Basic properties
| Modulus: | \(253\) | |
| Conductor: | \(253\) | 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 253.m
\(\chi_{253}(3,\cdot)\) \(\chi_{253}(4,\cdot)\) \(\chi_{253}(9,\cdot)\) \(\chi_{253}(16,\cdot)\) \(\chi_{253}(25,\cdot)\) \(\chi_{253}(26,\cdot)\) \(\chi_{253}(27,\cdot)\) \(\chi_{253}(31,\cdot)\) \(\chi_{253}(36,\cdot)\) \(\chi_{253}(48,\cdot)\) \(\chi_{253}(49,\cdot)\) \(\chi_{253}(58,\cdot)\) \(\chi_{253}(59,\cdot)\) \(\chi_{253}(64,\cdot)\) \(\chi_{253}(71,\cdot)\) \(\chi_{253}(75,\cdot)\) \(\chi_{253}(81,\cdot)\) \(\chi_{253}(82,\cdot)\) \(\chi_{253}(104,\cdot)\) \(\chi_{253}(108,\cdot)\) \(\chi_{253}(119,\cdot)\) \(\chi_{253}(124,\cdot)\) \(\chi_{253}(141,\cdot)\) \(\chi_{253}(146,\cdot)\) \(\chi_{253}(147,\cdot)\) \(\chi_{253}(163,\cdot)\) \(\chi_{253}(169,\cdot)\) \(\chi_{253}(170,\cdot)\) \(\chi_{253}(174,\cdot)\) \(\chi_{253}(179,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((24,166)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{3}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 253 }(192, a) \) | \(1\) | \(1\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) |