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.ba
\(\chi_{1012}(15,\cdot)\) \(\chi_{1012}(103,\cdot)\) \(\chi_{1012}(135,\cdot)\) \(\chi_{1012}(159,\cdot)\) \(\chi_{1012}(191,\cdot)\) \(\chi_{1012}(203,\cdot)\) \(\chi_{1012}(235,\cdot)\) \(\chi_{1012}(247,\cdot)\) \(\chi_{1012}(251,\cdot)\) \(\chi_{1012}(267,\cdot)\) \(\chi_{1012}(291,\cdot)\) \(\chi_{1012}(295,\cdot)\) \(\chi_{1012}(339,\cdot)\) \(\chi_{1012}(355,\cdot)\) \(\chi_{1012}(379,\cdot)\) \(\chi_{1012}(383,\cdot)\) \(\chi_{1012}(411,\cdot)\) \(\chi_{1012}(467,\cdot)\) \(\chi_{1012}(471,\cdot)\) \(\chi_{1012}(511,\cdot)\) \(\chi_{1012}(543,\cdot)\) \(\chi_{1012}(559,\cdot)\) \(\chi_{1012}(603,\cdot)\) \(\chi_{1012}(619,\cdot)\) \(\chi_{1012}(631,\cdot)\) \(\chi_{1012}(663,\cdot)\) \(\chi_{1012}(687,\cdot)\) \(\chi_{1012}(707,\cdot)\) \(\chi_{1012}(751,\cdot)\) \(\chi_{1012}(779,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((507,277,925)\) → \((-1,e\left(\frac{3}{5}\right),e\left(\frac{7}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(25\) |
| \( \chi_{ 1012 }(339, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{24}{55}\right)\) |