Basic properties
| Modulus: | \(2681\) | |
| Conductor: | \(2681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(382\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2681.l
\(\chi_{2681}(6,\cdot)\) \(\chi_{2681}(27,\cdot)\) \(\chi_{2681}(34,\cdot)\) \(\chi_{2681}(48,\cdot)\) \(\chi_{2681}(55,\cdot)\) \(\chi_{2681}(62,\cdot)\) \(\chi_{2681}(69,\cdot)\) \(\chi_{2681}(76,\cdot)\) \(\chi_{2681}(139,\cdot)\) \(\chi_{2681}(146,\cdot)\) \(\chi_{2681}(153,\cdot)\) \(\chi_{2681}(174,\cdot)\) \(\chi_{2681}(195,\cdot)\) \(\chi_{2681}(202,\cdot)\) \(\chi_{2681}(216,\cdot)\) \(\chi_{2681}(223,\cdot)\) \(\chi_{2681}(251,\cdot)\) \(\chi_{2681}(258,\cdot)\) \(\chi_{2681}(265,\cdot)\) \(\chi_{2681}(272,\cdot)\) \(\chi_{2681}(279,\cdot)\) \(\chi_{2681}(286,\cdot)\) \(\chi_{2681}(293,\cdot)\) \(\chi_{2681}(300,\cdot)\) \(\chi_{2681}(342,\cdot)\) \(\chi_{2681}(363,\cdot)\) \(\chi_{2681}(370,\cdot)\) \(\chi_{2681}(391,\cdot)\) \(\chi_{2681}(412,\cdot)\) \(\chi_{2681}(419,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{191})$ |
| Fixed field: | Number field defined by a degree 382 polynomial (not computed) |
Values on generators
\((2299,771)\) → \((-1,e\left(\frac{159}{191}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2681 }(55, a) \) | \(-1\) | \(1\) | \(e\left(\frac{105}{191}\right)\) | \(e\left(\frac{249}{382}\right)\) | \(e\left(\frac{19}{191}\right)\) | \(e\left(\frac{127}{382}\right)\) | \(e\left(\frac{77}{382}\right)\) | \(e\left(\frac{124}{191}\right)\) | \(e\left(\frac{58}{191}\right)\) | \(e\left(\frac{337}{382}\right)\) | \(e\left(\frac{170}{191}\right)\) | \(e\left(\frac{287}{382}\right)\) |