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(25\) |
| \( \chi_{ 1012 }(977, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{34}{55}\right)\) |