Basic properties
| Modulus: | \(575\) | |
| Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | 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.s
\(\chi_{575}(6,\cdot)\) \(\chi_{575}(16,\cdot)\) \(\chi_{575}(31,\cdot)\) \(\chi_{575}(36,\cdot)\) \(\chi_{575}(41,\cdot)\) \(\chi_{575}(71,\cdot)\) \(\chi_{575}(81,\cdot)\) \(\chi_{575}(96,\cdot)\) \(\chi_{575}(121,\cdot)\) \(\chi_{575}(131,\cdot)\) \(\chi_{575}(141,\cdot)\) \(\chi_{575}(146,\cdot)\) \(\chi_{575}(156,\cdot)\) \(\chi_{575}(186,\cdot)\) \(\chi_{575}(196,\cdot)\) \(\chi_{575}(211,\cdot)\) \(\chi_{575}(216,\cdot)\) \(\chi_{575}(236,\cdot)\) \(\chi_{575}(246,\cdot)\) \(\chi_{575}(256,\cdot)\) \(\chi_{575}(261,\cdot)\) \(\chi_{575}(266,\cdot)\) \(\chi_{575}(271,\cdot)\) \(\chi_{575}(311,\cdot)\) \(\chi_{575}(331,\cdot)\) \(\chi_{575}(361,\cdot)\) \(\chi_{575}(371,\cdot)\) \(\chi_{575}(381,\cdot)\) \(\chi_{575}(386,\cdot)\) \(\chi_{575}(416,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((277,51)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{9}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 575 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{3}{55}\right)\) |