Basic properties
| Modulus: | \(1150\) | |
| Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{575}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1150.s
\(\chi_{1150}(31,\cdot)\) \(\chi_{1150}(41,\cdot)\) \(\chi_{1150}(71,\cdot)\) \(\chi_{1150}(81,\cdot)\) \(\chi_{1150}(121,\cdot)\) \(\chi_{1150}(131,\cdot)\) \(\chi_{1150}(141,\cdot)\) \(\chi_{1150}(211,\cdot)\) \(\chi_{1150}(261,\cdot)\) \(\chi_{1150}(271,\cdot)\) \(\chi_{1150}(311,\cdot)\) \(\chi_{1150}(331,\cdot)\) \(\chi_{1150}(361,\cdot)\) \(\chi_{1150}(371,\cdot)\) \(\chi_{1150}(381,\cdot)\) \(\chi_{1150}(441,\cdot)\) \(\chi_{1150}(491,\cdot)\) \(\chi_{1150}(531,\cdot)\) \(\chi_{1150}(541,\cdot)\) \(\chi_{1150}(561,\cdot)\) \(\chi_{1150}(581,\cdot)\) \(\chi_{1150}(591,\cdot)\) \(\chi_{1150}(611,\cdot)\) \(\chi_{1150}(671,\cdot)\) \(\chi_{1150}(721,\cdot)\) \(\chi_{1150}(731,\cdot)\) \(\chi_{1150}(761,\cdot)\) \(\chi_{1150}(771,\cdot)\) \(\chi_{1150}(791,\cdot)\) \(\chi_{1150}(811,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((277,51)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{3}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
| \( \chi_{ 1150 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) |