Basic properties
| Modulus: | \(619\) | |
| Conductor: | \(619\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(103\) | 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.e
\(\chi_{619}(9,\cdot)\) \(\chi_{619}(20,\cdot)\) \(\chi_{619}(24,\cdot)\) \(\chi_{619}(31,\cdot)\) \(\chi_{619}(35,\cdot)\) \(\chi_{619}(38,\cdot)\) \(\chi_{619}(39,\cdot)\) \(\chi_{619}(42,\cdot)\) \(\chi_{619}(51,\cdot)\) \(\chi_{619}(64,\cdot)\) \(\chi_{619}(71,\cdot)\) \(\chi_{619}(73,\cdot)\) \(\chi_{619}(79,\cdot)\) \(\chi_{619}(81,\cdot)\) \(\chi_{619}(87,\cdot)\) \(\chi_{619}(89,\cdot)\) \(\chi_{619}(92,\cdot)\) \(\chi_{619}(104,\cdot)\) \(\chi_{619}(107,\cdot)\) \(\chi_{619}(110,\cdot)\) \(\chi_{619}(112,\cdot)\) \(\chi_{619}(125,\cdot)\) \(\chi_{619}(127,\cdot)\) \(\chi_{619}(129,\cdot)\) \(\chi_{619}(132,\cdot)\) \(\chi_{619}(136,\cdot)\) \(\chi_{619}(141,\cdot)\) \(\chi_{619}(150,\cdot)\) \(\chi_{619}(161,\cdot)\) \(\chi_{619}(164,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{103})$ |
| Fixed field: | Number field defined by a degree 103 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{55}{103}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 619 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{103}\right)\) | \(e\left(\frac{5}{103}\right)\) | \(e\left(\frac{7}{103}\right)\) | \(e\left(\frac{15}{103}\right)\) | \(e\left(\frac{60}{103}\right)\) | \(e\left(\frac{86}{103}\right)\) | \(e\left(\frac{62}{103}\right)\) | \(e\left(\frac{10}{103}\right)\) | \(e\left(\frac{70}{103}\right)\) | \(e\left(\frac{63}{103}\right)\) |