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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1012.z
\(\chi_{1012}(7,\cdot)\) \(\chi_{1012}(19,\cdot)\) \(\chi_{1012}(51,\cdot)\) \(\chi_{1012}(63,\cdot)\) \(\chi_{1012}(79,\cdot)\) \(\chi_{1012}(83,\cdot)\) \(\chi_{1012}(107,\cdot)\) \(\chi_{1012}(171,\cdot)\) \(\chi_{1012}(195,\cdot)\) \(\chi_{1012}(227,\cdot)\) \(\chi_{1012}(283,\cdot)\) \(\chi_{1012}(327,\cdot)\) \(\chi_{1012}(343,\cdot)\) \(\chi_{1012}(359,\cdot)\) \(\chi_{1012}(387,\cdot)\) \(\chi_{1012}(431,\cdot)\) \(\chi_{1012}(435,\cdot)\) \(\chi_{1012}(447,\cdot)\) \(\chi_{1012}(475,\cdot)\) \(\chi_{1012}(479,\cdot)\) \(\chi_{1012}(503,\cdot)\) \(\chi_{1012}(523,\cdot)\) \(\chi_{1012}(563,\cdot)\) \(\chi_{1012}(567,\cdot)\) \(\chi_{1012}(635,\cdot)\) \(\chi_{1012}(651,\cdot)\) \(\chi_{1012}(655,\cdot)\) \(\chi_{1012}(695,\cdot)\) \(\chi_{1012}(711,\cdot)\) \(\chi_{1012}(723,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((507,277,925)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{19}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(25\) |
| \( \chi_{ 1012 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{18}{55}\right)\) |