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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 253.p
\(\chi_{253}(5,\cdot)\) \(\chi_{253}(14,\cdot)\) \(\chi_{253}(15,\cdot)\) \(\chi_{253}(20,\cdot)\) \(\chi_{253}(37,\cdot)\) \(\chi_{253}(38,\cdot)\) \(\chi_{253}(42,\cdot)\) \(\chi_{253}(53,\cdot)\) \(\chi_{253}(60,\cdot)\) \(\chi_{253}(80,\cdot)\) \(\chi_{253}(86,\cdot)\) \(\chi_{253}(97,\cdot)\) \(\chi_{253}(102,\cdot)\) \(\chi_{253}(103,\cdot)\) \(\chi_{253}(113,\cdot)\) \(\chi_{253}(125,\cdot)\) \(\chi_{253}(126,\cdot)\) \(\chi_{253}(130,\cdot)\) \(\chi_{253}(135,\cdot)\) \(\chi_{253}(136,\cdot)\) \(\chi_{253}(148,\cdot)\) \(\chi_{253}(152,\cdot)\) \(\chi_{253}(157,\cdot)\) \(\chi_{253}(158,\cdot)\) \(\chi_{253}(159,\cdot)\) \(\chi_{253}(168,\cdot)\) \(\chi_{253}(180,\cdot)\) \(\chi_{253}(181,\cdot)\) \(\chi_{253}(191,\cdot)\) \(\chi_{253}(201,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((24,166)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{13}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 253 }(251, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) |