Basic properties
| Modulus: | \(233\) | |
| Conductor: | \(233\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(232\) | 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 233.h
\(\chi_{233}(3,\cdot)\) \(\chi_{233}(5,\cdot)\) \(\chi_{233}(6,\cdot)\) \(\chi_{233}(10,\cdot)\) \(\chi_{233}(11,\cdot)\) \(\chi_{233}(17,\cdot)\) \(\chi_{233}(20,\cdot)\) \(\chi_{233}(21,\cdot)\) \(\chi_{233}(22,\cdot)\) \(\chi_{233}(24,\cdot)\) \(\chi_{233}(27,\cdot)\) \(\chi_{233}(34,\cdot)\) \(\chi_{233}(35,\cdot)\) \(\chi_{233}(39,\cdot)\) \(\chi_{233}(40,\cdot)\) \(\chi_{233}(41,\cdot)\) \(\chi_{233}(42,\cdot)\) \(\chi_{233}(43,\cdot)\) \(\chi_{233}(44,\cdot)\) \(\chi_{233}(45,\cdot)\) \(\chi_{233}(47,\cdot)\) \(\chi_{233}(48,\cdot)\) \(\chi_{233}(53,\cdot)\) \(\chi_{233}(54,\cdot)\) \(\chi_{233}(57,\cdot)\) \(\chi_{233}(59,\cdot)\) \(\chi_{233}(61,\cdot)\) \(\chi_{233}(65,\cdot)\) \(\chi_{233}(67,\cdot)\) \(\chi_{233}(68,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{232})$ |
| Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{117}{232}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 233 }(230, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{117}{232}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{49}{232}\right)\) | \(e\left(\frac{189}{232}\right)\) | \(e\left(\frac{111}{116}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{1}{116}\right)\) | \(e\left(\frac{121}{232}\right)\) | \(e\left(\frac{81}{232}\right)\) |