Basic properties
| Modulus: | \(253\) | |
| Conductor: | \(253\) | 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 253.n
\(\chi_{253}(7,\cdot)\) \(\chi_{253}(17,\cdot)\) \(\chi_{253}(19,\cdot)\) \(\chi_{253}(28,\cdot)\) \(\chi_{253}(30,\cdot)\) \(\chi_{253}(40,\cdot)\) \(\chi_{253}(51,\cdot)\) \(\chi_{253}(57,\cdot)\) \(\chi_{253}(61,\cdot)\) \(\chi_{253}(63,\cdot)\) \(\chi_{253}(74,\cdot)\) \(\chi_{253}(79,\cdot)\) \(\chi_{253}(83,\cdot)\) \(\chi_{253}(84,\cdot)\) \(\chi_{253}(90,\cdot)\) \(\chi_{253}(106,\cdot)\) \(\chi_{253}(107,\cdot)\) \(\chi_{253}(112,\cdot)\) \(\chi_{253}(129,\cdot)\) \(\chi_{253}(134,\cdot)\) \(\chi_{253}(145,\cdot)\) \(\chi_{253}(149,\cdot)\) \(\chi_{253}(171,\cdot)\) \(\chi_{253}(172,\cdot)\) \(\chi_{253}(178,\cdot)\) \(\chi_{253}(182,\cdot)\) \(\chi_{253}(189,\cdot)\) \(\chi_{253}(194,\cdot)\) \(\chi_{253}(195,\cdot)\) \(\chi_{253}(204,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((24,166)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{19}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 253 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) |