Basic properties
| Modulus: | \(799\) | |
| Conductor: | \(799\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(368\) | 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 799.t
\(\chi_{799}(3,\cdot)\) \(\chi_{799}(6,\cdot)\) \(\chi_{799}(7,\cdot)\) \(\chi_{799}(12,\cdot)\) \(\chi_{799}(14,\cdot)\) \(\chi_{799}(24,\cdot)\) \(\chi_{799}(27,\cdot)\) \(\chi_{799}(28,\cdot)\) \(\chi_{799}(37,\cdot)\) \(\chi_{799}(54,\cdot)\) \(\chi_{799}(56,\cdot)\) \(\chi_{799}(61,\cdot)\) \(\chi_{799}(63,\cdot)\) \(\chi_{799}(65,\cdot)\) \(\chi_{799}(71,\cdot)\) \(\chi_{799}(74,\cdot)\) \(\chi_{799}(75,\cdot)\) \(\chi_{799}(79,\cdot)\) \(\chi_{799}(96,\cdot)\) \(\chi_{799}(97,\cdot)\) \(\chi_{799}(108,\cdot)\) \(\chi_{799}(112,\cdot)\) \(\chi_{799}(122,\cdot)\) \(\chi_{799}(126,\cdot)\) \(\chi_{799}(130,\cdot)\) \(\chi_{799}(131,\cdot)\) \(\chi_{799}(143,\cdot)\) \(\chi_{799}(147,\cdot)\) \(\chi_{799}(148,\cdot)\) \(\chi_{799}(150,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{368})$ |
| Fixed field: | Number field defined by a degree 368 polynomial (not computed) |
Values on generators
\((377,52)\) → \((e\left(\frac{13}{16}\right),e\left(\frac{5}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 799 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{184}\right)\) | \(e\left(\frac{59}{368}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{103}{368}\right)\) | \(e\left(\frac{165}{368}\right)\) | \(e\left(\frac{329}{368}\right)\) | \(e\left(\frac{159}{184}\right)\) | \(e\left(\frac{59}{184}\right)\) | \(e\left(\frac{209}{368}\right)\) | \(e\left(\frac{77}{368}\right)\) |