Basic properties
| Modulus: | \(381\) | |
| Conductor: | \(381\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 381.x
\(\chi_{381}(14,\cdot)\) \(\chi_{381}(23,\cdot)\) \(\chi_{381}(29,\cdot)\) \(\chi_{381}(53,\cdot)\) \(\chi_{381}(56,\cdot)\) \(\chi_{381}(65,\cdot)\) \(\chi_{381}(83,\cdot)\) \(\chi_{381}(86,\cdot)\) \(\chi_{381}(92,\cdot)\) \(\chi_{381}(101,\cdot)\) \(\chi_{381}(110,\cdot)\) \(\chi_{381}(116,\cdot)\) \(\chi_{381}(134,\cdot)\) \(\chi_{381}(170,\cdot)\) \(\chi_{381}(173,\cdot)\) \(\chi_{381}(182,\cdot)\) \(\chi_{381}(185,\cdot)\) \(\chi_{381}(194,\cdot)\) \(\chi_{381}(212,\cdot)\) \(\chi_{381}(218,\cdot)\) \(\chi_{381}(224,\cdot)\) \(\chi_{381}(233,\cdot)\) \(\chi_{381}(236,\cdot)\) \(\chi_{381}(239,\cdot)\) \(\chi_{381}(245,\cdot)\) \(\chi_{381}(257,\cdot)\) \(\chi_{381}(260,\cdot)\) \(\chi_{381}(266,\cdot)\) \(\chi_{381}(293,\cdot)\) \(\chi_{381}(299,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((128,130)\) → \((-1,e\left(\frac{61}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 381 }(14, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{3}{7}\right)\) |