Basic properties
Modulus: | \(127\) | |
Conductor: | \(127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(63\) | 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 127.k
\(\chi_{127}(9,\cdot)\) \(\chi_{127}(11,\cdot)\) \(\chi_{127}(13,\cdot)\) \(\chi_{127}(15,\cdot)\) \(\chi_{127}(17,\cdot)\) \(\chi_{127}(18,\cdot)\) \(\chi_{127}(21,\cdot)\) \(\chi_{127}(26,\cdot)\) \(\chi_{127}(30,\cdot)\) \(\chi_{127}(31,\cdot)\) \(\chi_{127}(34,\cdot)\) \(\chi_{127}(35,\cdot)\) \(\chi_{127}(36,\cdot)\) \(\chi_{127}(41,\cdot)\) \(\chi_{127}(42,\cdot)\) \(\chi_{127}(44,\cdot)\) \(\chi_{127}(49,\cdot)\) \(\chi_{127}(60,\cdot)\) \(\chi_{127}(62,\cdot)\) \(\chi_{127}(69,\cdot)\) \(\chi_{127}(70,\cdot)\) \(\chi_{127}(71,\cdot)\) \(\chi_{127}(72,\cdot)\) \(\chi_{127}(74,\cdot)\) \(\chi_{127}(79,\cdot)\) \(\chi_{127}(81,\cdot)\) \(\chi_{127}(82,\cdot)\) \(\chi_{127}(84,\cdot)\) \(\chi_{127}(88,\cdot)\) \(\chi_{127}(98,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\(3\) → \(e\left(\frac{53}{63}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 127 }(60, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{13}{63}\right)\) |