Basic properties
| Modulus: | \(575\) | |
| Conductor: | \(575\) | 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 575.u
\(\chi_{575}(4,\cdot)\) \(\chi_{575}(9,\cdot)\) \(\chi_{575}(29,\cdot)\) \(\chi_{575}(39,\cdot)\) \(\chi_{575}(54,\cdot)\) \(\chi_{575}(59,\cdot)\) \(\chi_{575}(64,\cdot)\) \(\chi_{575}(94,\cdot)\) \(\chi_{575}(104,\cdot)\) \(\chi_{575}(119,\cdot)\) \(\chi_{575}(144,\cdot)\) \(\chi_{575}(154,\cdot)\) \(\chi_{575}(164,\cdot)\) \(\chi_{575}(169,\cdot)\) \(\chi_{575}(179,\cdot)\) \(\chi_{575}(209,\cdot)\) \(\chi_{575}(219,\cdot)\) \(\chi_{575}(234,\cdot)\) \(\chi_{575}(239,\cdot)\) \(\chi_{575}(259,\cdot)\) \(\chi_{575}(269,\cdot)\) \(\chi_{575}(279,\cdot)\) \(\chi_{575}(284,\cdot)\) \(\chi_{575}(289,\cdot)\) \(\chi_{575}(294,\cdot)\) \(\chi_{575}(334,\cdot)\) \(\chi_{575}(354,\cdot)\) \(\chi_{575}(384,\cdot)\) \(\chi_{575}(394,\cdot)\) \(\chi_{575}(404,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((277,51)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{2}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 575 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{49}{110}\right)\) |