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 \(\chi_{253}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1012.be
\(\chi_{1012}(17,\cdot)\) \(\chi_{1012}(57,\cdot)\) \(\chi_{1012}(61,\cdot)\) \(\chi_{1012}(129,\cdot)\) \(\chi_{1012}(145,\cdot)\) \(\chi_{1012}(149,\cdot)\) \(\chi_{1012}(189,\cdot)\) \(\chi_{1012}(205,\cdot)\) \(\chi_{1012}(217,\cdot)\) \(\chi_{1012}(237,\cdot)\) \(\chi_{1012}(249,\cdot)\) \(\chi_{1012}(281,\cdot)\) \(\chi_{1012}(293,\cdot)\) \(\chi_{1012}(337,\cdot)\) \(\chi_{1012}(365,\cdot)\) \(\chi_{1012}(425,\cdot)\) \(\chi_{1012}(457,\cdot)\) \(\chi_{1012}(481,\cdot)\) \(\chi_{1012}(497,\cdot)\) \(\chi_{1012}(513,\cdot)\) \(\chi_{1012}(525,\cdot)\) \(\chi_{1012}(557,\cdot)\) \(\chi_{1012}(569,\cdot)\) \(\chi_{1012}(585,\cdot)\) \(\chi_{1012}(589,\cdot)\) \(\chi_{1012}(613,\cdot)\) \(\chi_{1012}(677,\cdot)\) \(\chi_{1012}(701,\cdot)\) \(\chi_{1012}(733,\cdot)\) \(\chi_{1012}(789,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((507,277,925)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{7}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(25\) |
| \( \chi_{ 1012 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{46}{55}\right)\) |