Basic properties
Modulus: | \(233\) | |
Conductor: | \(233\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(29\) | 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 233.e
\(\chi_{233}(2,\cdot)\) \(\chi_{233}(4,\cdot)\) \(\chi_{233}(8,\cdot)\) \(\chi_{233}(16,\cdot)\) \(\chi_{233}(19,\cdot)\) \(\chi_{233}(23,\cdot)\) \(\chi_{233}(32,\cdot)\) \(\chi_{233}(37,\cdot)\) \(\chi_{233}(38,\cdot)\) \(\chi_{233}(46,\cdot)\) \(\chi_{233}(51,\cdot)\) \(\chi_{233}(63,\cdot)\) \(\chi_{233}(64,\cdot)\) \(\chi_{233}(71,\cdot)\) \(\chi_{233}(74,\cdot)\) \(\chi_{233}(76,\cdot)\) \(\chi_{233}(92,\cdot)\) \(\chi_{233}(102,\cdot)\) \(\chi_{233}(117,\cdot)\) \(\chi_{233}(126,\cdot)\) \(\chi_{233}(128,\cdot)\) \(\chi_{233}(135,\cdot)\) \(\chi_{233}(142,\cdot)\) \(\chi_{233}(148,\cdot)\) \(\chi_{233}(152,\cdot)\) \(\chi_{233}(175,\cdot)\) \(\chi_{233}(184,\cdot)\) \(\chi_{233}(204,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\(3\) → \(e\left(\frac{23}{29}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 233 }(46, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) |