Basic properties
| Modulus: | \(619\) | |
| Conductor: | \(619\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(309\) | 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 619.g
\(\chi_{619}(4,\cdot)\) \(\chi_{619}(5,\cdot)\) \(\chi_{619}(6,\cdot)\) \(\chi_{619}(7,\cdot)\) \(\chi_{619}(16,\cdot)\) \(\chi_{619}(22,\cdot)\) \(\chi_{619}(23,\cdot)\) \(\chi_{619}(25,\cdot)\) \(\chi_{619}(26,\cdot)\) \(\chi_{619}(28,\cdot)\) \(\chi_{619}(30,\cdot)\) \(\chi_{619}(33,\cdot)\) \(\chi_{619}(34,\cdot)\) \(\chi_{619}(36,\cdot)\) \(\chi_{619}(37,\cdot)\) \(\chi_{619}(41,\cdot)\) \(\chi_{619}(45,\cdot)\) \(\chi_{619}(49,\cdot)\) \(\chi_{619}(53,\cdot)\) \(\chi_{619}(54,\cdot)\) \(\chi_{619}(57,\cdot)\) \(\chi_{619}(58,\cdot)\) \(\chi_{619}(61,\cdot)\) \(\chi_{619}(63,\cdot)\) \(\chi_{619}(80,\cdot)\) \(\chi_{619}(86,\cdot)\) \(\chi_{619}(88,\cdot)\) \(\chi_{619}(94,\cdot)\) \(\chi_{619}(96,\cdot)\) \(\chi_{619}(100,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{309})$ |
| Fixed field: | Number field defined by a degree 309 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{61}{309}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 619 }(22, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{309}\right)\) | \(e\left(\frac{83}{103}\right)\) | \(e\left(\frac{122}{309}\right)\) | \(e\left(\frac{232}{309}\right)\) | \(e\left(\frac{1}{309}\right)\) | \(e\left(\frac{101}{309}\right)\) | \(e\left(\frac{61}{103}\right)\) | \(e\left(\frac{63}{103}\right)\) | \(e\left(\frac{293}{309}\right)\) | \(e\left(\frac{274}{309}\right)\) |