Basic properties
| Modulus: | \(4729\) | |
| Conductor: | \(4729\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2364\) | 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 4729.o
\(\chi_{4729}(5,\cdot)\) \(\chi_{4729}(7,\cdot)\) \(\chi_{4729}(20,\cdot)\) \(\chi_{4729}(26,\cdot)\) \(\chi_{4729}(28,\cdot)\) \(\chi_{4729}(30,\cdot)\) \(\chi_{4729}(38,\cdot)\) \(\chi_{4729}(39,\cdot)\) \(\chi_{4729}(42,\cdot)\) \(\chi_{4729}(45,\cdot)\) \(\chi_{4729}(50,\cdot)\) \(\chi_{4729}(57,\cdot)\) \(\chi_{4729}(59,\cdot)\) \(\chi_{4729}(63,\cdot)\) \(\chi_{4729}(65,\cdot)\) \(\chi_{4729}(70,\cdot)\) \(\chi_{4729}(71,\cdot)\) \(\chi_{4729}(73,\cdot)\) \(\chi_{4729}(74,\cdot)\) \(\chi_{4729}(75,\cdot)\) \(\chi_{4729}(80,\cdot)\) \(\chi_{4729}(91,\cdot)\) \(\chi_{4729}(95,\cdot)\) \(\chi_{4729}(98,\cdot)\) \(\chi_{4729}(104,\cdot)\) \(\chi_{4729}(105,\cdot)\) \(\chi_{4729}(111,\cdot)\) \(\chi_{4729}(112,\cdot)\) \(\chi_{4729}(120,\cdot)\) \(\chi_{4729}(133,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{2364})$ |
| Fixed field: | Number field defined by a degree 2364 polynomial (not computed) |
Values on generators
\(17\) → \(e\left(\frac{889}{2364}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4729 }(1040, a) \) | \(1\) | \(1\) | \(e\left(\frac{231}{394}\right)\) | \(e\left(\frac{235}{394}\right)\) | \(e\left(\frac{34}{197}\right)\) | \(e\left(\frac{1043}{1182}\right)\) | \(e\left(\frac{36}{197}\right)\) | \(e\left(\frac{731}{1182}\right)\) | \(e\left(\frac{299}{394}\right)\) | \(e\left(\frac{38}{197}\right)\) | \(e\left(\frac{277}{591}\right)\) | \(e\left(\frac{185}{788}\right)\) |