Basic properties
| Modulus: | \(1012\) | |
| Conductor: | \(1012\) | 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 1012.bc
\(\chi_{1012}(35,\cdot)\) \(\chi_{1012}(39,\cdot)\) \(\chi_{1012}(95,\cdot)\) \(\chi_{1012}(123,\cdot)\) \(\chi_{1012}(127,\cdot)\) \(\chi_{1012}(151,\cdot)\) \(\chi_{1012}(167,\cdot)\) \(\chi_{1012}(211,\cdot)\) \(\chi_{1012}(215,\cdot)\) \(\chi_{1012}(239,\cdot)\) \(\chi_{1012}(255,\cdot)\) \(\chi_{1012}(259,\cdot)\) \(\chi_{1012}(271,\cdot)\) \(\chi_{1012}(303,\cdot)\) \(\chi_{1012}(315,\cdot)\) \(\chi_{1012}(347,\cdot)\) \(\chi_{1012}(371,\cdot)\) \(\chi_{1012}(403,\cdot)\) \(\chi_{1012}(491,\cdot)\) \(\chi_{1012}(519,\cdot)\) \(\chi_{1012}(535,\cdot)\) \(\chi_{1012}(547,\cdot)\) \(\chi_{1012}(579,\cdot)\) \(\chi_{1012}(591,\cdot)\) \(\chi_{1012}(607,\cdot)\) \(\chi_{1012}(611,\cdot)\) \(\chi_{1012}(623,\cdot)\) \(\chi_{1012}(679,\cdot)\) \(\chi_{1012}(699,\cdot)\) \(\chi_{1012}(739,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((507,277,925)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{10}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(25\) |
| \( \chi_{ 1012 }(403, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{23}{55}\right)\) |